Agostino Capponi - Academia.edu (original) (raw)

Papers by Agostino Capponi

In this thesis we study problems arising in the design of sense and respond systems and present a... more In this thesis we study problems arising in the design of sense and respond systems and present analytical solutions to them as well as results from experiments dealing with real systems. Sense and respond systems employ sensors and other sources of data to sense what is happening in their environments, process the obtained information, and respond appropriately. A goal of the processing stage is to reconstruct the best possible estimate of the state of the environment using messages received from sensors. Due to the large number of messages that need to be processed, it is desirable to have algorithms that can incrementally process the received measurements and recover the state. The state estimation process becomes more problematic if measurements obtained from the sensors are noisy or they are sent at unpredictable times. First, we study models of state estimation and present algorithms that can incrementally compute accurate linear state estimates of the surrounding environment....

This thesis proposes a novel credit risk model which deals with incomplete information on the fir... more This thesis proposes a novel credit risk model which deals with incomplete information on the firm's asset value. Such incompleteness is due to reporting bias deliberately introduced by insider managers and executives of the firm and unobserved by outsiders. The pricing of corporate securities and the evaluation of default measures in our credit risk framework requires the solution of a computationally unfeasible nonlinear filtering problem. The model introduces computational issues arising from the fact that the optimal probability density on the firm's asset value is the solution of a nonlinear filtering problem, which is computationally unfeasible. We propose a polynomial time-sequential Bayesian approximation scheme which employs convex optimization methods to iteratively approximate the optimal conditional density of the state on the basis of received market observations. We also provide an upper bound on the total variation distance between the actual filter density an...

Mathematics and Financial Economics, 2021

It has been a dozen years since the largest financial crisis hit the global economy after the Gre... more It has been a dozen years since the largest financial crisis hit the global economy after the Great Depression. Since this event, understanding the mechanism underlying the origination, transmission, and mitigation of systemic risk has been a priority for academics, practitioners, and regulators worldwide. This investigation has led to many important research contributions recently surveyed in review articles (e.g. [14,16]). Despite enormous progress having been made, the topic of systemic risk, along with its implications for the real economy and policy making, remains a subject of active investigation. The continued interest in this topic is manifested by the many conferences, workshops and special events organized each year by central banks and academic institutions on this theme. Agostino Capponi (Columbia), Robert Jarrow (Cornell), and Ulrich Horst (Humboldt University) have decided to dedicate a special issue to the topic of systemic risk and financial networks. The objective of this issue is to provide an overview of research directions currently being pursued by the community. The hope is to both incite interest in this topic among graduate students and young academic and to provide a platform for discussion among professionals who wish the push forward the frontiers of systemic risk research. The contributions to this Special Issue touch upon critical issues in the measurement, modeling, and management of systemic risk. They illustrate the various approaches to the problem put forward by theoretical and empirical research, as well as the integration of data methodologies appropriate for this investigation. Common to many financial crises is the bursting of bubbles. For example, the global 2007-2008 financial crisis was preceded by the bursting of the house price bubble. Jarrow and Lamichhane [17] investigate the theoretical underpinnings of this mechanism in a general equilibrium framework. They show that the interaction of market liquidity, asset price bubbles B Agostino Capponi

Mathematical Finance, 2020

We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a c... more We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the exact return rate of her counterparty's bond, but she knows it lies within an uncertainty interval. We derive both upper and lower bounds for the XVA process of the portfolio, and show that these bounds may be recovered as solutions of nonlinear ordinary differential equations. The presence of collateralization and closeout payoffs leads to important differences with respect to classical credit risk valuation. The value of the superreplicating portfolio cannot be directly obtained by plugging one of the extremes of the uncertainty interval in the valuation equation, but rather depends on the relation between the XVA replicating portfolio and the close-out value throughout the life of the transaction. Our comparative statics analysis indicates that credit contagion has a nonlinear effect on the replication strategies and on the XVA.

SSRN Electronic Journal, 2019

Automated investment managers, or robo-advisors, have emerged as an alternative to traditional fi... more Automated investment managers, or robo-advisors, have emerged as an alternative to traditional financial advisors. Their viability crucially depends on timely communication of information from the clients they serve. We introduce and develop a novel human-machine interaction framework, in which the robo-advisor solves an adaptive mean-variance control problem, with the risk-return tradeoff dynamically updated based on the risk profile communicated by the client. Our model predicts that clients who value a personalized portfolio are more suitable for robo-advising. Clients who place higher emphasis on delegation and clients with a risk profile that changes frequently benefit less from robo-advising.

SSRN Electronic Journal, 2019

We consider an investor who maximizes portfolio's expected returns conditioned on the occurrence ... more We consider an investor who maximizes portfolio's expected returns conditioned on the occurrence of a systemic event: financial system return being at, or at most at, its VaR level and portfolio's returns being below the CoVaR level. We obtain a closed-form solution to the portfolio selection problem, and show how VaR and CoVaR quantiles control, respectively, the relative importance of "portfolio-system correlation" and "portfolio variance". Our empirical analysis demonstrates that the investor attains a higher Sharpe ratio, compared to well known benchmark portfolio criteria, during times of market downturn. Portfolios that perform best in adverse market conditions are less diversified and concentrate on few stocks whose correlation with the financial system is low.

Mathematics of Operations Research, 2017

We consider an optimal risk-sensitive portfolio allocation problem accounting for the possibility... more We consider an optimal risk-sensitive portfolio allocation problem accounting for the possibility of cascading defaults. Default events have an impact on the distress state of the surviving stocks in the portfolio. We study the recursive system of non-Lipschitz quasilinear parabolic HJB-PDEs associated with the value function of the control problem in the different default states of the economy. We show the existence of a classical solution to this system via super-sub solution techniques and give an explicit characterization of the optimal feedback strategy in terms of the value function. We prove a verification theorem establishing the uniqueness of the solution. A numerical analysis indicates that the investor significantly accounts for contagion effects when making investment decisions, and that his strategy depends nonmonotonically on the aggregate risk level.

SSRN Electronic Journal, 2017

The U.S. Treasury market is highly intermediated by nonbank principal trading firms (PTFs). Limit... more The U.S. Treasury market is highly intermediated by nonbank principal trading firms (PTFs). Limited capital forces PTFs to end the trading day roughly flat. We construct a continuous time market making model to analyze the trade-off faced by a profit-maximizing firm with overnight inventory costs, and develop closed-form representations of the optimal price policy functions. Our model reveals that bid-ask spreads widen as the end of the trading day approaches, and that increases in order arrival rates do not always lead to higher price volatility. Our empirical analysis shows that Treasury security trading costs increase as the close of trading approaches, consistent with model predictions.

SSRN Electronic Journal, 2017

We develop a dynamic model of interbank borrowing and lending activities in which banks are organ... more We develop a dynamic model of interbank borrowing and lending activities in which banks are organized into clusters, and adjust their monetary reserve levels to meet prescribed capital requirements. Each bank has its own initial monetary reserve level and faces idiosyncratic risks characterized by an independent Brownian motion; whereas system wide, the banks form a hierarchical structure of clusters. We model the interbank transactional dynamics through a set of interacting measure-valued processes. Each individual process describes the intra-cluster borrowing/lending activities, and the interactions among the processes capture the inter-cluster financial transactions. We establish the weak limit of the interacting measure-valued processes as the number of banks in the system grows large. We then use the weak limit to develop asymptotic approximations of two proposed macro-measures, the liquidity stress index and the concentration index, both capturing the dynamics of systemic risk. We use numerical examples to illustrate the applications of the asymptotics and conduct related sensitivity analysis with respect to various indicators of financial activity.

This paper endogenizes intervention in financial crises as the strategic negotiation between a re... more This paper endogenizes intervention in financial crises as the strategic negotiation between a regulator and creditors of distressed banks. Incentives for banks to contribute to a voluntary bail-in arise from their exposure to credit and price-mediated contagion. In equilibrium, a bail-in is possible only if the regulator's threat to not bail out insolvent banks is credible. Contrary to models without intervention or government bailouts only, sparse networks are beneficial in our model for two main reasons: they improve the credibility of the regulator's no-bailout threat for large shocks and they reduce free-riding incentives among bail-in contributors when the threat is credible. Financial institutions are linked to each other via bilateral contractual obligations and are thus exposed to counterparty risk of their obligors. If one institution defaults on its liabilities, it affects the solvency of its creditors. Since the creditors are also borrowers, they may not be able to repay what they owe and default themselves-problems in one financial institution spread to others in what is known as financial contagion. Large shocks can trigger a cascade of defaults, which impose negative externalities on the economy. The extent of these cascades-the magnitude of the systemic risk-depends on the nature of the linkages, i.e., the structure of the financial system. In the 2008 crisis, it became apparent that the financial system had evolved in a way which enhanced its ability to absorb small shocks but made it more fragile in the face of a large shock. While a few studies called attention to these issues before the crisis, it was only after the crisis that the impact of the network structure on systemic risk became a major object of analysis. 1 Most of the existing studies analyze the systemic risk implications of a default cascade, taking into account the network structure, asset liquidation costs, and different forms of inefficiencies that

SIAM Journal on Financial Mathematics, 2015

We develop a mean field model of interbanking borrowing and lending activities. Each bank borrows... more We develop a mean field model of interbanking borrowing and lending activities. Each bank borrows from or lends to other counterparties at an idiosyncratic rate, and is exposed to sudden shocks affecting the level of its monetary reserves. Using weak convergence analysis, we provide an explicit characterization of the measure-valued process associated with a large interbanking system. We use the limit process to construct law of large number approximations for systemic indicators assessing average distance to default and measuring the total volume of interbanking activities. We illustrate the predictive power and accuracy of our framework via a detailed numerical analysis, showing that indicators are sensitive to lending preferences, volatility, and occurrences of negative events.

SIAM Journal on Financial Mathematics, 2015

We consider a dynamic multitask principal-agent model in which the agent allocates his resources ... more We consider a dynamic multitask principal-agent model in which the agent allocates his resources on two tasks of different types: effort and accident prevention. We explicitly characterize the optimal contract as well as optimal effort and prevention actions applied by the agent. In contrast to the linear incentive scheme for effort, accident prevention leads to a log-linear punishment scheme if the agent is risk averse, becoming linear only if the agent is risk neutral. Both the sublinearity of the contract and the allocation of resources on the two tasks crucially depend on the risk aversion of the agent. Accident prevention ties up some of the agent's capacity and induces him to substitute resources away from effort to prevention.

SSRN Electronic Journal, 2015

We develop a fixed income portfolio framework which accounts for self-exciting default effects. O... more We develop a fixed income portfolio framework which accounts for self-exciting default effects. Our empirically driven credit model captures the contagion mechanism through which the default of an obligor impacts the credit quality of others, as well as the time decaying of contagious effects. We obtain explicit expressions for the optimal feedback strategies as well as for the value function of the dynamic optimization problem. Our formulas indicate that contagion induces the investor to account both for price depreciations and changes in expected investor's utility due to obligors' defaults, when deciding on the optimal strategies. We prove a verification theorem establishing the equivalence between the value function and the solution of a recursive system of HJB-PDEs. Numerical results confirm the high sensitivity of strategies to risk aversion and self-excitation.

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 2009

We propose the use of copula methods to recover the dependence structure between prediction marke... more We propose the use of copula methods to recover the dependence structure between prediction markets. Copula methods are flexible tools to measure associations among probabilities because they encompass both linear and non linear relationship among variables. We apply the proposed methodology to three actual prediction markets, the Saddam Security, the market of oil spot prices and the Saddameter. We find that the Saddam Security is nearly independent of the oil market, while being highly correlated to the Saddameter. The results obtained appear to suggest that the Saddam Security prediction market may be noisy or overlooking some political factors which are instead considered by Saddameter and the oil market.

2006 Fortieth Asilomar Conference on Signals, Systems and Computers, 2006

In this paper, we characterize the localization performance and connectivity of sensors networks ... more In this paper, we characterize the localization performance and connectivity of sensors networks consisting of binary proximity sensors using a random sensor management strategy. The sensors are deployed uniformly at random over an area, and to limit the energy dissipation, each sensor node switches between an active and idle state according to random mechanisms regulated by a birth-and-death stochastic process. We first develop an upper bound for the minimum transmitting range which guarantees connectivity of the active nodes in the network with a desired probability. Then, we derive an analytical formula for predicting the mean-squared localization error of the active nodes when assuming a centroid localization scheme. Simulations are used to verify the theoretical claims for various localization schemes that operate only over connected active nodes.

Signal Processing, 2010

We generalize the results presented in [1] regarding the relation between the Kalman filter and t... more We generalize the results presented in [1] regarding the relation between the Kalman filter and the Fibonacci sequence. We consider more general filtering models and relate the finite dimensional Kalman and Benes filters to the Fibonacci sequence and to the Golden Section. We also prove that Fibonacci numbers may be expressed as the convolution of the Fibonacci and Padovan sequence, thus extending the connection between stochastic filtering and Fibonacci sequence to the Padovan sequence.

SSRN Electronic Journal, 2011

This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk ... more This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk to the case where collateral is included, with possible re-hypotecation. We analyze how the payout of claims is modified when collateral margining is included in agreement with current ISDA documentation. We then specialize our analysis to interestrate swaps as underlying portfolio, and allow for mutual dependences between the default times of the investor and the counterparty and the underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models, including also the effect of interest rate and credit spread volatilities. The impact of re-hypotecation, of collateral margining frequency and of dependencies on the bilateral counterparty risk adjustment is illustrated with a numerical example.

SSRN Electronic Journal, 2009

We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in ... more We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, including default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net value of the contract at the relevant default times. We allow for correlation between the default times of the investor, counterparty and underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models. We then specialize our analysis to Credit Default Swaps (CDS) as underlying portfolio, generalizing the work of Brigo and Chourdakis (2008) [10] who deal with unilateral and asymmetric counterparty risk. We introduce stochastic intensity models and a trivariate copula function on the default times exponential variables to model default dependence. Similarly to [10], we find that both default correlation and credit spread volatilities have a relevant and structured impact on the adjustment. Differently from [10], the two parties will now agree on the credit valuation adjustment. We study a case involving British Airways, Lehman Brothers and Royal Dutch Shell, illustrating the bilateral adjustments in concrete crisis situations.

Lecture Notes in Computer Science, 2006

In this thesis we study problems arising in the design of sense and respond systems and present a... more In this thesis we study problems arising in the design of sense and respond systems and present analytical solutions to them as well as results from experiments dealing with real systems. Sense and respond systems employ sensors and other sources of data to sense what is happening in their environments, process the obtained information, and respond appropriately. A goal of the processing stage is to reconstruct the best possible estimate of the state of the environment using messages received from sensors. Due to the large number of messages that need to be processed, it is desirable to have algorithms that can incrementally process the received measurements and recover the state. The state estimation process becomes more problematic if measurements obtained from the sensors are noisy or they are sent at unpredictable times. First, we study models of state estimation and present algorithms that can incrementally compute accurate linear state estimates of the surrounding environment....

This thesis proposes a novel credit risk model which deals with incomplete information on the fir... more This thesis proposes a novel credit risk model which deals with incomplete information on the firm's asset value. Such incompleteness is due to reporting bias deliberately introduced by insider managers and executives of the firm and unobserved by outsiders. The pricing of corporate securities and the evaluation of default measures in our credit risk framework requires the solution of a computationally unfeasible nonlinear filtering problem. The model introduces computational issues arising from the fact that the optimal probability density on the firm's asset value is the solution of a nonlinear filtering problem, which is computationally unfeasible. We propose a polynomial time-sequential Bayesian approximation scheme which employs convex optimization methods to iteratively approximate the optimal conditional density of the state on the basis of received market observations. We also provide an upper bound on the total variation distance between the actual filter density an...

Mathematics and Financial Economics, 2021

It has been a dozen years since the largest financial crisis hit the global economy after the Gre... more It has been a dozen years since the largest financial crisis hit the global economy after the Great Depression. Since this event, understanding the mechanism underlying the origination, transmission, and mitigation of systemic risk has been a priority for academics, practitioners, and regulators worldwide. This investigation has led to many important research contributions recently surveyed in review articles (e.g. [14,16]). Despite enormous progress having been made, the topic of systemic risk, along with its implications for the real economy and policy making, remains a subject of active investigation. The continued interest in this topic is manifested by the many conferences, workshops and special events organized each year by central banks and academic institutions on this theme. Agostino Capponi (Columbia), Robert Jarrow (Cornell), and Ulrich Horst (Humboldt University) have decided to dedicate a special issue to the topic of systemic risk and financial networks. The objective of this issue is to provide an overview of research directions currently being pursued by the community. The hope is to both incite interest in this topic among graduate students and young academic and to provide a platform for discussion among professionals who wish the push forward the frontiers of systemic risk research. The contributions to this Special Issue touch upon critical issues in the measurement, modeling, and management of systemic risk. They illustrate the various approaches to the problem put forward by theoretical and empirical research, as well as the integration of data methodologies appropriate for this investigation. Common to many financial crises is the bursting of bubbles. For example, the global 2007-2008 financial crisis was preceded by the bursting of the house price bubble. Jarrow and Lamichhane [17] investigate the theoretical underpinnings of this mechanism in a general equilibrium framework. They show that the interaction of market liquidity, asset price bubbles B Agostino Capponi

Mathematical Finance, 2020

We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a c... more We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the exact return rate of her counterparty's bond, but she knows it lies within an uncertainty interval. We derive both upper and lower bounds for the XVA process of the portfolio, and show that these bounds may be recovered as solutions of nonlinear ordinary differential equations. The presence of collateralization and closeout payoffs leads to important differences with respect to classical credit risk valuation. The value of the superreplicating portfolio cannot be directly obtained by plugging one of the extremes of the uncertainty interval in the valuation equation, but rather depends on the relation between the XVA replicating portfolio and the close-out value throughout the life of the transaction. Our comparative statics analysis indicates that credit contagion has a nonlinear effect on the replication strategies and on the XVA.

SSRN Electronic Journal, 2019

Automated investment managers, or robo-advisors, have emerged as an alternative to traditional fi... more Automated investment managers, or robo-advisors, have emerged as an alternative to traditional financial advisors. Their viability crucially depends on timely communication of information from the clients they serve. We introduce and develop a novel human-machine interaction framework, in which the robo-advisor solves an adaptive mean-variance control problem, with the risk-return tradeoff dynamically updated based on the risk profile communicated by the client. Our model predicts that clients who value a personalized portfolio are more suitable for robo-advising. Clients who place higher emphasis on delegation and clients with a risk profile that changes frequently benefit less from robo-advising.

SSRN Electronic Journal, 2019

We consider an investor who maximizes portfolio's expected returns conditioned on the occurrence ... more We consider an investor who maximizes portfolio's expected returns conditioned on the occurrence of a systemic event: financial system return being at, or at most at, its VaR level and portfolio's returns being below the CoVaR level. We obtain a closed-form solution to the portfolio selection problem, and show how VaR and CoVaR quantiles control, respectively, the relative importance of "portfolio-system correlation" and "portfolio variance". Our empirical analysis demonstrates that the investor attains a higher Sharpe ratio, compared to well known benchmark portfolio criteria, during times of market downturn. Portfolios that perform best in adverse market conditions are less diversified and concentrate on few stocks whose correlation with the financial system is low.

Mathematics of Operations Research, 2017

We consider an optimal risk-sensitive portfolio allocation problem accounting for the possibility... more We consider an optimal risk-sensitive portfolio allocation problem accounting for the possibility of cascading defaults. Default events have an impact on the distress state of the surviving stocks in the portfolio. We study the recursive system of non-Lipschitz quasilinear parabolic HJB-PDEs associated with the value function of the control problem in the different default states of the economy. We show the existence of a classical solution to this system via super-sub solution techniques and give an explicit characterization of the optimal feedback strategy in terms of the value function. We prove a verification theorem establishing the uniqueness of the solution. A numerical analysis indicates that the investor significantly accounts for contagion effects when making investment decisions, and that his strategy depends nonmonotonically on the aggregate risk level.

SSRN Electronic Journal, 2017

The U.S. Treasury market is highly intermediated by nonbank principal trading firms (PTFs). Limit... more The U.S. Treasury market is highly intermediated by nonbank principal trading firms (PTFs). Limited capital forces PTFs to end the trading day roughly flat. We construct a continuous time market making model to analyze the trade-off faced by a profit-maximizing firm with overnight inventory costs, and develop closed-form representations of the optimal price policy functions. Our model reveals that bid-ask spreads widen as the end of the trading day approaches, and that increases in order arrival rates do not always lead to higher price volatility. Our empirical analysis shows that Treasury security trading costs increase as the close of trading approaches, consistent with model predictions.

SSRN Electronic Journal, 2017

We develop a dynamic model of interbank borrowing and lending activities in which banks are organ... more We develop a dynamic model of interbank borrowing and lending activities in which banks are organized into clusters, and adjust their monetary reserve levels to meet prescribed capital requirements. Each bank has its own initial monetary reserve level and faces idiosyncratic risks characterized by an independent Brownian motion; whereas system wide, the banks form a hierarchical structure of clusters. We model the interbank transactional dynamics through a set of interacting measure-valued processes. Each individual process describes the intra-cluster borrowing/lending activities, and the interactions among the processes capture the inter-cluster financial transactions. We establish the weak limit of the interacting measure-valued processes as the number of banks in the system grows large. We then use the weak limit to develop asymptotic approximations of two proposed macro-measures, the liquidity stress index and the concentration index, both capturing the dynamics of systemic risk. We use numerical examples to illustrate the applications of the asymptotics and conduct related sensitivity analysis with respect to various indicators of financial activity.

This paper endogenizes intervention in financial crises as the strategic negotiation between a re... more This paper endogenizes intervention in financial crises as the strategic negotiation between a regulator and creditors of distressed banks. Incentives for banks to contribute to a voluntary bail-in arise from their exposure to credit and price-mediated contagion. In equilibrium, a bail-in is possible only if the regulator's threat to not bail out insolvent banks is credible. Contrary to models without intervention or government bailouts only, sparse networks are beneficial in our model for two main reasons: they improve the credibility of the regulator's no-bailout threat for large shocks and they reduce free-riding incentives among bail-in contributors when the threat is credible. Financial institutions are linked to each other via bilateral contractual obligations and are thus exposed to counterparty risk of their obligors. If one institution defaults on its liabilities, it affects the solvency of its creditors. Since the creditors are also borrowers, they may not be able to repay what they owe and default themselves-problems in one financial institution spread to others in what is known as financial contagion. Large shocks can trigger a cascade of defaults, which impose negative externalities on the economy. The extent of these cascades-the magnitude of the systemic risk-depends on the nature of the linkages, i.e., the structure of the financial system. In the 2008 crisis, it became apparent that the financial system had evolved in a way which enhanced its ability to absorb small shocks but made it more fragile in the face of a large shock. While a few studies called attention to these issues before the crisis, it was only after the crisis that the impact of the network structure on systemic risk became a major object of analysis. 1 Most of the existing studies analyze the systemic risk implications of a default cascade, taking into account the network structure, asset liquidation costs, and different forms of inefficiencies that

SIAM Journal on Financial Mathematics, 2015

We develop a mean field model of interbanking borrowing and lending activities. Each bank borrows... more We develop a mean field model of interbanking borrowing and lending activities. Each bank borrows from or lends to other counterparties at an idiosyncratic rate, and is exposed to sudden shocks affecting the level of its monetary reserves. Using weak convergence analysis, we provide an explicit characterization of the measure-valued process associated with a large interbanking system. We use the limit process to construct law of large number approximations for systemic indicators assessing average distance to default and measuring the total volume of interbanking activities. We illustrate the predictive power and accuracy of our framework via a detailed numerical analysis, showing that indicators are sensitive to lending preferences, volatility, and occurrences of negative events.

SIAM Journal on Financial Mathematics, 2015

We consider a dynamic multitask principal-agent model in which the agent allocates his resources ... more We consider a dynamic multitask principal-agent model in which the agent allocates his resources on two tasks of different types: effort and accident prevention. We explicitly characterize the optimal contract as well as optimal effort and prevention actions applied by the agent. In contrast to the linear incentive scheme for effort, accident prevention leads to a log-linear punishment scheme if the agent is risk averse, becoming linear only if the agent is risk neutral. Both the sublinearity of the contract and the allocation of resources on the two tasks crucially depend on the risk aversion of the agent. Accident prevention ties up some of the agent's capacity and induces him to substitute resources away from effort to prevention.

SSRN Electronic Journal, 2015

We develop a fixed income portfolio framework which accounts for self-exciting default effects. O... more We develop a fixed income portfolio framework which accounts for self-exciting default effects. Our empirically driven credit model captures the contagion mechanism through which the default of an obligor impacts the credit quality of others, as well as the time decaying of contagious effects. We obtain explicit expressions for the optimal feedback strategies as well as for the value function of the dynamic optimization problem. Our formulas indicate that contagion induces the investor to account both for price depreciations and changes in expected investor's utility due to obligors' defaults, when deciding on the optimal strategies. We prove a verification theorem establishing the equivalence between the value function and the solution of a recursive system of HJB-PDEs. Numerical results confirm the high sensitivity of strategies to risk aversion and self-excitation.

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 2009

We propose the use of copula methods to recover the dependence structure between prediction marke... more We propose the use of copula methods to recover the dependence structure between prediction markets. Copula methods are flexible tools to measure associations among probabilities because they encompass both linear and non linear relationship among variables. We apply the proposed methodology to three actual prediction markets, the Saddam Security, the market of oil spot prices and the Saddameter. We find that the Saddam Security is nearly independent of the oil market, while being highly correlated to the Saddameter. The results obtained appear to suggest that the Saddam Security prediction market may be noisy or overlooking some political factors which are instead considered by Saddameter and the oil market.

2006 Fortieth Asilomar Conference on Signals, Systems and Computers, 2006

In this paper, we characterize the localization performance and connectivity of sensors networks ... more In this paper, we characterize the localization performance and connectivity of sensors networks consisting of binary proximity sensors using a random sensor management strategy. The sensors are deployed uniformly at random over an area, and to limit the energy dissipation, each sensor node switches between an active and idle state according to random mechanisms regulated by a birth-and-death stochastic process. We first develop an upper bound for the minimum transmitting range which guarantees connectivity of the active nodes in the network with a desired probability. Then, we derive an analytical formula for predicting the mean-squared localization error of the active nodes when assuming a centroid localization scheme. Simulations are used to verify the theoretical claims for various localization schemes that operate only over connected active nodes.

Signal Processing, 2010

We generalize the results presented in [1] regarding the relation between the Kalman filter and t... more We generalize the results presented in [1] regarding the relation between the Kalman filter and the Fibonacci sequence. We consider more general filtering models and relate the finite dimensional Kalman and Benes filters to the Fibonacci sequence and to the Golden Section. We also prove that Fibonacci numbers may be expressed as the convolution of the Fibonacci and Padovan sequence, thus extending the connection between stochastic filtering and Fibonacci sequence to the Padovan sequence.

SSRN Electronic Journal, 2011

This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk ... more This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk to the case where collateral is included, with possible re-hypotecation. We analyze how the payout of claims is modified when collateral margining is included in agreement with current ISDA documentation. We then specialize our analysis to interestrate swaps as underlying portfolio, and allow for mutual dependences between the default times of the investor and the counterparty and the underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models, including also the effect of interest rate and credit spread volatilities. The impact of re-hypotecation, of collateral margining frequency and of dependencies on the bilateral counterparty risk adjustment is illustrated with a numerical example.

SSRN Electronic Journal, 2009

We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in ... more We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, including default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net value of the contract at the relevant default times. We allow for correlation between the default times of the investor, counterparty and underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models. We then specialize our analysis to Credit Default Swaps (CDS) as underlying portfolio, generalizing the work of Brigo and Chourdakis (2008) [10] who deal with unilateral and asymmetric counterparty risk. We introduce stochastic intensity models and a trivariate copula function on the default times exponential variables to model default dependence. Similarly to [10], we find that both default correlation and credit spread volatilities have a relevant and structured impact on the adjustment. Differently from [10], the two parties will now agree on the credit valuation adjustment. We study a case involving British Airways, Lehman Brothers and Royal Dutch Shell, illustrating the bilateral adjustments in concrete crisis situations.

Lecture Notes in Computer Science, 2006