paresh date - Profile on Academia.edu (original) (raw)
Papers by paresh date
Risks
In micro-lending markets, lack of recorded credit history is a significant impediment to assessin... more In micro-lending markets, lack of recorded credit history is a significant impediment to assessing individual borrowers’ creditworthiness and therefore deciding fair interest rates. This research compares various machine learning algorithms on real micro-lending data to test their efficacy at classifying borrowers into various credit categories. We demonstrate that off-the-shelf multi-class classifiers such as random forest algorithms can perform this task very well, using readily available data about customers (such as age, occupation, and location). This presents inexpensive and reliable means to micro-lending institutions around the developing world with which to assess creditworthiness in the absence of credit history or central credit databases.
Sensors
This paper focuses on developing a particle filter based solution for randomly delayed measuremen... more This paper focuses on developing a particle filter based solution for randomly delayed measurements with an unknown latency probability. A generalized measurement model that includes measurements randomly delayed by an arbitrary but fixed maximum number of time steps along with random packet drops is proposed. Owing to random delays and packet drops in receiving the measurements, the measurement noise sequence becomes correlated. A model for the modified noise is formulated and subsequently its probability density function (pdf) is derived. The recursion equation for the importance weights is developed using pdf of the modified measurement noise in the presence of random delays. Offline and online algorithms for identification of the unknown latency parameter using the maximum likelihood criterion are proposed. Further, this work explores the conditions that ensure the convergence of the proposed particle filter. Finally, three numerical examples, one with a non-stationary growth mo...
Journal of Computational and Applied Mathematics
In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. T... more In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. The proposed filter is named as adaptive sparse-grid Gauss-Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the dimensions equally, whereas the ASGHF assigns a fewer number of points along the dimensions with lower nonlinearity. It uses adaptive tensor product to construct multidimensional points until a predefined error tolerance level is reached. The performance of the proposed filter is illustrated with two nonlinear filtering problems. Simulation results demonstrate that the new algorithm achieves a similar accuracy as compared to sparse-grid
A New Method for Generating Sigma Points and Weights for Nonlinear Filtering
IEEE Control Systems Letters
A modified sequential Monte Carlo procedure for the efficient recursive estimation of extreme quantiles
Journal of Forecasting
A minimum variance filter for continuous discrete systems with additive-multiplicative noise
2016 24th European Signal Processing Conference (EUSIPCO), 2016
IET Control Theory & Applications, 2016
The filtering of nonlinear continuous-discrete systems is widely applicable in real-life and exte... more The filtering of nonlinear continuous-discrete systems is widely applicable in real-life and extensive literature is available to deal with such problems. However, all of these approaches are constrained with the assumption that the current measurement is available at every time step, although delay in measurement is natural in real-life applications. To deal with this problem, we re-derive the conventional Bayesian approximation framework for solving the continuous-discrete filtering problems. In practice, the delay is often smaller than one sampling time, which is the main case considered here. During the filtering of such systems, the actual time of correspondence should be known for a measurement received at the k th time instant. In this paper, a simple and intuitively justified cost function is used to decide the time to which the measurement at k th time instant actually corresponds. The performance of the proposed filter is compared with a conventional filter based on numerical integration which ignores random delays for a continuousdiscrete tracking problem. We show that the conventional filter fails to track the target while the modification proposed in this paper successfully deals with random delays. The proposed method may be seen as a valuable addition to the tools available for continuous-discrete filtering in nonlinear systems.
Brief paper: Positivity-preserving H∞ model reduction for positive systems
Automatica, Jul 1, 2011
Validation of closed-loop behaviour from noisy frequency response measurements
2003 European Control Conference, Sep 1, 2003
Applied Mathematical Modelling, 2016
In this paper, two existing quadrature filters, viz., the Gauss-Hermite filter (GHF) and the spar... more In this paper, two existing quadrature filters, viz., the Gauss-Hermite filter (GHF) and the sparse-grid Gauss-Hermite filter (SGHF) are extended to solve nonlinear filtering problems with one step randomly delayed measurements. The developed filters are applied to solve a maneuvering target tracking problem with one step randomly delayed measurements. Simulation results demonstrate the enhanced accuracy of the proposed delayed filters compared to the delayed cubature Kalman filter and delayed unscented Kalman filter.
IMA Journal of Management Mathematics, 2015
We propose a way of measuring the risk of a sovereign debt portfolio by using a simple two-factor... more We propose a way of measuring the risk of a sovereign debt portfolio by using a simple two-factor short rate model. The model is calibrated from data and then the changes in the bond prices are simulated by using a Kalman filter. The bond prices being simulated remain arbitrage-free, in contrast with principal component analysis based strategies for simulation and risk measurement of debt portfolios. In liquid sovereign debt markets, a risk measurement methodology which allows the future bond price scenarios to be arbitrage-free may be seen as a potentially more realistic way of measuring the debt portfolio risk due to interest rate fluctuations. We demonstrate the performance of this methodology with calibration and backtesting, both on simulated data as well as on a real portfolio of US government bonds.
Circuits and Systems, 2003 …, 2003
This paper investigates the problem of state estimation for discrete-time stochastic systems with... more This paper investigates the problem of state estimation for discrete-time stochastic systems with linear dynamics perturbed by unknown nonlinearities. The Extended Kalman Filter (EKF) can not be applied in this framework, because the lack of knowledge on the nonlinear terms forbids a reliable linear approximation of the perturbed system. Following the idea to compensate this lack of knowledge suitably exploiting the information brought by the measured output, a recursive linear¯lter is developed according to the minimum error variance criterion. Di®erently from what happens for the EKF, the gain of the proposed¯lter can be computed o®-line. Numerical simulations show the e®ectiveness of the¯ltering algorithm.
We consider the problem of optimal state estimation for a wide class of nonlinear time series mod... more We consider the problem of optimal state estimation for a wide class of nonlinear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in engineering where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples.
Pricing and risk management of interest rate swaps
ABSTRACT This paper reformulates the valuation of interest rate swaps, swap leg payments and swap... more ABSTRACT This paper reformulates the valuation of interest rate swaps, swap leg payments and swap risk measures, all under stochastic interest rates, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations which solves this system is developed and allows for fast and accurate computation. The proposed method provides a computationally efficient alternative to Monte Carlo based valuations and risk measurement of swaps. This is demonstrated by conducting numerical experiments and so our method provides a potentially important real-time application for analysis and calculation in markets.
Applied Mathematics and Computation, 2008
We consider the problem of optimal state estimation for a wide class of nonlinear time series mod... more We consider the problem of optimal state estimation for a wide class of nonlinear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in engineering where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples.
Algorithms for worst case identification in I and in the nu-gap metric
Automatica, 2004
This paper considers two robustly convergent algorithms for the identification of a linear system... more This paper considers two robustly convergent algorithms for the identification of a linear system from (possibly) noisy frequency response data. Both algorithms are based on the same principle; obtaining a good worst case fit to the data under a smoothness constraint on the obtained model. However they differ in their notions of distance and smoothness. The first algorithm yields an
Automatica, Jul 1, 2011
This paper is concerned with the model reduction of positive systems. For a given stable positive... more This paper is concerned with the model reduction of positive systems. For a given stable positive system, our attention is focused on the construction of a reduced-order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed H 1 performance. Based upon a system augmentation approach, a novel characterization on the stability with H 1 performance of the error system is …rst obtained in terms of linear matrix inequality (LMI). Then, a necessary and su¢ cient condition for the existence of a desired reduced-order model is derived accordingly. A signi…cance of the proposed approach is that the reduced-order system matrices can be parametrized by a positive de…nite matrix with ‡exible structure, which is fully independent of the Lyapunov matrix; thus, the positivity constraint on the reduced-order system can be readily embedded in the model reduction problem. Furthermore, iterative LMI approaches with primal and dual forms are developed to solve the positivity-preserving H 1 model reduction problem. Finally, a compartmental network is provided to show the e¤ectiveness of the proposed techniques.
The problem of estimating the latent states of a dynamical system from observed data often arises... more The problem of estimating the latent states of a dynamical system from observed data often arises in many branches of physical and social sciences, including image processing, navigation, econometrics, finance and meteorology. Filtering refers to any method for obtaining such state estimates, recursively in time, by combining model predictions with noisy observations. While the solution to the filtering problem for a linear dynamic system is well understood and has been studied extensively since 1960s, the optimal solution to the nonlinear filtering still poses challenging problems in maintaing a complete description of the conditional probability density. A number of suboptimal approximations, mainly based on Bayesian methods, have been proposed for solving the nonlinear filtering problem arising in different fields such as image processing, meteorology and econometrics, each offering an application-specific compromise between estimation accuracy, computational burden andnumerical robustness. Because of the diversity of applications, researchers from different fields have developed both methodological and application specific innovations that often remain restricted to their respective fields. The purpose of this special issue on the mathematics of filtering and its applications is to collect experiences in filtering from different fields by including some papers, selected from the homonym workshop held at Brunel University in July 2011, which are representative of different application areas including financial mathematics, robotics and artificial intelligence. We are thankful to the editor Prof. V.J. Rayward-Smith for allocating a special issue dedicated to this topic.
Journal of Loss Prevention in the Process Industries, Jul 1, 2009
This paper proposes a new algorithm to compute the residual risk of failure of an explosion prote... more This paper proposes a new algorithm to compute the residual risk of failure of an explosion protection system on an industrial process plant. A graph theoretic framework is used to model the process. Both the main reasons of failure are accounted for, viz. hardware failure and inadequate protection even when the protection hardware functions according to specifications. The algorithm is shown to be both intuitive and simple to implement in practice. Its application is demonstrated with a realistic example of a protection system installation on a spray drier.
European Journal of Operational Research, May 1, 2009
This paper provides a significant numerical evidence for out-of-sample forecasting ability of lin... more This paper provides a significant numerical evidence for out-of-sample forecasting ability of linear Gaussian interest rate models with unobservable underlying factors. We calibrate one, two and three factor linear Gaussian models using the Kalman filter on two different bond yield data sets and compare their out-of-sample forecasting performance. One step ahead as well as four step ahead out-of-sample forecasts are analyzed based on the weekly data.
Risks
In micro-lending markets, lack of recorded credit history is a significant impediment to assessin... more In micro-lending markets, lack of recorded credit history is a significant impediment to assessing individual borrowers’ creditworthiness and therefore deciding fair interest rates. This research compares various machine learning algorithms on real micro-lending data to test their efficacy at classifying borrowers into various credit categories. We demonstrate that off-the-shelf multi-class classifiers such as random forest algorithms can perform this task very well, using readily available data about customers (such as age, occupation, and location). This presents inexpensive and reliable means to micro-lending institutions around the developing world with which to assess creditworthiness in the absence of credit history or central credit databases.
Sensors
This paper focuses on developing a particle filter based solution for randomly delayed measuremen... more This paper focuses on developing a particle filter based solution for randomly delayed measurements with an unknown latency probability. A generalized measurement model that includes measurements randomly delayed by an arbitrary but fixed maximum number of time steps along with random packet drops is proposed. Owing to random delays and packet drops in receiving the measurements, the measurement noise sequence becomes correlated. A model for the modified noise is formulated and subsequently its probability density function (pdf) is derived. The recursion equation for the importance weights is developed using pdf of the modified measurement noise in the presence of random delays. Offline and online algorithms for identification of the unknown latency parameter using the maximum likelihood criterion are proposed. Further, this work explores the conditions that ensure the convergence of the proposed particle filter. Finally, three numerical examples, one with a non-stationary growth mo...
Journal of Computational and Applied Mathematics
In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. T... more In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. The proposed filter is named as adaptive sparse-grid Gauss-Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the dimensions equally, whereas the ASGHF assigns a fewer number of points along the dimensions with lower nonlinearity. It uses adaptive tensor product to construct multidimensional points until a predefined error tolerance level is reached. The performance of the proposed filter is illustrated with two nonlinear filtering problems. Simulation results demonstrate that the new algorithm achieves a similar accuracy as compared to sparse-grid
A New Method for Generating Sigma Points and Weights for Nonlinear Filtering
IEEE Control Systems Letters
A modified sequential Monte Carlo procedure for the efficient recursive estimation of extreme quantiles
Journal of Forecasting
A minimum variance filter for continuous discrete systems with additive-multiplicative noise
2016 24th European Signal Processing Conference (EUSIPCO), 2016
IET Control Theory & Applications, 2016
The filtering of nonlinear continuous-discrete systems is widely applicable in real-life and exte... more The filtering of nonlinear continuous-discrete systems is widely applicable in real-life and extensive literature is available to deal with such problems. However, all of these approaches are constrained with the assumption that the current measurement is available at every time step, although delay in measurement is natural in real-life applications. To deal with this problem, we re-derive the conventional Bayesian approximation framework for solving the continuous-discrete filtering problems. In practice, the delay is often smaller than one sampling time, which is the main case considered here. During the filtering of such systems, the actual time of correspondence should be known for a measurement received at the k th time instant. In this paper, a simple and intuitively justified cost function is used to decide the time to which the measurement at k th time instant actually corresponds. The performance of the proposed filter is compared with a conventional filter based on numerical integration which ignores random delays for a continuousdiscrete tracking problem. We show that the conventional filter fails to track the target while the modification proposed in this paper successfully deals with random delays. The proposed method may be seen as a valuable addition to the tools available for continuous-discrete filtering in nonlinear systems.
Brief paper: Positivity-preserving H∞ model reduction for positive systems
Automatica, Jul 1, 2011
Validation of closed-loop behaviour from noisy frequency response measurements
2003 European Control Conference, Sep 1, 2003
Applied Mathematical Modelling, 2016
In this paper, two existing quadrature filters, viz., the Gauss-Hermite filter (GHF) and the spar... more In this paper, two existing quadrature filters, viz., the Gauss-Hermite filter (GHF) and the sparse-grid Gauss-Hermite filter (SGHF) are extended to solve nonlinear filtering problems with one step randomly delayed measurements. The developed filters are applied to solve a maneuvering target tracking problem with one step randomly delayed measurements. Simulation results demonstrate the enhanced accuracy of the proposed delayed filters compared to the delayed cubature Kalman filter and delayed unscented Kalman filter.
IMA Journal of Management Mathematics, 2015
We propose a way of measuring the risk of a sovereign debt portfolio by using a simple two-factor... more We propose a way of measuring the risk of a sovereign debt portfolio by using a simple two-factor short rate model. The model is calibrated from data and then the changes in the bond prices are simulated by using a Kalman filter. The bond prices being simulated remain arbitrage-free, in contrast with principal component analysis based strategies for simulation and risk measurement of debt portfolios. In liquid sovereign debt markets, a risk measurement methodology which allows the future bond price scenarios to be arbitrage-free may be seen as a potentially more realistic way of measuring the debt portfolio risk due to interest rate fluctuations. We demonstrate the performance of this methodology with calibration and backtesting, both on simulated data as well as on a real portfolio of US government bonds.
Circuits and Systems, 2003 …, 2003
This paper investigates the problem of state estimation for discrete-time stochastic systems with... more This paper investigates the problem of state estimation for discrete-time stochastic systems with linear dynamics perturbed by unknown nonlinearities. The Extended Kalman Filter (EKF) can not be applied in this framework, because the lack of knowledge on the nonlinear terms forbids a reliable linear approximation of the perturbed system. Following the idea to compensate this lack of knowledge suitably exploiting the information brought by the measured output, a recursive linear¯lter is developed according to the minimum error variance criterion. Di®erently from what happens for the EKF, the gain of the proposed¯lter can be computed o®-line. Numerical simulations show the e®ectiveness of the¯ltering algorithm.
We consider the problem of optimal state estimation for a wide class of nonlinear time series mod... more We consider the problem of optimal state estimation for a wide class of nonlinear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in engineering where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples.
Pricing and risk management of interest rate swaps
ABSTRACT This paper reformulates the valuation of interest rate swaps, swap leg payments and swap... more ABSTRACT This paper reformulates the valuation of interest rate swaps, swap leg payments and swap risk measures, all under stochastic interest rates, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations which solves this system is developed and allows for fast and accurate computation. The proposed method provides a computationally efficient alternative to Monte Carlo based valuations and risk measurement of swaps. This is demonstrated by conducting numerical experiments and so our method provides a potentially important real-time application for analysis and calculation in markets.
Applied Mathematics and Computation, 2008
We consider the problem of optimal state estimation for a wide class of nonlinear time series mod... more We consider the problem of optimal state estimation for a wide class of nonlinear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in engineering where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples.
Algorithms for worst case identification in I and in the nu-gap metric
Automatica, 2004
This paper considers two robustly convergent algorithms for the identification of a linear system... more This paper considers two robustly convergent algorithms for the identification of a linear system from (possibly) noisy frequency response data. Both algorithms are based on the same principle; obtaining a good worst case fit to the data under a smoothness constraint on the obtained model. However they differ in their notions of distance and smoothness. The first algorithm yields an
Automatica, Jul 1, 2011
This paper is concerned with the model reduction of positive systems. For a given stable positive... more This paper is concerned with the model reduction of positive systems. For a given stable positive system, our attention is focused on the construction of a reduced-order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed H 1 performance. Based upon a system augmentation approach, a novel characterization on the stability with H 1 performance of the error system is …rst obtained in terms of linear matrix inequality (LMI). Then, a necessary and su¢ cient condition for the existence of a desired reduced-order model is derived accordingly. A signi…cance of the proposed approach is that the reduced-order system matrices can be parametrized by a positive de…nite matrix with ‡exible structure, which is fully independent of the Lyapunov matrix; thus, the positivity constraint on the reduced-order system can be readily embedded in the model reduction problem. Furthermore, iterative LMI approaches with primal and dual forms are developed to solve the positivity-preserving H 1 model reduction problem. Finally, a compartmental network is provided to show the e¤ectiveness of the proposed techniques.
The problem of estimating the latent states of a dynamical system from observed data often arises... more The problem of estimating the latent states of a dynamical system from observed data often arises in many branches of physical and social sciences, including image processing, navigation, econometrics, finance and meteorology. Filtering refers to any method for obtaining such state estimates, recursively in time, by combining model predictions with noisy observations. While the solution to the filtering problem for a linear dynamic system is well understood and has been studied extensively since 1960s, the optimal solution to the nonlinear filtering still poses challenging problems in maintaing a complete description of the conditional probability density. A number of suboptimal approximations, mainly based on Bayesian methods, have been proposed for solving the nonlinear filtering problem arising in different fields such as image processing, meteorology and econometrics, each offering an application-specific compromise between estimation accuracy, computational burden andnumerical robustness. Because of the diversity of applications, researchers from different fields have developed both methodological and application specific innovations that often remain restricted to their respective fields. The purpose of this special issue on the mathematics of filtering and its applications is to collect experiences in filtering from different fields by including some papers, selected from the homonym workshop held at Brunel University in July 2011, which are representative of different application areas including financial mathematics, robotics and artificial intelligence. We are thankful to the editor Prof. V.J. Rayward-Smith for allocating a special issue dedicated to this topic.
Journal of Loss Prevention in the Process Industries, Jul 1, 2009
This paper proposes a new algorithm to compute the residual risk of failure of an explosion prote... more This paper proposes a new algorithm to compute the residual risk of failure of an explosion protection system on an industrial process plant. A graph theoretic framework is used to model the process. Both the main reasons of failure are accounted for, viz. hardware failure and inadequate protection even when the protection hardware functions according to specifications. The algorithm is shown to be both intuitive and simple to implement in practice. Its application is demonstrated with a realistic example of a protection system installation on a spray drier.
European Journal of Operational Research, May 1, 2009
This paper provides a significant numerical evidence for out-of-sample forecasting ability of lin... more This paper provides a significant numerical evidence for out-of-sample forecasting ability of linear Gaussian interest rate models with unobservable underlying factors. We calibrate one, two and three factor linear Gaussian models using the Kalman filter on two different bond yield data sets and compare their out-of-sample forecasting performance. One step ahead as well as four step ahead out-of-sample forecasts are analyzed based on the weekly data.