Marzia De Donno - Academia.edu (original) (raw)

Papers by Marzia De Donno

Ann Appl Probab, 2005

We introduce a theory of stochastic integration with respect to a family of semimartingales depen... more We introduce a theory of stochastic integration with respect to a family of semimartingales depending on a continuous parameter, as a mathematical background to the theory of bond markets. We apply our results to the problem of super-replication and utility maximization from terminal wealth in a bond market. Finally, we compare our approach to those already existing in literature.

Working Papers, 2013

Relevant capital investment options and American derivatives embedded into popular secured loans ... more Relevant capital investment options and American derivatives embedded into popular secured loans can be reduced to American option problems with an endogenous negative 'interest rate'. We show that such problems can entail a non-standard double continuation region: option exercise is optimally postponed not only when the option is insu¢ ciently in the money but also when it is excessively in the money. We fully characterize the existence, the monotonicity, the continuity, the limits and the asymptotic behavior at maturity of the double free boundary that separates the exercise region from the double continuation region. Our results apply to real options whose project values enjoy robust growth rates while investment costs also markedly escalate. The gold loan is an in-vogue contract of collateralized borrowing whose optimal redeeming strategy constitutes another interesting application of our results.

Quant Financ, 2010

If the average risk-adjusted growth rate of the project's present value V overcomes the discount ... more If the average risk-adjusted growth rate of the project's present value V overcomes the discount rate but is dominated by the average risk-adjusted growth rate of the cost I of entering the project, a non-standard double continuation region can arise: The firm waits to invest in the project if V is insufficiently above I as well as if V is comfortably above I. Under a framework with diffusive uncertainty, we give exact characterization to the value of the option to invest, to the structure of the double continuation region, and to the subset of the primitives' values that support such a region. yAlthough they do not explicitly appear, the correlations between V and I and their local volatilities contribute towards defining thê P drifts via the price(s) of risk and the associated risk adjustment.

Journal of Financial Risk Management, 2015

Journal of Probability and Statistics, 2015

We study the problem of utility maximization from termi-nal wealth in a semimartingale model with... more We study the problem of utility maximization from termi-nal wealth in a semimartingale model with countably many assets. After discussing in this context the appropriate notion of admissible strategy, we give a characterization result for the superreplication price of a contingent claim. Utility maximization problems are then studied with the convex du-ality method, and we extend finite-dimensional results to this setting. The existence of an optimizer is proved in a suitable class of general-ized strategies: this class has also the property that maximal utility is the limit of maximal utilities in finite-dimensional submarkets. Counterexamples are then given, which illustrate several phenomena which arise in presence of infinitely many assets.

We extend to the Heston stochastic volatility framework the parity result of McDonald and Schrode... more We extend to the Heston stochastic volatility framework the parity result of McDonald and Schroder (1998) for American call and put options.

In Memoriam Paul-André Meyer, 2006

Motivated by a problem in mathematical finance, which, however, will not be discussed in this not... more Motivated by a problem in mathematical finance, which, however, will not be discussed in this note, we propose a theory of stochastic integration with respect to a sequence of semimartingales. The case of stochastic integration with respect to a sequence of square ...

Séminaire de Probabilités XL, 2007

Management Science, 2014

SSRN Electronic Journal, 2000

Stochastic Processes and their Applications, 2005

We study the problems of super-replication and utility maximization from terminal wealth in a sem... more We study the problems of super-replication and utility maximization from terminal wealth in a semimartingale model with countably many assets. After introducing a suitable definition of admissible strategy, we characterize superreplicable contingent claims in terms of martingale measures. Utility maximization problems are then studied with the convex duality method, and we extend finite-dimensional results to this setting. The existence of an optimizer is proved in a suitable class of generalized strategies: this class has also the property that maximal expected utility is the limit of maximal expected utilities in finite-dimensional submarkets. Finally, we illustrate our results with some examples in infinite dimensional factor models.

Quantitative Finance, 2012

Journal of Mathematical Economics, 2011

Frankfurt, Seminaire Bachelier-Institut Henri Poincaré for useful comments and suggestions. We gr... more Frankfurt, Seminaire Bachelier-Institut Henri Poincaré for useful comments and suggestions. We gratefully acknowledge …nancial support from Bocconi University, MIUR, and the Sanger Chair of Banking and Risk Management at the Hebrew University of Jerusalem. The usual disclaimer applies.

Finance and Stochastics, 2004

We propose here a theory of cylindrical stochastic integration, recently developed by Mikuleviciu... more We propose here a theory of cylindrical stochastic integration, recently developed by Mikulevicius and Rozovskii, as mathematical background to the theory of bond markets. In this theory, since there is a continuum of securities, it seems natural to define a portfolio as a measure on maturities. However, it turns out that this set of strategies is not complete, and the theory of cylindrical integration allows one to overcome this difficulty. Our approach generalizes the measure-valued strategies: this explains some known results, such as approximate completeness, but at the same time it also shows that either the optimal strategy is based on a finite number of bonds or it is not necessarily a measure-valued process. The first author gratefully acknowledges financial support from the CNR Strategic Project "Modellizzazione matematica di fenomeni economici".

ABSTRACT Given a class A of non-satiated investors with continuous and convex preferences, a one-... more ABSTRACT Given a class A of non-satiated investors with continuous and convex preferences, a one-period security market is viable if some agent in A finds an optimal trade. Harrison and Kreps (1979) show that viability is equivalent to the existence of linear pricing rules. Our first contribution is to extend Harrison and Kreps' result to the case of intertemporal consumption and preferences for intermediate consumption that may exhibit satiation, non-convexity and discontinuity. Then we show that the set of linear pricing rules is characterized in terms of agents' marginal utilities of optimal intertemporal wealth even if the marginal utility of consumption fails to exist, and hence the envelope condition equating the marginal utility of wealth to marginal utility of consumption cannot be invoked. We prove this result for period utilities that can be explicitly dependent on the state of nature. Moreover we relate linear pricing

The Annals of Applied Probability, 2005