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PORTFOLIO OPTIMIZATION IN A DEFAULT MODEL UNDER FULL/PARTIAL INFORMATION

Published online by Cambridge University Press:  14 July 2015

Thomas Lim  and
Marie-Claire Quenez
Thomas Lim
Affiliation:
Laboratoire de Mathématiques et, Modélisation d'Evry, CNRS, UMR 8071, ENSIIE E-mail: [email protected]
Marie-Claire Quenez
Affiliation:
Laboratoire de Probabilités et, Modèles Aléatoires.CNRS, UMR 7599 Université Paris 7 E-mail: [email protected]
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Abstract

In this paper, we consider a financial market with an asset exposed to a risk inducing a jump in the asset price, and which can still be traded after the default time. We use a default-intensity modeling approach, and address in this incomplete market context the problem of maximization of expected utility from terminal wealth for logarithmic, power and exponential utility functions. We study this problem as a stochastic control problem both under full and partial information. Our contribution consists of showing that the optimal strategy can be obtained by a direct approach for the logarithmic utility function, and the value function for the power (resp. exponential) utility function can be determined as the minimal (resp. maximal) solution of a backward stochastic differential equation. For the partial information case, we show how the problem can be divided into two problems: a filtering problem and an optimization problem. We also study the indifference pricing approach to evaluate the price of a contingent claim in an incomplete market and the information price for an agent with insider information.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 4 , October 2015 , pp. 565 - 587
Copyright
Copyright © Cambridge University Press 2015 

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