Portfolio optimization in a default model under full/partial information

TL;DR

This paper addresses portfolio optimization in markets with jump risks and default events, using stochastic control under full and partial information, and explores utility maximization, indifference pricing, and insider information valuation.

Contribution

It introduces a direct approach for logarithmic utility and characterizes the power utility value function via backward stochastic differential equations, advancing incomplete market optimization methods.

Findings

Optimal strategies derived for logarithmic utility via direct approach.

Power utility value function characterized by backward stochastic differential equations.

Methodology for partial information involving filtering and optimization problems.

Abstract

In this paper, we consider a financial market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. 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 in showing that the optimal strategy can be obtained by a direct approach for the logarithmic utility function, and the value function for the power utility function can be determined as the minimal 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.