Jump-Diffusion Risk-Sensitive Asset Management

Mark H. A. Davis; Sebastien Lleo

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arXiv · 0905.4740

Jump-Diffusion Risk-Sensitive Asset Management

Mark H. A. Davis·Sebastien Lleo

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Abstract

This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion 'factor' process. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance.) By using a change of measure technique introduced by Kuroda and Nagai we show that the problem reduces to solving a certain stochastic control problem in the factor process, which has no jumps. The main result of the paper is that the Hamilton-Jacobi-Bellman equation for this problem has a classical solution. The proof uses Bellman's "policy improvement" method together with results on linear parabolic PDEs due to Ladyzhenskaya et al.

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BibTeX RIS

Mark H. A. Davis, Sebastien Lleo. 2010-03-12. Jump-Diffusion Risk-Sensitive Asset Management. https://arxiv.org/abs/0905.4740

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