Risk-sensitive investment in a finite-factor model

Abstract

A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion maximization problem in this setting. We provide an ODE for the optimal value function, which may be efficiently solved numerically. Relevant probability measure changes are discussed in the appendix. The recently introduced approach of Klebaner and Liptser (2013) is used to prove the martingale property of the relevant density processes.

Keywords:

• Portfolio optimization
• risk-sensitive control
• factor model
• exponential martingale

AMS Subject Classifications:

• 34A12
• 60H05
• 91G10
• 93E20

Notes

No potential conflict of interest was reported by the author.

This paper is dedicated to Bernt Øksendal on the occasion of his 70th birthday.

1 ‘Alpha’ is the excess return of a portfolio relative to the return of a benchmark index.

2 Note that this constitutes a very simple model for stochastic interest rates.