Risk-Based Asset Allocation Under Markov-Modulated Pure Jump Processes

Abstract

We consider a risk-based asset allocation problem in a Markov, regime-switching, pure jump model. With a convex risk measure of the terminal wealth of an investor as a proxy for risk, we formulate the risk-based asset allocation problem as a zero-sum, two-person, stochastic differential game between the investor and the market. The HJB dynamic programming approach is used to discuss the game problem. A semi-analytical solution of the game problem is obtained in a particular case.

Keywords:

• Asset allocation
• Convex risk measures
• Pure jump processes
• Regime switching
• Stochastic differential games

Mathematics Subject Classification:

• Primary 91G10
• Secondary 91A15

Notes

Frittelli and Rosazza Gianin [12] also gave the definition of a convex risk measure on the space L ^p (Ω, ℱ, P) of p-integrable random variables on (Ω, ℱ, P).