Investment with Sequence Losses in an Uncertain Environment and Mean-Variance Hedging

Abstract

In a market with a discontinuous filtration, whose price is influenced by a random factor, we study an optimization problem of an investor who is facing a sequence of losses driven by a Cox process. We give a form of variance-optimal martingale measure by changing the filtration. By using the solutions of the stochastic Riccati equation and another associated backward stochastic equation, we obtain a solution of the optimization problem of the investor.

Keywords:

• Backward stochastic differential equations
• Mean-variance portfolio selection
• Stochastic Riccati equation
• Variance-optimal martingale measure

Mathematics Subject Classification:

• 91B28
• 93E20
• 60H30
• 60G44

Notes

Supported by National Natural Science Foundation of China under Grant No. 10171066 and Shanghai Key Project under Grant No. 02DJ14063