## Portfolio optimization in a hidden Markov model for stock returns with jumps

- Date: 03/29/2007

Ulrich Haussmann (University of British Columbia)

University of British Columbia

In a market consisting of a money market and one stock with

price process dS(t)=S(t)[a(t) dt + b dW(t) + g dM(t)] where W is a

Wiener process and M is a compensated Poisson process, an agent invests

his initial wealth in a portfolio to maximize utility of wealth at

terminal time T. The portfolio strategy may only depend on the observed

stock price S(t). The constants b and g may be inferred from this, but

not the unknown drift a(t). It is assumed to be a Markov process with

known states and rate matrix.We reduce the problem to a martingale

representation problem for Levy processes.

This is joint work with Dr. Joern Sass.

MITACS Math Finance Seminar 2007