Optimal Portfolio Selection when Stock Price Returns Follow Jump-Diffusions
by Daniel Michelbrink
Abstract: We consider an investor who wishes to maximise expected utility from terminal wealth and consumption.
The investor can thereby invest into a stock or a riskless bond. The problem has been solved for the classical Black-Scholes model but turns out to be more difficult in case that the stock returns follow a jump diffusion process.
For this kind of problems one usually tries to find a solution either by using a martingale approach or by using stochastic control. In case of stochastic control one has to solve a PDE (or PIDE) - the Hamilton-Jacobi-Bellman equation - whereas in case of the martingale approach one uses various stochastic calculus tools to get a solution. In the talk we focus on the martingale approach, but also compare some concrete examples with the stochastic control solutions.
For More Information: Daniel Dufresne email@example.com