Portfolio Optimization: How Jumps Modify the Standard Merton Message?
39 Pages Posted: 5 Jul 2010
Date Written: September 2, 2005
Abstract
The standard Merton approach of portfolio optimization reduces the problem to the understanding of three key objects: the expected returns, a covariance matrix expectation and a risk aversion behavior. It is the aim of this paper to understand whether these results are preserved or not when the underlying may jump. To do so, this problem is addressed in a simple market model, sometimes called \Mixed Model", driven by both standard Brownian and Poisson processes. All results presented in this article are related to the so-called Martingale approach of the portfolio optimization problem. Via this approach, we provide, for particular utility functions, the optimal portfolio value, the optimal strategy and an interpretation of the optimal risk-neutral probability measure.
Keywords: Asset management, jumps, portfolio allocation
JEL Classification: G11, C61
Suggested Citation: Suggested Citation