Portfolio Optimization: How Jumps Modify the Standard Merton Message?

39 Pages Posted: 5 Jul 2010

See all articles by Nicolas Gaussel

Nicolas Gaussel

Metori Capital Management; Université Paris 1 Panthéon-Sorbonne

Grégoire Deyirmendjian

affiliation not provided to SSRN

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

Gaussel, Nicolas and Deyirmendjian, Grégoire, Portfolio Optimization: How Jumps Modify the Standard Merton Message? (September 2, 2005). Available at SSRN: https://ssrn.com/abstract=1634104 or http://dx.doi.org/10.2139/ssrn.1634104

Nicolas Gaussel (Contact Author)

Metori Capital Management ( email )

9 rue de la Paix
Paris, 75002
France

HOME PAGE: http://www.metori.com

Université Paris 1 Panthéon-Sorbonne ( email )

ISJPS
5, Place du Panthéon
Paris, 75005
France

Grégoire Deyirmendjian

affiliation not provided to SSRN

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