Portfolio Optimisation with Jumps: Illustration with a Pension Accumulation Scheme

36 Pages Posted: 9 Oct 2012 Last revised: 11 Apr 2016

See all articles by Olivier Le Courtois

Olivier Le Courtois

EM Lyon (Ecole de Management de Lyon) - Department of Economics, Finance, Control

Francesco Menoncin

University of Brescia - Department of Economics

Date Written: June 6, 2012

Abstract

In this paper, we address portfolio optimisation when stock prices follow general Lévy processes in the context of a pension accumulation scheme. The optimal portfolio weights are obtained in quasi-closed form and the optimal consumption in closed form. To solve the optimisation problem, we show how to switch back and forth between the stochastic differential and standard exponentials of the Lévy processes. We apply this procedure to both the Variance Gamma process and a Lévy process whose arrival rate of jumps exponentially decreases with size. We show through a numerical example that when jumps, and therefore asymmetry and leptokurtosis, are suitably taken into account, then the optimal portfolio share of the risky asset is around half that obtained in the Gaussian framework.

Keywords: Optimal Portfolio, Pension Fund, Lévy process, Stochastic Exponential

JEL Classification: G13, G22

Suggested Citation

Le Courtois, Olivier Arnaud and Menoncin, Francesco, Portfolio Optimisation with Jumps: Illustration with a Pension Accumulation Scheme (June 6, 2012). Journal of Banking and Finance, Vol. 60, p. 127-137, 2015.. Available at SSRN: https://ssrn.com/abstract=2083655 or http://dx.doi.org/10.2139/ssrn.2083655

Olivier Arnaud Le Courtois (Contact Author)

EM Lyon (Ecole de Management de Lyon) - Department of Economics, Finance, Control ( email )

23, av. Guy de Collongue
69134 Ecully Cedex
France

Francesco Menoncin

University of Brescia - Department of Economics ( email )

Via San Faustino 74B
Brescia, 25122
Italy
0039-0302988806 (Phone)
0039-0302988837 (Fax)

HOME PAGE: http://www.eco.unibs.it/~menoncin/

Register to save articles to
your library

Register

Paper statistics

Downloads
71
rank
308,969
Abstract Views
531
PlumX Metrics