Management of Pension Funds When Asset Returns are Driven by Lévy Processes

Olivier Arnaud Le Courtois, Francesco Menoncin
2012 Social Science Research Network  
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
more » ... al 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.
doi:10.2139/ssrn.2083655 fatcat:serftf3ibzd6lkanj4gmupoacq