Portfolio optimisation with jumps: Illustration with a pension accumulation scheme |
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| Institution: | 1. EMLyon Business School, Avenue Guy de Collongue, 23 – 69130 Ecully, France;2. University of Brescia, Via S. Faustino, 74/B – 25122 Brescia, Italy;1. Department of Finance, Warwick Business School, Coventry CV4 7AL, United Kingdom;2. Department of Finance, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 106, Taiwan;1. UTS Business School, University of Technology Sydney, NSW 2007, Australia;2. Department of Economics, University of Leicester, LE17RH, UK;1. The Wang Yanan Institute for Studies in Economics, Xiamen University, Fujian 361005, China;2. Department of Economics, Cornell University, Ithaca, NY 14853, USA;1. Department of Economics and Finance, Tobin College of Business, St. John’s University, Queens, NY 11439, USA;2. Department of Finance, College of Business, East Carolina University, Greenville, NC 27858, USA;3. Department of Finance, Muma College of Business, University of South Florida, Tampa, FL 33620, USA;4. J. Mack Robinson College of Business, Georgia State University, Atlanta, GA 30303, USA |
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| 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. |
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| Keywords: | Optimal portfolio Lévy process Stochastic exponential Pension fund |
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