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Management of Pension Funds under Market Jump Risk
in 29th Spring International Conference of the French Finance Association, Strasbourg, France, May 14th-16th, 2012 Affi, Association française de finance / French Finance Association 2012 - 25 p.
We solve the optimal portfolio problem of a pension fund maximizing the expected present value of the remaining wealth at the death time of a representative subscriber. The fund can invest in a risky and a riskless asset. Both contributions and pensions are assumed to be constant, while risky asset returns are modeled by a general L´evy process. Assuming a CRRA utility function, we are able to obtain a quasi-closed-form formula for optimal weights. In order to solve fully a portfolio/pension
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fund problem with L´evy processes, it is necessary to switch back and forth between the stochastic differential and the standard exponential representations. We develop this procedure, and then illustrate it with two dynamics: the Variance Gamma process and a process introduced by A¨ıt-Sahalia, Cacho-Diaz, and Hurd (2009). We compute the optimal portfolio fund allocation in these two sub-settings and in the standard mean-variance framework. We show that when market stylized features (i.e. asymmetry, leptokurtosis and jumps) are suitably taken into account, the optimal portfolio share in the risky asset may be around half that obtained in the mean-variance framework.
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