Footnote:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments January 27, 2006 erstellt
Description:
In this study, we generalize the model of Pham (Pham [2003]) to jump diffusion models. Based on (Pham [2003]), we first consider an investment model where we construct a portfolio of a riskless asset and a risky one which is assumed to follow a jump diffusion process so as to overperform a given benchmark. We perturb up to the second order the dynamics of the economic indicator process with respect to the jump step of the risky asset so as to obtain a large deviation probability control problem with its duality which is an risk sensitive control problem on the optimal logarithmic moment generating function that can be explicitly derived. We then prove without relying on the ergodicity of the economic indicator process that the logarithmic moment generating function (or exponential utility function) is definitely optimal. Last we use the large deviation theorem to state the equivalence between optimal probabilistic risk and optimal growth rate of the portfolio management