Di. 25.11.2014, Mathematisches Kolloquium

Thema: Stability of Merton’s portfolio optimization problem for Lévy models, Referent: Dr. Maren Schmeck, Universität Köln, Zeit: 10:15 Uhr, Raum: ENC D-223.

Mathematisches Kolloquium 

 

      Stability of Merton’s portfolio optimization problem for Lévy models   

 

Dienstag, den 25.11.2014, 10:15 Uhr,  Raum  ENC D-223

Referent:   Dr. Maren Schmeck,   (Universität Köln) 

 

Abstrakt: Merton's classical portfolio optimization problem for an investor, who can trade in a risk-free bond and a stock, can be extended to the case where the driving noise of the logreturns is a pure jump process instead of a Brownian motion. Benth et al. [4,5] solved the problem and found the optimal control implicitly given by an integral equation in the hyperbolic absolute risk aversion (HARA) utility case. There are several ways to approximate a Levy process with infinite activity by neglecting the small jumps or approximating them with a Brownian motion, as discussed in Asmussen and Rosinski [1]. In this setting, we study stability of the corresponding optimal investment problems. The optimal controls are solutions of integral equations, for which we study convergence. We are able to characterize the rate of convergence in terms of the variance of the small jumps. Additionally, we prove convergence of the corresponding wealth processes and indirect utilities (value functions).