Seminar in Applied Mathematics and Statistics

SPEAKER: Frank Seifried, University of Kaiserslautern

TITLE: Small-Cost Asymptotics for Long-Term Growth Rates in Incomplete Markets

ABSTRACT: We provide a rigorous asymptotic analysis of the long-term growth rate under both proportional and Morton-Pliska transaction costs.

Using a dynamic programming approach, we determine the leading orders in the relevant expansions of the value functions ($\epsilon^{4/3}$ and $\epsilon$, respectively) as well as of the long-term growth rate ($\epsilon^{2/3}$ and $\epsilon^{1/2}$) with respect to the small cost parameter $\epsilon$. In addition, we determine the leading-order coefficients and construct trading strategies that maximize the corresponding long-term growth rates at the leading order. Finally, we analyze the performance of Morton-Pliska strategies in settings with small proportional transaction costs.

Tea and chocolate will be served in room 04.3.15 after the seminar.