Power Utility Maximization Research Articles

Risk aversion asymptotics for power utility maximization

We consider the economic problem of optimal consumption and investment with power utility. We study the optimal strategy as the relative risk aversion tends to infinity or to one. The convergence of the optimal consumption is obtained for general semimartingale models while the convergence of the optimal trading strategy is obtained for continuous models. The limits are related to exponential and logarithmic utility. To derive these results, we combine approaches from optimal control, convex analysis and backward stochastic differential equations (BSDEs).

Power utility maximization under partial information: Some convergence results

In this paper we consider the power utility maximization problem under partial information in a continuous semimartingale setting. Investors construct their strategies using the available information, which possibly may not even include the observation of the asset prices. Resorting to stochastic filtering, the problem is transformed into an equivalent one, which is formulated in terms of observable processes. The value process, related to the equivalent optimization problem, is then characterized as the unique bounded solution of a semimartingale backward stochastic differential equation (BSDE). This yields a unified characterization for the value process related to the power and exponential utility maximization problems, the latter arising as a particular case. The convergence of the corresponding optimal strategies is obtained by means of BSDEs. Finally, we study some particular cases where the value process admits an explicit expression.

Recent Developments in Financial and Insurance Mathematics and the Interplay with the Industry

Recent Developments in Financial and Insurance Mathematics and the Interplay with the Industry

Power Utility Maximization in an Exponential Lévy Model Without a Risk-free Asset

We consider the problem of maximizing the expected power utility from terminal wealth in a market where logarithmic securities prices follow a Levy process. By Girsanov’s theorem, we give explicit solutions for power utility of undiscounted terminal wealth in terms of the Levy-Khintchine triplet.