Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation

The Bellman equation for power utility maximization with semimartingales

We study utility maximization for power utility random elds with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the corresponding Bellman equation. The optimal strategies are described pointwise in terms of the opportunity process, which is characterized as the minimal solution of...

On Robust Utility Maximization

Abstract. This paper studies the problem of optimal investment in incomplete markets, robust with respect to stopping times. We work on a Brownian motion framework and the stopping times are adapted to the Brownian filtration. Robustness can only be achieved for logartihmic utility, otherwise a cashflow should be added to the investor’s wealth. The cashflow can be decomposed into the sum of an ...

Performance Limits of Solutions to Network Utility Maximization Problems

We study performance limits of solutions to utility maximization problems (e.g., max-min problems) in wireless networks as a function of the power budget p̄ available to transmitters. Special focus is devoted to the utility and the transmit energy efficiency (i.e., utility over transmit power) of the solution. Briefly, we show tight bounds for the general class of network utility optimization pr...

Utility Maximization with Discretionary Stopping

Utility maximization problems of mixed optimal stopping /control type are considered, which can be solved by reduction to a family of related pure optimal stopping problems. Sufficient conditions for the existence of optimal strategies are provided in the context of continuous-time, Itô process models for complete markets. The mathematical tools used are those of optimal stopping theory, contin...

Anomalies: Utility Maximization and Experienced Utility