Stochastic Optimal Control with Applications in Financial Engineering

In this chapter, it is shown how stochastic optimal control theory can be used in order to solve problems of optimal asset allocation under consideration of risk aversion. Two types of problems are presented: a problem type with a power utility function with a constant relative risk aversion coefficient and a problem type with an exponential utility function with a constant absolute risk aversion coefficient. The problems can be solved analytically in the unconstrained cases. In order to keep this chapter reasonably self-contained, short introductions to deterministic optimal control theory, stochastic processes, stochastic dynamic systems, and stochastic optimal control theory are given.