Optimal Dynamic Risk Taking
Mathematics of Operations Research, Forthcoming
54 Pages Posted: 3 Jul 2016 Last revised: 21 Sep 2016
There are 2 versions of this paper
Optimal Dynamic Risk Taking
Date Written: August 29, 2016
Abstract
We analyze a continuous-time stochastic control problem that arises in the study of several important issues in financial economics. An agent controls the drift and volatility of a diffusion output process by dynamically selecting one of an arbitrary (but finite) number of projects and the termination time. The optimal policy depends on the projects' risk-adjusted drifts that are determined by their drifts, volatilities and the curvature (or relative risk aversion) of the agent's payoff function. We prove that the optimal policy only selects projects in the spanning subset. Further, if the projects' risk-adjusted drifts are consistently ordered for all output values, then the optimal policy is characterized by at most K-1 switching triggers, where K is the number of projects in the spanning subset. We also characterize the optimal policy when the consistent ordering condition does not hold, and outline a general and tractable computational algorithm to derive the optimal policies.
Keywords: dynamic project choices, stochastic control, stochastic switching, dynamic risk management
JEL Classification: C61, D92, G11, G31
Suggested Citation: Suggested Citation