Optimal Dynamic Risk Taking

Ajay Subramanian () and Baozhong Yang ()
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Ajay Subramanian: Department of Risk Management and Insurance and Department of Finance, Georgia State University, Atlanta, Georgia 30303
Baozhong Yang: Deparatment of Finance, Georgia State University, Atlanta, Georgia 30303

Mathematics of Operations Research, 2017, vol. 42, issue 3, 599-625

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 . Furthermore, 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 we outline a general and tractable computational algorithm to derive the optimal policies.

Keywords: dynamic project choices; stochastic control; stochastic switching; dynamic risk management (search for similar items in EconPapers)
Date: 2017
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