Optimal Dynamic Risk Taking

Mathematics of Operations Research, Forthcoming

54 Pages Posted: 3 Jul 2016 Last revised: 21 Sep 2016

See all articles by Ajay Subramanian

Ajay Subramanian

Georgia State University

Baozhong Yang

Georgia State University - Robinson College of Business

Multiple version iconThere are 2 versions of this paper

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

Subramanian, Ajay and Yang, Baozhong, Optimal Dynamic Risk Taking (August 29, 2016). Mathematics of Operations Research, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2802785

Ajay Subramanian

Georgia State University ( email )

Depts. of Finance & Risk Management and Insurance
P.O. Box 4050
Atlanta, GA 30303
United States
404-413-7483 (Phone)

HOME PAGE: http://robinson.gsu.edu/profile/ajay-subramanian/

Baozhong Yang (Contact Author)

Georgia State University - Robinson College of Business ( email )

35 Broad Street
Atlanta, GA 30303-3083
United States
404-413-7350 (Phone)
404-413-7312 (Fax)

HOME PAGE: http://sites.google.com/view/baozhongyang/

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