Optimal Dynamic Risk Taking

• 成果类型: Article
• 署名作者: Subramanian, Ajay; Yang, Baozhong
• 署名单位: University System of Georgia; Georgia State University; University System of Georgia; Georgia State University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2016.0819
• 发表日期: 2017
• 页码: 599-625
• 关键词: explicit solution; AGENCY COSTS; consumption; INVESTMENT

摘要

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.