Optimal Dynamic Risk Taking
研究一个连续时间随机控制问题，代理人通过动态选择项目和终止时间来调整扩散过程的漂移和波动率，最优策略取决于项目的风险调整漂移和代理人的风险厌恶程度。
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.