Optimal Dynamic Risk Taking

We analyze a continuous-time model of dynamic project choices by an agent that is relevant to various important issues in financial economics. An agent controls the drift and volatility of a lognormal output process by dynamically selecting one of N projects. Under broad conditions, the optimal risk-taking policy is characterized by at most K − 1 unique switching triggers, where K is the number of spanning projects. As an application, we analyze a continuous-time structural model of capital structure with asset substitution, and obtain novel implications for the effects of systematic risk on capital structure. In contrast with previous studies, there are substantial agency costs of asset substitution, which generate leverage ratios and credit spreads consistent with empirical values.