Risk management and optimal investment with inalienable human capital

Abstract

We consider a moral hazard problem in a continuous-time model, where project risk is controllable. The unobservability of agent behavior creates information asymmetry, consequently influencing investor decisions. We utilize martingale methods to determine the optimal policy. The investor’s scaled value function is represented using an ordinary differential equation. We find that the manager’s search for new investors impacts the boundary conditions due to inalienable human capital. Using comparative static analysis, we find that the endogenous no-saving condition helps eliminate information asymmetry caused by unobserved effort. Moreover, as the agent’s continuation value increases, the company’s risk management target approaches the optimal risk management target under full information. A higher manager’s continuation value leads to inferior investment opportunities.