Abstract
In this paper, we study an optimal dynamic control problem of an insurance company with excess-of-loss reinsurance and investment. Three practical borrowing constraints are studied individually: (B1) borrowed dollar amount is no more than a borrowing limit K; (B2) borrowed proportion to surplus level is no more than k; and (B3) borrowing rate is higher than risk free rate of return (saving rate). The optimal criterion is to minimize probability of ruin. Classical stochastic control theory is applied to solve the problem. Under each of the constraints, minimal ruin probability functions are obtained in closed form by solving Hamilton–Jacobi–Bellman (HJB) equations. Their associated optimal reinsurance–investment control policies are found as well.