OPTIMAL REINSURANCE AND INVESTMENT PROBLEMS TO MINIMIZE THE PROBABILITY OF DRAWDOWN

. This paper investigates the problem of optimal investment and proportional reinsurance in a dynamic asset model for an insurance company. The objective is to minimize the probability of drawdown, which is defined as the probability of an asset reaching a fixed proportion of its historical maximum. We assume that the debt of the company's wealth process is a deterministic function of its value. We discuss the problem separately according to the two cases that the historical maximum value is less than the safety value and greater than the safety value. By utilizing stochastic control theory, we derive the optimal investment and reinsurance strategy along with the corresponding minimum drawdown probability. We show that when the historical maximum is relatively low (below the safety level), raising the historical maximum to the safety level is the optimal strategy. Finally, we provide examples to illustrate the impact of model parameters on the optimal results.