Optimal Reporting Stategy of an Insured -Dynamic Programming Approach-

We consider an insured who wishes to determine his optimal reporting strategy over a given planning horizon, when he has option of reporting of not reporting his at-fault accidents. Assuming that the premium in future period is continually adjusted by the insured's loss experience, the insured would not report every loss incurred. Rather, considering the benefits and costs of each decision, the insured may want to seek a way of optimizing his interests over the planning horizon. The situation is modeled as a dynamic programming problem. We consider an insured's discounted expected cost minimization problem, where the premium increase in future period is affected by the size of the current claim. More specifically, we examine two cases ; (1) the premium increase in the next is a linear function (a constant fraction) of the current claim size; (2) the premium increase in the next period is a concave function of the current claim size. In each case, we derive the insured's optimal reporting strategy.