Budget-Constrained Optimal Insurance with an Upper Limit on the Insurer's Exposure

Abstract

This thesis studies the problem of budget-constrained optimal insurance indemnification when the insurer imposes an upper limit on disbursement. In balancing the trade-off between the cost of paying the insurance premium and the benefit of receiving the indemnity, the risk-averse insured aims to maximize his/her subjective expected utility of terminal wealth, subject to a budget constraint, and to the constraint that the insurer has an upper bound on the indemnification disbursement. We assume that the insured's subjective probability measure is obtained from the insurer's probability measure by a transformation such as in Furman and Zitikis (2009), and that the insurer uses a distortion-type premium principle. We also assume that the insurer can observe the realized loss by incurring a state-verification cost. We show that in the presence of an upper limit on disbursement, the optimal indemnification function is a limited variable deductible. We then examine three numerical applications, and we illustrate the optimal indemnity and retention function in each case.