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Pricing dynamic insurance risks using the principle of equivalent utility. (English) Zbl 1039.91049

This article deals with an expected utility approach to price insurance risks in a dynamic financial market setting. The authors introduce the principle of expected utility and define the reservation prices of insurance claims. In the absence of market frictions this price coincides with the Black-Scholes price of the claim. In the case where liabilities are payable at a fixed time \(T\) and are independent of the underlying risky asset the authors consider a single insured life and calculate the reservation price for the term life insurance, then this model is extended to one that includes more than one independent life. Next, the authors consider pure endowment insurance and the model of insurance risks as diffusion and Poisson processes. In each case the reservation prices are calculated via optimal expected utility of terminal wealth that are shown to be solution of the Hamilton-Jacobi-Bellman equations. Insurance payable at the time of incurrence of the loss, and claims involving a random time, such as the time of death are considered.

MSC:

91B30 Risk theory, insurance (MSC2010)
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