Abstract
Optimal forms of reinsurance policies have been studied for a long time in the actuarial literature. Most existing results are from the insurer’s point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is understandable that a reinsurance arrangement that might be very attractive to one party (e.g., the insurer) can be quite unacceptable to the other party (e.g., the reinsurer). In this paper, we follow this point of view and study forms of Pareto-optimal reinsurance policies whereby one party’s risk, measured by its value-at-risk (VaR), cannot be reduced without increasing the VaR of the counter-party in the reinsurance transaction. We show that the Pareto-optimal policies can be determined by minimizing linear combinations of the VaR s of the two parties in the reinsurance transaction. Consequently, we succeed in deriving user-friendly, closed-form, optimal reinsurance policies and their parameter values.
Highlights
Reinsurance is a transaction whereby one insurance company agrees to indemnify another insurance company against all or part of the loss that the latter sustains under a policy or policies that it has issued
The feature of the current paper is that we extend the geometric approach of [12] to our optimization problem that considers the interests of the two parties
We have extended the geometric approach of [12] to obtain the optimal reinsurance policies accommodating both the cedent’s and the reinsurer’s interests
Summary
Reinsurance is a transaction whereby one insurance company (the reinsurer) agrees to indemnify another insurance company (the reinsured, cedent or primary company) against all or part of the loss that the latter sustains under a policy or policies that it has issued. Using the results of [20], Fang and Qu [21] derive optimal retentions of combined quota-share and excess-of-loss reinsurance that maximize the joint survival probability of the two parties. We determine Pareto-optimal reinsurance policies under which one party’s risk, measured by its VaR, cannot be reduced without increasing that of the other party in the reinsurance contract. The additional requirement of the convexity of f in C 1 essentially requires that f ( x ) approaches infinity linearly when x → ∞ and disallows the popular layered reinsurance policies This class includes the important quota-share and the excess-of-loss reinsurance policies.
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