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Excess-of-loss reinsurance for a company with debt liability and constraints on risk reduction. (English) Zbl 1405.91251
Summary: We consider a problem of risk control and dividend optimization for a financial corporation facing a constant liability payment. More specifically, we investigate the case of excess-of-loss reinsurance for an insurance company. In this scheme, the insurance company diverts a part of its premium stream to another company, the reinsurer, in exchange for an obligation to pick up that amount of each claim which exceeds a certain level \(a\). The objective of the insurer is to maximize the expected present value of total future dividend pay-outs. We consider cases when there is restriction on the rate of dividend pay-outs and when there is no restriction. In both cases we describe explicitly the optimal return function as well as the optimal policy.

MSC:
91B30 Risk theory, insurance (MSC2010)
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