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Derivatives trading for insurers. (English) Zbl 1419.91387
Summary: We investigate optimal strategies for a constant absolute risk aversion (CARA) insurer to manage its business risk through not only equity investment and proportional reinsurance but also trading derivatives of the equity. We obtain the optimal strategies in closed-form and quantify the value of derivatives trading by means of certainty-equivalence. Some numerical examples and sensitivity analysis are presented to illustrate our theoretical results. Our numerical results show that, unlike standard CRRA investors, the gain from trading derivatives to a CARA insurer is small and the insurer needs to expose itself to a relatively large position to fully enjoy the gain.

MSC:
91B30 Risk theory, insurance (MSC2010)
91G20 Derivative securities (option pricing, hedging, etc.)
91G10 Portfolio theory
93E20 Optimal stochastic control
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