Abstract
This paper studies a Pareto-optimal reinsurance contract in the presence of negative statistical dependence between the insurance claim and the random recovery rate. In the context of symmetric information model and asymmetric information model, we investigate properties of the Pareto-optimal indemnity schedules. For risk neutral reinsurer with proportional cost and associated expense, we present possible forms of the Pareto-optimal indemnity schedule as well.
Highlights
In reinsurance market, due to the conflict between the interest of the insurer and that of the reinsurer, it is impossible to build an optimal reinsurance contract simultaneously maximizing the interest of both parties
For the recovery rate independent of and stochastically decreasing in the insurance claim, we investigate properties of the Pareto-optimal indemnity schedules for asymmetric information model in Sections 4 and 5, respectively
We present two technical lemmas on monotonicity and supermodularity concerned with the recovery rate stochastically decreasing in the insured risk, which will be employed to build the important results in the sequel
Summary
Due to the conflict between the interest of the insurer and that of the reinsurer, it is impossible to build an optimal reinsurance contract simultaneously maximizing the interest of both parties. Bernard and Ludkovski (2012) considered loss-dependent probability of default and partial recovery in the event of contract non-performance, and studied the Pareto-optimal reinsurance contracts with counter-party risk for risk neutral reinsurer and risk averse insurer. When the reinsurer and insurer share a common view about the default risk, one has the so-called symmetric information model, under which we consider the Pareto-optimal problem: max E[u(ω − X1 + X2 r ( X1 ) − p)]. For the recovery rate independent of and stochastically decreasing in the insurance claim, we investigate properties of the Pareto-optimal indemnity schedules for asymmetric information model in Sections 4 and 5, respectively. All proofs of main results are deferred to the Appendixes A–L
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