City Research Online

Abstract

The problem of optimal excess of loss reinsurance with a limiting and a retention level is considered. It is demonstrated that this problem can be solved, combining specific risk and performance measures, under some relatively general assumptions for the risk model, under which the premium income is modelled by any non-negative, non-decreasing function, claim arrivals follow a Poisson process and claim amounts are modelled by any continuous joint distribution. As a performance measure, we define the expected profits at time x of the direct insurer and the reinsurer, given their joint survival up to x, and derive explicit expressions for their numerical evaluation. The probability of joint survival of the direct insurer and the reinsurer up to the finite time horizon x is employed as a risk measure. An efficient frontier type approach to setting the limiting and the retention levels, based on the probability of joint survival considered as a risk measure and on the expected profit given joint survival, considered as a performance measure is introduced. Several optimality problems are defined and their solutions are illustrated numerically on several examples of appropriate claim amount distributions, both for the case of dependent and independent claim severities

Publication Type:	Article
Publisher Keywords:	optimal excess of loss reinsurance, probability of ruin, Appell polynomials, joint survival of cedent and reinsurer, expected profit, efficient frontier, copula functions
Subjects:	H Social Sciences > HG Finance
Departments:	Bayes Business School > Actuarial Science & Insurance
SWORD Depositor:	Symplectic Administrator

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