Abstract
In this paper, discrete time risk models under an excess of loss reinsurance are studied. Adjustment coefficients of the cedent and the reinsurer are established as functions of quota share level and retention level. By the martingale method, ruin probabilities of the cedent and the reinsurer still have exponential form. Finally, numerical examples are provided to illustrate the results obtained in this paper.
Highlights
We consider the insurer’s surplus in period n, n = 1, 2, denoted as Un is defined by: n n Un = u + ∑ Yi − ∑ Xi, n = 1, 2, =i 1 =i 1 (1.1)
This paper investigates the effect of an excess of loss reinsurance on the ultimate ruin probabilities of the cedent and the reinsurer in the discrete-time model
The author shows that for given value there exists a quota share level and a retention level so that both the ruin probabilities of the cedent and the reinsurer are less than value
Summary
Yn denotes the premium income in period n (i.e., from time n −1 to time n), Y = {Yn}n>0 is a sequence of independent and identically distributed (i.i.d.) non-negative random variables;. With surplus process (1.2), the upper bound of the insurer’s ruin probability was established by the martingale and inductive methods in [2]. This paper investigates the effect of an excess of loss reinsurance on the ultimate ruin probabilities of the cedent and the reinsurer in the discrete-time model. The author shows that for given value there exists a quota share level and a retention level so that both the ruin probabilities of the cedent and the reinsurer are less than value.
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