Large Deviations for a Model of Excess of Loss Re-Insurance

M. Kelbert, I. Manolopoulou, I. Sazonov, Yu.M. Suhov

2007, v.13, №1, 137-158

ABSTRACT

A risk model of a joint business (insurer/re-insurer) is studied in the Large Deviations (LD) regime. In the model considered, the premium paid by the insurer to the re-insurer changes if the insurer's capital falls below a certain level P. An optimal premium arrangement for the both business participants is investigated. By a proper choice of parameters involved, it is possible to increase the rate function, i.e. reduce the ruin probability of insurer, in such a way that the expected profit of re-insurer remains controllable, i.e., does not exceed a given percentage of the total loss.

Keywords: fluid approximation,large deviations,optimal trajectories,ruin time,risk models

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