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An extension of arrow's result on optimal reinsurance contract.

ABSTRACT

We consider the problem of finding reinsurance policies that maximize the expected utility, the stability and the survival probability of the cedent for a fixed reinsurance premium calculated according to the maximal possible claims principle. We show that the limited stop loss and the truncated stop loss are the optimal contracts.

INTRODUCTION

Let X, a nonnegative random variable on a given probability space ([OMEGA], S, P), represent the aggregate claim amount for an insurance portfolio in a certain time period. Suppose the insurer wants to buy a reinsurance policy R arranged on X basis; i.e., R(X) is the part of X covered by the reinsurer and X - R(X) ...

<0. Given a reinsurer's premium P><[m.sub.0] and c(m)>

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