Optimal stop-loss reinsurance: a dependence analysis

Abstract

The stop-loss reinsurance is one of the most important reinsurance contracts in the insurance market. From the insurer point of view, it presents an interesting property: it is optimal if the criterion of minimizing the variance of the cost of the insurer is used. The aim of the paper is to contribute to the analysis of the stop-loss contract in one period from the point of view of the insurer and the reinsurer. Firstly, the influence of the parameters of the reinsurance contract on the correlation coefficient between the cost of the insurer and the cost of the reinsurer is studied. Secondly, the optimal stop-loss contract is obtained if the criterion used is the maximization of the joint survival probability of the insurer and the reinsurer in one period.

Stop-Loss Reinsurance Threshold for Dependent Risks

“…The model was a quantile-measure extension of [21] which applied variance measures for threshold determination by using two approaches: a minimum variance derived by maximizing the covariance between insurer and reinsurer in Proposition 3.1. such that:…”

“…The comparison applied a Gamma distribution with a mean Results were compared with this paper's model using numerical approximation, and noted [21] fails to perform for small samples (less than 500), but our model provides several optimal thresholds for smaller groups, as shown in Table 1. When 0.5 η = retention threshold does not depend on the survival function (constant for combinations of parameters) as summarized in Table 2.…”

“…First this work adds to dependency analysis for multiple risks by establishing a connect between risk measures in [17] and cost analysis for non independent risks in [20]. The paper contributes to quantitative analysis of decentralized insurance in [21] by relaxing assumption of independence which understates claims leading to liquidity problems. Finally this paper derives a simple threshold easily understood by practitioners, which is an important area of inclusive finance that encourage hybrid products between banking and insurance services; a merger which was suggested in [22].…”

Optimal investment strategy and liability ratio for insurer with Lévy risk process

“…In addition to minimizing the ruin probability of insurer, optimal reinsurance policy is achieved by maximizing the survival function of the insurer in the literature. (See Castañer and Claramunt [3] ) Hipp and Plum [8] investigate the optimal investment strategy by minimizing the ruin probability for compound Poisson process. Jump structure has also naturally been introduced to insurer's problem as the compound Poisson process approximates to the jump-diffusion process at the limit [15].…”

Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account

“…Cai et al [22] study the optimal forms of reinsurance policies that minimize the convex combination of the VaRs of the cedent and the reinsurer under two types of constraints that describe the interests of the two parties. For the determination of the optimal excess of loss contract considering the dependency between the losses of the insurer and the reinsurer, we refer to [23] and the references therein.…”