Optimal retention for a stop-loss reinsurance with incomplete information

Abstract

This paper considers the determination of optimal retention in a stop-loss reinsurance. Assume that we only have incomplete information on a risk X for an insurer, we calculate an upper bound for the value at risk (VaR) of the total loss of an insurer after stop-loss reinsurance arrangement. The adopted method is a distribution-free approximation which allows to construct the extremal random variables with respect to the stochastic dominance order and the stop-loss order. We develop an optimization criterion for deriving the optimal retention such that the obtained upper bound of the VaR attains the minimum. We formally establish the sufficient and necessary conditions for the existence of the nontrivial optimal stop-loss reinsurance. For illustration purpose, some numerical examples are included and compared with the results yielded in Theorem 2.1 of Cai and Tan (2007).

Hierarchical Capacity Provisioning for Fog Computing

“…Moreover, in practice, we usually know the average of λ i n 's rather than their distribution function. There are a few studies such as [37], [38], that consider the case when incomplete information of X is available. However, those solutions are not applicable here because they either have to know at least the average and variance of X or they are interested in finding the optimal retention d or estimating the minimal stop-loss rather than the optimum value of X.…”

The Optimal Reinsurance Strategy under Conditional Tail Expectation (CTE) and Wang’s Premium Principle

“…Cai and Tan [3] hypothesized that the form of insurance is a stop-loss reinsurance, and the minimality of gross loss of the insurer measured by VaR and CTE as the objective function, and the optimal deductible is calculated under the principle of expected premium. Hu et al [4] researched the calculation of the optimal retention of stoploss reinsurance under the condition of incomplete information on the aggregate loss function of the insurance company, while minimizing the VaR risk metric, and contrasted with the results of Cai and Tan [3]. Kong et al [5] studied the optimal reinsurance issues in which both insurers and reinsurers face risks and uncertainties under general premium principles.…”

Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle

“…To our knowledge, the most widely used premium principle in the existing works turns out to be the expected premium principle, see Cheung, et al [19], Lu, et al [16], Cai, et al [5], Chi and Tan [17], etc.. Assa [20], Zheng and Cui [21], Cui, et al [22] extended their premium principle to the distortion premium principle. Zhu, et al [23] further extended their premium principle to very general one that satisfies three mild conditions: distribution invariance, risk loading and preserving the convex order, see also Chi and Tan [24]. (c) Generalizing the risk measures.…”

“…(c) Generalizing the risk measures. Using the VaR, CTE, AVaR, respectively, Hu, et al [25], Cai and Tan [26], Cai, et al [12], Cheung [14] and Chi and Tan [24] found the optimal reinsurance contract. In Asimit, et al [27], a quantile-based risk measure was adopted in accordance with the insurer's appetite.…”