On randomized reinsurance contracts

Abstract

In this paper we discuss the potential of randomizing reinsurance treaties for efficient risk management. While it may be considered counter-intuitive to introduce additional external randomness in the determination of the retention function for a given occurred loss, we indicate why and to what extent randomizing a treaty can be interesting for the insurer. We illustrate the approach with a detailed analysis of the effects of randomizing a stop-loss treaty on the expected profit after reinsurance in the framework of a one-year reinsurance model under regulatory solvency constraints and cost of capital considerations.

Optimal allocation of policy limits in layer reinsurance treaties

“…As a parallel study, it would be of interest to study the optimal allocations of deductibles when the policy limits are predetermined. Furthermore, it is meaningful in practice to assume that the summation of the policy limit and deductible for each loss is fixed (e.g., optimal ceded loss functions derived under VaR or TVaR); see Chi and Tan [15] and Section 6 of Albrecher and Cani [1]. Besides, the study on stochastic properties of extreme claim amounts arising from a set of heterogeneous layer reinsurance contracts is also worth investigating.…”

“…Albrecher and Cani [1] discussed randomized reinsurance treaties for insurers to conduct efficient risk management. They argued that a randomized reinsurance treaty might be interesting for the insurer to transfer the risk to the reinsurer.…”

“…Albrecher and Cani [1] advocated that randomized reinsurance treaties might be offered from the reinsurer for the insurer to conduct efficient risk management. Though it might be counter-intuitive to impose external randomness on the determination of the retained loss, the authors showed why and to what extent a randomized reinsurance treaty can be interesting for the insurer (see the introduction and Section 6 of Albrecher and Cani [1] for more relevant detailed discussions). As the second aim of the present work, we shall consider the problem of optimal allocations of policy limits for randomized layer reinsurance treaties designed for a set of heterogeneous and dependent risks.…”

“…The past several decades have witnessed extensive development on optimal reinsurance design from different perspectives; see for example Borch [5,6], Arrow [3], Raviv [35], Young [40], Kaluszka [27], Cai et al [9], Cheung [12], Cui et al [18], Cheung et al [13,14], and the references therein. Under the assumption that both the insurer and reinsurer are obligated to pay more when the underlying claim is getting larger, 1 Chi and Tan [16] proved that the layer reinsurance contract is quite robust in the sense that it is always optimal over both value-at-risk (VaR) and tail value-at-risk (TVaR) measures under general premium principles including Wang's and Dutch premium principles as special cases. Recently, under the setting that all insurers use VaR or range value-at-risk (RVaR) measures, Bäuerle and Glauner [4] considered the optimal reinsurance problem from a macroeconomic point of view when there are 𝑛 insurance companies each bearing a certain risk and one representative reinsurer, and showed the optimality of the layer reinsurance treaty under certain conditions.…”