Optimal reinsurance for both an insurer and a reinsurer under general premium principles

Guo, Cheng; Qu, Zhongfeng

doi:10.3934/math.2020208

Cited by 8 publications

(3 citation statements)

References 27 publications

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“…The optimal reinsurance strategy that the insurer believes may not be optimal for the reinsurer. So it is necessary to study the optimal reinsurance strategy based on the perspective of both the insurer and the reinsurer, see Liu et al [6] and Fang et al [7]. In this paper, we consider the interests of both parties and study the optimal reinsurance strategy under certain constraints.…”

Section: Introductionmentioning

confidence: 99%

Pareto-Optimal Reinsurance Based on TVaR Premium Principle and Vajda Condition

Chang,

Fang

2023

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Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing number of total losses in the insurance market, the insurer might expect the reinsurer to bear an increasing proportion of the total loss, that is the insurer might expect the reinsurer to pay an increasing proportion of the total claim amount when he faces an increasing number of total claims in the insurance market. Motivated by this, we study the optimal reinsurance problem under the Vajda condition. To prevent moral hazard and reflect the spirit of reinsurance, we assume that the retained loss function is increasing and the ceded loss function satisfies the Vajda condition. We derive the explicit expression of the optimal reinsurance under the TVaR risk measure and TVaR premium principle from the perspective of both an insurer and a reinsurer. Our results show that the explicit expression of the optimal reinsurance is in the form of two or three interconnected line segments. Under an additional mild constraint, we get the optimal parameters and find the optimal reinsurance strategy is full reinsurance, no reinsurance, stop loss reinsurance, or quota-share reinsurance. Finally, we gave an example to analyze the impact of the weighting factor on optimal reinsurance.

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Section: Introductionmentioning

confidence: 99%

Pareto-Optimal Reinsurance Based on TVaR Premium Principle and Vajda Condition

Chang,

Fang

2023

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“…e first type is on the design of optimal proportional or excess-of-loss reinsurance under various constraints. Recent references include Cai and Tan [34], Tan et al [35], Yusong and Jin [36], Chi and Tan [37], Cai et al [38,39], Zhang et al [40], Liang and Young [41], Han et al [42], Fang et al [43], and the references therein. e second type is on the design of optimal combinational proportional and excess-of-loss reinsurance under different optimization criteria.…”

Section: Introductionmentioning

confidence: 99%

Optimal Insurance Indemnity and Reinsurance Strategy for Health Insurance

Zhang

Yao

2021

Mathematical Problems in Engineering

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“Health insurance + health management” package has recently become one of the most important nonlife insurance products, and its pricing technique has drawn attention from both academia and industry. This paper investigates the optimal indemnity design and per-loss reinsurance strategy for the health insurance package, where the reinsurance contract is assumed to combine the quota-share type and the excess-of-loss type. By applying the Lagrange multiplier method and optimal control technique, we develop the solutions to the corresponding optimization problems and obtain the optimal deductible. Then, we proceed to solve the optimal quota-share proportion and the optimal stop-loss retention based on the optimal insurance indemnity. In addition to theoretical results, numerical examples are also given to illustrate the effects of various key parameters on the optimal indemnity design and combinational reinsurance strategy.

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“…To maximize the joint survival probability of the insurer and the reinsurer, Fang and Qu [14] studied the optimal policy of combination of quota-share reinsurance and stop-loss reinsurance. Fang et al [15] studied the optimal reinsurance models from the perspective of both the insurer and the reinsurer by minimizing their total costs under the criteria of the loss function which is defined by the joint Value-at-Risk. Cai et al [16] studied the optimal reinsurance strategy, which was based on the minimum convex combination of the VaR of the insurer and the reinsurer under two types of constraints.…”

Section: Introductionmentioning

confidence: 99%

Pareto-Optimal Reinsurance Revisited: A Two-Stage Optimisation Procedure Approach

Wang¹,

Yu³

2020

Mathematical Problems in Engineering

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In this paper, based on the Tail-Value-at-Risk (TVaR) measure, we revisit the Pareto-optimal reinsurance policies for the insurer and the reinsurer via a two-stage optimisation procedure. To reduce ex-post moral hazard, we assume that reinsurance contracts satisfy the principle of indemnity and the incentive compatible constraint which have been advocated by Huberman et al. (1983). We show that the Pareto-optimal reinsurance policy exists if the reinsurance premiums can be expressed as an integral form. The proposed class of premium principles encompasses the net premium principle, expected value premium principle, TVaR premium principle, generalized percentile premium principle, and so on. We further use the TVaR premium principle and the expected value premium principle as examples to illustrate the two-stage optimisation procedure by deriving explicitly the Pareto-optimal reinsurance policies. We extend the results by Cai et al. (2017) when the expected value premium principle is replaced by the TVaR premium principle.

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Optimal reinsurance for both an insurer and a reinsurer under general premium principles

Cited by 8 publications

References 27 publications

Pareto-Optimal Reinsurance Based on TVaR Premium Principle and Vajda Condition

Pareto-Optimal Reinsurance Based on TVaR Premium Principle and Vajda Condition

Optimal Insurance Indemnity and Reinsurance Strategy for Health Insurance

Pareto-Optimal Reinsurance Revisited: A Two-Stage Optimisation Procedure Approach

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