A continuous-time theory of reinsurance chains

Lv, Chen; Shen, Yang; Su, Jianxi

doi:10.1016/j.insmatheco.2020.09.005

Cited by 5 publications

(9 citation statements)

References 44 publications

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“…The authors assume that the reinsurance contract can be adjusted dynamically by the reinsurer and the insurer. Further papers on Stackelberg games in the context of insurance-reinsurance interaction are Chen and Shen (2019), Bai et al (2019), Chen, Shen, andSu (2020), Yuan, Liang, and Han (2021), Yang, Zhang, andZhu (2021), andZhong (2021). In all of them, the reinsurance is offered on the whole portfolio of aggregated insurance obligations and the reinsurance can be dynamically adjusted over the investment horizon.…”

Section: Literature Overviewmentioning

confidence: 99%

“…In all of them, the reinsurance is offered on the whole portfolio of aggregated insurance obligations and the reinsurance can be dynamically adjusted over the investment horizon. Chen and Shen (2018), Chen and Shen (2019) and Chen et al (2020) assume that the reinsurer and the insurer invest only their surplus process risk-free, whereas in Bai et al (2019) the parties invest in a more complex financial market that includes one risky asset. Gavagan, Hu, Lee, Liu, and Weixel (2021) studies the Stackelberg game between a reinsurer and an insurer with model uncertainty, assuming that the reinsurance is not dynamically adjusted.…”

Section: Literature Overviewmentioning

confidence: 99%

“…For more details on the theory of Stackelberg games, see Osborne and Rubinstein (1994), Fudenberg and Tirole (1991), or Bressan (2011). For applications of Stackelberg games in the context of reinsurance see Chen and Shen (2018), Chen and Shen (2019), Chen et al (2020), Asmussen et al (2019), or Bai et al (2019).…”

Section: Problem Settingmentioning

confidence: 99%

See 2 more Smart Citations

Risk sharing in equity-linked insurance products: Stackelberg equilibrium between an insurer and a reinsurer

Havrylenko¹,

Hinken²,

Zagst³

2022

Preprint

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Equity-linked insurance products often have capital guarantees. Common investment strategies ensuring these guarantees are challenged nowadays by low interest rates. Thus, we study an alternative strategy when an insurance company shares financial risk with a reinsurance company. We model this situation as a Stackelberg game. The reinsurer is the leader in the game and maximizes its expected utility by selecting its optimal investment strategy and a safety loading in the reinsurance contract it offers to the insurer. The reinsurer can assess how the insurer will rationally react on each action of the reinsurer. The insurance company is the follower and maximizes its expected utility by choosing its investment strategy and the amount of reinsurance the company purchases at the price offered by the reinsurer. In this game, we derive the Stackelberg equilibrium for general utility functions. For power utility functions, we calculate the equilibrium explicitly and find that the reinsurer selects the largest reinsurance premium such that the insurer may still buy the maximal amount of reinsurance. Since in the equilibrium the insurer is indifferent in the amount of reinsurance, in practice, the reinsurer should consider charging a smaller reinsurance premium than the equilibrium one. Therefore, we propose several criteria for choosing such a discount rate and investigate its wealth-equivalent impact on the utilities of both parties.

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Section: Literature Overviewmentioning

confidence: 99%

Section: Literature Overviewmentioning

confidence: 99%

See 1 more Smart Citation

Risk sharing in equity-linked insurance products: Stackelberg equilibrium between an insurer and a reinsurer

Havrylenko¹,

Hinken²,

Zagst³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The authors assume that the reinsurance contract can be adjusted dynamically by the reinsurer and the insurer. Further papers on Stackelberg games in the context of insurance-reinsurance interaction are Chen and Shen (2019), Bai et al (2022), Chen et al (2020), Yuan et al (2022), Yang et al (2022), andBai et al (2021). In all of them, the reinsurance is offered on the whole portfolio of aggregated insurance obligations and the reinsurance can be dynamically adjusted over the investment horizon.…”

Section: Introductionmentioning

confidence: 99%

Risk sharing in equity-linked insurance products: Stackelberg equilibrium between an insurer and a reinsurer

Havrylenko,

Hinken,

Zagst

2023

ASTIN Bull.

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We study the optimal investment-reinsurance problem in the context of equity-linked insurance products. Such products often have a capital guarantee, which can motivate insurers to purchase reinsurance. Since a reinsurance contract implies an interaction between the insurer and the reinsurer, we model the optimization problem as a Stackelberg game. The reinsurer is the leader in the game and maximizes its expected utility by selecting its optimal investment strategy and a safety loading in the reinsurance contract it offers to the insurer. The reinsurer can assess how the insurer will rationally react on each action of the reinsurer. The insurance company is the follower and maximizes its expected utility by choosing its investment strategy and the amount of reinsurance the company purchases at the price offered by the reinsurer. In this game, we derive the Stackelberg equilibrium for general utility functions. For power utility functions, we calculate the equilibrium explicitly and find that the reinsurer selects the largest reinsurance premium such that the insurer may still buy the maximal amount of reinsurance. Since in the equilibrium the insurer is indifferent in the amount of reinsurance, in practice, the reinsurer should consider charging a smaller reinsurance premium than the equilibrium one. Therefore, we propose several criteria for choosing such a discount rate and investigate its wealth-equivalent impact on the expected utility of each party.

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“…For the consideration of reinsurance aspects in this context we refer to Zeng (2010), Jin et al (2013) who propose a zero-sum two-player dynamic reinsurance game, and Chen & Shen (2018), Chen et al (2020) where transactions between reinsurance buyers and sellers are formulated through Stackelberg games.…”

Section: Introductionmentioning

confidence: 99%

On a Markovian Game Model for Competitive Insurance Pricing

Mouminoux

Dutang

Loisel

et al. 2021

Methodol Comput Appl Probab

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In this paper, we extend the non-cooperative one-period game of Dutang et al. (2013) to model a non-life insurance market over several periods by considering the repeated (one-period) game. Using Markov chain methodology, we derive general properties of insurer portfolio sizes given a price vector. In the case of a regulated market (identical premium), we are able to obtain convergence measures of long run market shares. We also investigate the consequences of the deviation of one player from this regulated market. Finally, we provide some insights of long-term patterns of the repeated game as well as numerical illustrations of leadership and ruin probabilities.

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A continuous-time theory of reinsurance chains

Cited by 5 publications

References 44 publications

Risk sharing in equity-linked insurance products: Stackelberg equilibrium between an insurer and a reinsurer

Risk sharing in equity-linked insurance products: Stackelberg equilibrium between an insurer and a reinsurer

Risk sharing in equity-linked insurance products: Stackelberg equilibrium between an insurer and a reinsurer

On a Markovian Game Model for Competitive Insurance Pricing

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