Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation

Asmussen, Søren; Christensen, Bent Jesper; Thøgersen, Julie

doi:10.3390/risks7020049

Cited by 6 publications

(6 citation statements)

References 41 publications

(44 reference statements)

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“…However, the authors do not consider investment strategies in the game. Another application of Stackelberg games in insurance, for example, is the model of Asmussen, Christensen, and Thøgersen (2019). The authors used the framework of a Stackelberg game to model the competition of two insurance companies for their clients.…”

Section: Literature Overviewmentioning

confidence: 99%

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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%

“…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%

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 goal of the hybrid game is to seek the equilibrium by solving the optimization problems of three parties. Refer to Chen and Shen (2018), Chen and Shen (2019) and Asmussen et al (2019), the procedure of solving the Stackelberg game is to solve the leader's and followers' optimization problems sequentially, based on the idea of backward induction. To be more specific, the procedure can be divided into the following three steps:…”

Section: The Hybrid Game Problemmentioning

confidence: 99%

A hybrid stochastic differential reinsurance and investment game with bounded memory

Bai

Zhou

Xiao

et al. 2019

Preprint

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This paper investigates a hybrid stochastic differential reinsurance and investment game between one reinsurer and two insurers, including a stochastic Stackelberg differential subgame and a non-zero-sum stochastic differential subgame. The reinsurer, as the leader of the Stackelberg game, can price reinsurance premium and invest its wealth in a financial market that contains a risk-free asset and a risky asset. The two insurers, as the followers of the Stackelberg game, can purchase proportional reinsurance from the reinsurer and invest in the same financial market. The competitive relationship between two insurers is modeled by the non-zero-sum game, and their decision making will consider the relative performance measured by the difference in their terminal wealth. We consider wealth processes with delay to characterize the bounded memory feature. This paper aims to find the equilibrium strategy for the reinsurer and insurers by maximizing the expected utility of the reinsurer's terminal wealth with delay and maximizing the expected utility of the combination of insurers' terminal wealth and the relative performance with delay. By using the idea of backward induction and the dynamic programming approach, we derive the equilibrium strategy and value functions explicitly. Then, we provide the corresponding verification theorem. Finally, some numerical examples and sensitivity analysis are presented to demonstrate the effects of model parameters on the equilibrium strategy. We find the delay factor discourages or stimulates investment depending on the length of delay. Moreover, competitive factors between two insurers make their optimal reinsurance-investment strategy interact, and reduce reinsurance demand and reinsurance premium price.

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“…However, the authors do not consider investment strategies in the game. Another application of Stackelberg games in insurance, for example, is the model of Asmussen et al (2019). The authors used the framework of a Stackelberg game to model the competition of two insurance companies for their clients.…”

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.

show abstract

Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation

Cited by 6 publications

References 41 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

A hybrid stochastic differential reinsurance and investment game with bounded memory

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

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