Robust two-player differential investment game of defined contribution pension plans under multiple risks

Zhang, Yumo; Lind, Peter Pommergård; Xiang, Hanqing

doi:10.1080/03461238.2024.2401399

Scandinavian Actuarial Journal

2024

DOI: 10.1080/03461238.2024.2401399

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Robust two-player differential investment game of defined contribution pension plans under multiple risks

Yumo Zhang,

Peter Pommergård Lind,

Hanqing Xiang

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2024

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Two stackelberg games in life insurance: Mean-variance criterion

Liang,

Young

2024

ASTIN Bull.

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We study two continuous-time Stackelberg games between a life insurance buyer and seller over a random time horizon. The buyer invests in a risky asset and purchases life insurance, and she maximizes a mean-variance criterion applied to her wealth at death. The seller chooses the insurance premium rate to maximize its expected wealth at the buyer’s random time of death. We consider two life insurance games: one with term life insurance and the other with whole life insurance—the latter with pre-commitment of the constant investment strategy. In the term life insurance game, the buyer chooses her life insurance death benefit and investment strategy continuously from a time-consistent perspective. We find the buyer’s equilibrium control strategy explicitly, along with her value function, for the term life insurance game by solving the extended Hamilton–Jacobi–Bellman equations. By contrast, in the whole life insurance game, the buyer pre-commits to a constant life insurance death benefit and a constant amount to invest in the risky asset. To solve the whole life insurance problem, we first obtain the buyer’s objective function and then we maximize that objective function over constant controls. Under both models, the seller maximizes its expected wealth at the buyer’s time of death, and we use the resulting optimal life insurance premia to find the Stackelberg equilibria of the two life insurance games. We also analyze the effects of the parameters on the Stackelberg equilibria, and we present some numerical examples to illustrate our results.

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Two stackelberg games in life insurance: Mean-variance criterion

Liang,

Young

2024

ASTIN Bull.

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Robust two-player differential investment game of defined contribution pension plans under multiple risks

Cited by 1 publication

References 47 publications

Two stackelberg games in life insurance: Mean-variance criterion

Two stackelberg games in life insurance: Mean-variance criterion

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