Time-consistent investment and reinsurance strategies for mean-variance insurers with relative performance concerns under the Heston model

Zhu, Huainian; Cao, Ming; Zhang, Chengke

doi:10.1016/j.frl.2018.10.009

Cited by 25 publications

(7 citation statements)

References 20 publications

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“…While the conditions in Dynkin's Theorem can be ensured by the smoothness of the functions, which are the assumptions of Theorem 3.4. Many studies have also removed the above restriction on the function space, see Liang and Song [22], Wu et al [45], Zeng et al [51], Zhu et al [56] and so on.…”

Section: Remark 8 (I)mentioning

confidence: 99%

“…The reason is that our selection of the ambiguity preference functions (23)-(24) are based on the expressions of q * 1 (t, x, l, u), q * 2 (t, x, l, u) and H(t, x, l; q * ) in equations (55), (56) and (11), such that the optimal control u deduced from the HJB equation (57) takes a linear form of variables x and l. Only with this linear form of u, we can separate equations (21) and (22) into a system of ODEs by the order of variables x and l, in other words, we can obtain analytical solutions for our problem.…”

Section: Remark 8 (I)mentioning

confidence: 99%

“…Note that Φ 1 (t, x, l) and Φ 2 (t, x, l) take the form of (23) and (24), substituting them into (55) and (56) gives the equations (28) and (29).…”

Section: B Proof Of Proposition 35mentioning

confidence: 99%

See 2 more Smart Citations

Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

Wang¹,

Chen²,

Yang³

2021

Journal of Industrial &Amp; Management Optimization

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Section: Remark 8 (I)mentioning

confidence: 99%

Section: Remark 8 (I)mentioning

confidence: 99%

See 1 more Smart Citation

Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

Wang¹,

Chen²,

Yang³

2021

Journal of Industrial &Amp; Management Optimization

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“…In addition, we could see that the insurer's investment strategy π * 1 (t) in Theorem 3.1 which is similar to [28] contains two parts: the first part α−ρσ2 B(t) m1A(t) is standard component and the second part k α−ρσ2 B(t) m2A(t) is k times the reinsurer's investment strategy which is the hedge components coming from the relative concerns, and this means the insurer would imitate the reinsurer's investment strategy. Specifically, if the insurer does not take the wealth gap between itself and the reinsurer, and same as the reinsurer the amount invested in the risky asset is anti-related to the risk-averse coefficient (i.e.…”

mentioning

confidence: 74%

A Stackelberg reinsurance-investment game under Heston's stochastic volatility model

Zhou

Qiu

2023

JIMO

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<p style='text-indent:20px;'>This paper studies the optimal reinsurance-investment problem under Heston's stochastic volatility (SV) in the framework of Stackelberg stochastic differential game, in which an insurer and a reinsurer are the two players. The aim of the insurer as the follower in the game is to find the optimal reinsurance strategy and investment strategy such that its mean-variance cost functional is maximized, while the aim of the reinsurer as the leader is to maximize its mean-variance cost functional through finding its optimal premium pricing strategy and investment strategy. To overcome the time-inconsistency problem in the game, we derive the optimization problems of the two players as embedded games and obtain the corresponding extended Hamilton–Jacobi–Bellman (HJB) equations. Then we present the verification theorem and get the equilibrium reinsurance-investment strategies and the corresponding value functions of both the insurer and the reinsurer. Finally, we provide some numerical examples to draw the findings.</p>

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“…With respect to maximizing the expected utility of the relative performance, Bensoussan et al (2014) studied a non-zero-sum stochastic differential investment and reinsurance game between two insurers whose surplus processes were modulated by continuous-time Markov chains; Deng et al (2018) investigated the implications of strategic interaction between two constant absolute risk aversion (CARA) insurers on their reinsurance-investment policies with default risk under the framework of non-zero-sum stochastic differential game. There are still many studies on the non-zero-sum stochastic differential reinsurance-investment game problem, such as Meng et al (2015), Pun and Wong (2016), Guan and Liang (2016), Yan et al (2017), Zhu et al (2018), etc.…”

Section: Introductionmentioning

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.

show abstract

Time-consistent investment and reinsurance strategies for mean-variance insurers with relative performance concerns under the Heston model

Cited by 25 publications

References 20 publications

Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

Robust equilibrium control-measure policy for a DC pension plan with state-dependent risk aversion under mean-variance criterion

A Stackelberg reinsurance-investment game under Heston's stochastic volatility model

A hybrid stochastic differential reinsurance and investment game with bounded memory

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