Open-loop equilibrium strategy for mean–variance portfolio problem under stochastic volatility

Yan, Tingjin; Wong, Hoi Ying

doi:10.1016/j.automatica.2019.05.044

Cited by 35 publications

(16 citation statements)

References 24 publications

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“…is section is devoted to obtain the closed-loop equilibrium reinsurance-investment strategy and the corresponding value function for problem (16) in the postdefault case (z � 1) and the predefault case (z � 0), respectively.…”

Section: The Main Resultsmentioning

confidence: 99%

“…Obviously, if set c(x) � c, we can obtain problem ( 16) (or problem ( 17)) from problem (18). In this paper, we only study problem (16), and problem ( 18) will be studied in the future. Now, we provide the definition of the equilibrium strategy for problem (16).…”

Section: Time-consistent Mean-variance Problem With Inside Informationmentioning

confidence: 99%

“…In this paper, we only study problem (16), and problem ( 18) will be studied in the future. Now, we provide the definition of the equilibrium strategy for problem (16). Definition 2.…”

Section: Time-consistent Mean-variance Problem With Inside Informationmentioning

confidence: 99%

“…the closed-loop equilibrium investment strategies are given by 16 Mathematical Problems in Engineering…”

Section: A(t) > 0 In This Section We Assume Thatmentioning

confidence: 99%

“…Sun and Guo [15] studied a time-inconsistent linear quadratic control problem with stochastic coefficients and random jumps and then studied its application in mean-variance portfolio selection problem. Yan and Wong [16] investigated the mean-variance portfolio problem in incomplete markets with stochastic volatility.…”

Section: Introductionmentioning

confidence: 99%

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Closed-Loop Equilibrium Reinsurance-Investment Strategy with Insider Information and Default Risk

Yang

2021

Mathematical Problems in Engineering

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This paper studies the closed-loop equilibrium reinsurance-investment problem with insider information and default risk. The financial market consists of one risky asset, one defaultable bond, and one risk-free asset. The surplus process is governed by a jump-diffusion process. Two kinds of dependencies between the insurance market and the financial market are considered. In addition, the insurer has some extra claims information available from the beginning of the trading interval. The objective of the insurer is to choose a time-consistent reinsurance-investment strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. Since this problem is time-inconsistent, using closed-loop control approach from the perspective of game theory, we establish the extended Hamilton–Jacobi–Bellman (HJB) equations for the postdefault case and the predefault case, respectively. Closed-form solutions for the closed-loop equilibrium reinsurance-investment strategy and the corresponding value function are obtained. Finally, we provide a series of numerical examples to illustrate the effects of insider information and other some important model parameters on the closed-loop equilibrium reinsurance and investment strategies. The result analyses reveal some interesting phenomena and provide useful guidances for reinsurance and investment in reality.

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Section: The Main Resultsmentioning

confidence: 99%

Section: Time-consistent Mean-variance Problem With Inside Informationmentioning

confidence: 99%

“…In this paper, we only study problem (16), and problem ( 18) will be studied in the future. Now, we provide the definition of the equilibrium strategy for problem (16). Definition 2.…”

Section: Time-consistent Mean-variance Problem With Inside Informationmentioning

confidence: 99%

“…the closed-loop equilibrium investment strategies are given by 16 Mathematical Problems in Engineering…”

Section: A(t) > 0 In This Section We Assume Thatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Closed-Loop Equilibrium Reinsurance-Investment Strategy with Insider Information and Default Risk

Yang

2021

Mathematical Problems in Engineering

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Robust time-consistent mean–variance portfolio selection problem with multivariate stochastic volatility

et al. 2020

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Time consistent mean-variance asset allocation for a DC plan with regime switching under a jump-diffusion model

Guambe

Kufakunesu

Zyl

et al. 2021

Japan J. Indust. Appl. Math.

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In this paper, we study a time consistent solution for a defined contribution pension plan under a mean-variance criterion with regime switching in a jump-diffusion setup, during the accumulation phase. We consider a market consisting of a risk-free asset and a geometric jump-diffusion risky asset process. Our solution allows the fund manager to incorporate a clause which allows for the distribution of a member's premiums to his surviving dependents, should the member die before retirement. Applying the extended Hamilton-Jacobi-Bellman (HJB) equation, we derive the explicit time consistent equilibrium strategy and the value function. We then provide some numerical simulations to illustrate our results.

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Open-loop equilibrium strategy for mean–variance portfolio problem under stochastic volatility

Cited by 35 publications

References 24 publications

Closed-Loop Equilibrium Reinsurance-Investment Strategy with Insider Information and Default Risk

Closed-Loop Equilibrium Reinsurance-Investment Strategy with Insider Information and Default Risk

Robust time-consistent mean–variance portfolio selection problem with multivariate stochastic volatility

Time consistent mean-variance asset allocation for a DC plan with regime switching under a jump-diffusion model

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