Open-loop equilibrium reinsurance-investment strategy under mean–variance criterion with stochastic volatility

Yan, Tingjin; Wong, Hoi Ying

doi:10.1016/j.insmatheco.2019.11.003

Cited by 30 publications

(22 citation statements)

References 35 publications

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“…In this subsection, we consider the case where claim processes of new and original businesses are the same, that is a 2 = a 1 , b 21 = b 1 and b 22 = 0. This is the most popular case studied in literature which allows the retention level of insurer larger than one (see, e.g., [23], [37], [31] and [33]). Furthermore, we assume that 0 < θ 2 < η in this case 1 , and we set σ 2 = 0 for simplicity of presentation.…”

Section: 1mentioning

confidence: 99%

“…The open-loop equilibrium strategy is usually studied by using backward stochastic differential equations (BSDEs, for short). For example, [31] and [16] investigated open-loop equilibrium reinsurance-investment strategies for mean-variance insurers under models with bounded and unbounded random coefficients, respectively; [33] derived an open-loop equilibrium MV reinsuranceinvestment strategy under general stochastic volatility models.…”

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confidence: 99%

“…Here, q is called the retention level of the insurer, which is obviously valued in [0, 1]. To the best of our knowledge, in most of existing literature, it is usually assumed that q ∈ [0, ∞) and the case of q ∈ (1, ∞) is interpreted as acquiring new business, see [2], [23], [37], [31] and [33], etc. However, this assumption of acquiring new business is too strong, since it implies that original/old and new businesses are the same and the premium rate of new business and that of the reinsurance are also the same.…”

mentioning

confidence: 99%

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Open-loop equilibrium mean-variance reinsurance, new business and investment strategies with constraints

Zhang

Wang

Wei

2022

JIMO

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<p style='text-indent:20px;'>In this paper, we study a general mean-variance reinsurance, new business and investment problem, where the claim processes of original and new businesses are modeled by two different risk processes and the safety loadings of reinsurance and new business are different. The retention level of the insurer is constrained in <inline-formula><tex-math id="M1">\begin{document}$ [0,1] $\end{document}</tex-math></inline-formula> and the controls of new business and risky investment are required to be non-negative. This model relaxes the limitations of those in existing research. By using the projection onto the convex set controls valued in, we obtain an open-loop equilibrium reinsurance-new business-investment strategy explicitly. We also show that the obtained equilibrium strategy is the optimal one among all deterministic strategies in the sense that it yields the smallest mean-variance cost. In the case where original and new businesses are the same, the equilibrium strategy is given in closed-form and its sensitivities to safety loadings are shown by numerical examples. At last, by comparing with the case where acquiring new business is prohibited, we show that allowing writing new policies indeed improves the performance of the insurer's risk management.</p>

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Section: 1mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Open-loop equilibrium mean-variance reinsurance, new business and investment strategies with constraints

Zhang

Wang

Wei

2022

JIMO

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“…is problem can be viewed as a dynamic mean-variance problem, since the objective of the insurer updates as state (t, x, m, z) changes. 16) (or problem (17)) is a special case of the following problem:…”

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

confidence: 99%

“…e same authors continued to study the reinsurance-investment problem under the general stochastic volatility model in Yan and Wong [17]. Wang [18] investigated the uniqueness issue of open-loop equilibrium investment strategies of dynamic mean-variance portfolio selection problem with stochastic coefficients.…”

Section: Introductionmentioning

confidence: 99%

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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Robust Investment and Proportional Reinsurance Strategy with Delay and Jumps in a Stochastic Stackelberg Differential Game

Zhang,

Cui

2024

Methodol Comput Appl Probab

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Open-loop equilibrium reinsurance-investment strategy under mean–variance criterion with stochastic volatility

Cited by 30 publications

References 35 publications

Open-loop equilibrium mean-variance reinsurance, new business and investment strategies with constraints

Open-loop equilibrium mean-variance reinsurance, new business and investment strategies with constraints

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

Robust Investment and Proportional Reinsurance Strategy with Delay and Jumps in a Stochastic Stackelberg Differential Game

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