Robust optimal investment and reinsurance of an insurer under variance premium principle and default risk

Sun, Zhongyang; Zheng, Xiaoxiao; Zhang, Xin

doi:10.1016/j.jmaa.2016.09.053

Cited by 61 publications

(25 citation statements)

References 25 publications

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“…e reinsurance includes the reinsurance premium and reinsurance type. In most of the above results, the reinsurance premium principle is calculated according to the expected value principle or variance principle, such as Liang and Bayraktar [22] and Sun et al [23]. In previous conclusions, two types of reinsurance policies are most commonly studied in the literature.…”

Section: Introductionmentioning

confidence: 99%

Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

Deng

et al. 2020

Mathematical Problems in Engineering

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In this paper, we consider a robust optimal investment-reinsurance problem with a default risk. The ambiguity-averse insurer (AAI) may carry out transactions on a risk-free asset, a stock, and a defaultable corporate bond. The stock’s price is described by a jump-diffusion process, and both the jump intensity and the distribution of jump amplitude are uncertain, i.e., the jump is ambiguous. The AAI’s surplus process is assumed to follow an approximate diffusion process. In particular, the reinsurance premium is calculated according to the generalized mean-variance premium principle, and the reinsurance type has to follow a self-reinsurance function. In performing dynamic programming, both the predefault case and the postdefault case are analyzed, and the optimal strategies and the corresponding value functions are derived under the worst-case scenario. Moreover, we give a detailed proof of the verification theorem and give some special cases and numerical examples to illustrate our theoretical results.

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Section: Introductionmentioning

confidence: 99%

Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

Deng

et al. 2020

Mathematical Problems in Engineering

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“…Reference [16] studied the robust optimal proportional reinsurance and investment strategies for both an insurer and a reinsurer. Reference [17] took default risk into account and derived the robust optimal control strategy under variance premium. Different from the above-mentioned literature, [18] analyzed a robust optimal problem of excess-of-loss reinsurance and investment in a model with jumps for an AAI.…”

Section: Introductionmentioning

confidence: 99%

Robust Optimal Excess-of-Loss Reinsurance and Investment Problem with Delay and Dependent Risks

Zhang

Zhao

2019

Discrete Dynamics in Nature and Society

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This paper investigates a robust optimal excess-of-loss reinsurance and investment problem with delay and dependent risks for an ambiguity-averse insurer (AAI). The AAI’s wealth process is assumed to be two dependent classes of insurance business. He/she can purchase excess-of-loss reinsurance from the reinsurer and invest in a risk-free asset and a risky asset whose price follows Heston model. We obtain the explicit expressions of the optimal excess-of-loss reinsurance and investment strategy by maximizing the expected exponential utility of AAI’s terminal wealth. Finally, we give the proof of the verification theorem. Our models and results posed here can be regarded as a generalization of the existing results in the literature.

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“…Yi et al [12] focus on an optimal portfolio selection problem under SV model with model uncertainty. For more details, we refer the reader to Li et al [13], Sun et al [14] and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…Under the criteria of maximizing the expected utility of terminal wealth, most of the literature mentioned above are based on expected value premium principle due to its simplicity and popularity in practice. Sun et al [14] consider the optimal investment-reinsurance strategies under variance premium principle. Zeng et al [17] and Gu et al [18] investigate the optimal proportional reinsurance-investment problem for an insurer with mispricing, model ambiguity with mean-reversion under expected value premium principle.…”

Section: Introductionmentioning

confidence: 99%

Optimal Investment-Reinsurance Strategies for Insurers with Mean-Reversion and Mispricing under Variance Premium Principle

Wen¹

2018

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This paper considers a robust optimal reinsurance-investment problem for an insurer with mispricing and model ambiguity. The surplus process is described by a classical Cramér-Lunderg model and the financial market contains a market index, a risk-free asset and a pair of mispriced stocks, where the expected return rate of the stocks and the mispricing follow mean reverting processes which take into account liquidity constraints. In particular, both the insurance and reinsurance premium are assumed to be calculated via the variance premium principle. By employing the dynamic programming approach, we derive the explicit optimal robust reinsurance-investment strategy and the optimal value function.Open Access , , ,0 ,be a probability space, in which Ω is the state space and  is a σ-algebra on Ω . 0 T > is a fixed constant, representing the time horizon, { } 0 t t≥  is a filtration, which describes the flow Y. Z. Wen DOI: 10.4236/am.2018.97056 808 Applied Mathematics of information over time, the σ-algebra { } t  describes the information available up to time t, and { } 0 t t ≥  satisfies the usual condition (it contains all P-nullsets and is right continuous). We denote P as a reference measure and suppose that all stochastic processes given in the following are assumed to be adapted on this space. aa J represent the value function's partial derivative t t J J wb t J bJ J J

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Robust optimal investment and reinsurance of an insurer under variance premium principle and default risk

Cited by 61 publications

References 25 publications

Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

Optimal Strategies for an Ambiguity-Averse Insurer under a Jump-Diffusion Model and Defaultable Risk

Robust Optimal Excess-of-Loss Reinsurance and Investment Problem with Delay and Dependent Risks

Optimal Investment-Reinsurance Strategies for Insurers with Mean-Reversion and Mispricing under Variance Premium Principle

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