Optimal reinsurance-investment strategy for a dynamic contagion claim model

Cao, Jingyi; Landriault, David

doi:10.1016/j.insmatheco.2020.04.013

Cited by 25 publications

(20 citation statements)

References 24 publications

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“…with g given in (7). Our objective is to characterize the forward dynamic exponential utility (Problem 1), i.e.,…”

Section: Forward Exponential Utility Preferencesmentioning

confidence: 99%

“…In the actuarial framework, optimal reinsurance and investment problems have been widely investigated for different risk models and under different criteria, especially via expected utility maximization, ruin probability minimization or mean-variance criteria. However, to the best of our knowledge, all these contributions only employ classical backward utilities preferences, see, e.g., Brachetta and Ceci [6], Cao et al [7], Ceci et al [8], Gu et al [9], Liu and Ma [10] and references therein. A recent application of the forward utility approach to insurance can be found in Chong [11], where an evaluation problem of equity-linked life insurance contracts is investigated.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

2021

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In this paper, we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the optimal investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters.

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“…with g given in (7). Our objective is to characterize the forward dynamic exponential utility (Problem 1), i.e.,…”

Section: Forward Exponential Utility Preferencesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

2021

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show abstract

“…In this appendix, we briefly discuss the connection between the stochastic maximum approach and the HJB equation approach, since both approaches can be applied to solve the quadratic-loss minimization problem (2.15). We refer interested readers to Aït-Sahalia and Hurd (2016), Cao et al (2020), andLiu et al (2021) for the applications of the HJB approach to optimal investment problems under the Hawkes jump models.…”

Section: Connection With the Hjb Equation Approachmentioning

confidence: 99%

“…Another related paper is Bo et al (2019), which solves a portfolio optimization problem under a defaultable market modeled by mean-reverting diffusion processes enhanced with self-excitation. Cao et al (2020) apply a Hawkes process to model the claim frequency for an insurer and seek the optimal strategy to the insurer's optimal reinsurance problem. Liu et al (2021) study an optimal investment, consumption, and life insurance problem in a self-contagious market (i.e., there is only one risky asset) for a utilitymaximizing household with a bequest motive.…”

Section: Introductionmentioning

confidence: 99%

Mean-Variance Portfolio Selection in Contagious Markets

Shen¹,

Zou²

2021

Preprint

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We consider a mean-variance portfolio selection problem in a financial market with contagion risk. The risky assets follow a jump-diffusion model, in which jumps are driven by a multivariate Hawkes process with mutual-excitation effect. The mutual-excitation feature of the Hawkes process captures the contagion risk in the sense that each price jump of an asset increases the likelihood of future jumps not only in the same asset but also in other assets. We apply the stochastic maximum principle, backward stochastic differential equation theory, and linear-quadratic control technique to solve the problem and obtain the efficient strategy and efficient frontier in semi-closed form, subject to a non-local partial differential equation. Numerical examples are provided to illustrate our results.

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“…They have been widely investigated under different criteria, especially via expected utility maximization, mean-variance criterion and ruin probability minimization (see e.g. Irgens and Paulsen [16], Liu and Ma [21], Shen and Zeng [26], Gu et al [13], Brachetta and Ceci [6], Cao et al [10] and references therein). Despite the richness of contributions, only a few papers on optimal investment-reinsurance address the problem in relation to dependent risks.…”

Section: Introductionmentioning

confidence: 99%

Optimal Reinsurance and Investment under Common Shock Dependence Between Financial and Actuarial Markets

Ceci¹,

Colaneri²,

Cretarola³

2021

Preprint

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We study optimal proportional reinsurance and investment strategies for an insurance company which experiences both ordinary and catastrophic claims and wishes to maximize the expected exponential utility of its terminal wealth. We propose a model where the insurance framework is affected by environmental factors, and aggregate claims and stock prices are subject to common shocks, i.e. drastic events such as earthquakes, extreme weather conditions, or even pandemics, that have an immediate impact on the financial market and simultaneously induce insurance claims. Using the classical stochastic control approach based on the Hamilton-Jacobi-Bellman equation, we provide a verification result for the value function via classical solutions to two backward partial differential equations and characterize the optimal reinsurance and investment strategies. Finally, we make a comparison analysis to discuss the effect of common shock dependence.

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Optimal reinsurance-investment strategy for a dynamic contagion claim model

Cited by 25 publications

References 24 publications

Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

Mean-Variance Portfolio Selection in Contagious Markets

Optimal Reinsurance and Investment under Common Shock Dependence Between Financial and Actuarial Markets

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