Optimal Control with Restrictions for a Diffusion Risk Model Under Constant Interest Force

Peng, Xiaofan; Bai, Ling; Guo, Jian

doi:10.1007/s00245-015-9295-3

Cited by 5 publications

(3 citation statements)

References 20 publications

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“…In the context of dynamic proportional reinsurance, [7] derived the optimal reinsurance strategy that maximizes the expected discounted future surpluses; [16] derived the optimal reinsurance strategy which minimizes the ruin probability in the classical risk model and its diffusion approximation; [10] studied optimal reinsurance under the criterion of maximizing adjustment coefficient for a diffusion risk model as well as a jump-diffusion risk model; [22] considered the objective of maximizing the expected exponential utility and derived optimal reinsurance strategy for a risk model with common shock dependence under the expected value premium principle; [11] examined the same optimal problem under the variance premium principle; and [14] studied optimal dividend problems in a diffusion risk model under constant interest force.…”

Section: Xin Jiang Kam Chuen Yuen and MI Chenmentioning

confidence: 99%

Optimal investment and reinsurance with premium control

Jiang¹,

Yuen²,

Chen³

2020

Journal of Industrial &Amp; Management Optimization

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This paper studies the optimal investment and reinsurance problem for a risk model with premium control. It is assumed that the insurance safety loading and the time-varying claim arrival rate are connected through a monotone decreasing function, and that the insurance and reinsurance safety loadings have a linear relationship. Applying stochastic control theory, we are able to derive the optimal strategy that maximizes the expected exponential utility of terminal wealth. We also provide a few numerical examples to illustrate the impact of the model parameters on the optimal strategy.

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Section: Xin Jiang Kam Chuen Yuen and MI Chenmentioning

confidence: 99%

Optimal investment and reinsurance with premium control

Jiang¹,

Yuen²,

Chen³

2020

Journal of Industrial &Amp; Management Optimization

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“…e study of dividend strategies for the insurance risk model was first proposed by De Finetti [1], and he found that the optimal strategy must be a barrier strategy in the studied discrete time model. Since then, many scholars have tried to work out the dividend problems under more general and more realistic model assumptions, for example, Claramunt et al [2], Zhou [3], Landriault [4], Gerber et al [5], Chen et al [6], Chen and Yuen [7], and Peng et al [8,9].…”

Section: Introductionmentioning

confidence: 99%

On a Discrete Markov-Modulated Risk Model with Random Premium Income and Delayed Claims

Nie

Chen

Liu³

et al. 2020

Mathematical Problems in Engineering

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In this paper, a discrete Markov-modulated risk model with delayed claims, random premium income, and a constant dividend barrier is proposed. It is assumed that the random premium income and individual claims are affected by a Markov chain with finite state space. The model proposed is an extension of the discrete semi-Markov risk model with random premium income and delayed claims. Explicit expressions for the total expected discounted dividends until ruin are obtained by the method of generating function and the theory of difference equations. Finally, the effect of related parameters on the total expected discounted dividends are shown in several numerical examples.

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“…The extensively studied risk models for the optimal dividend problem in the literature include diffusion model, Cramér-Lundberg model, jump-diffusion model and Lévy risk model. For example, Asmussen and Taksar (1997), Højgaard and Taksar (1999), Asmussen et al (2000), Paulsen (2003), Gerber and Shiu (2004), Løkka and Zervos (2008), He and Liang (2008), Bai et al (2010), Chen et al (2013), Yao et al (2014Yao et al ( , 2016, Peng et al (2016), Vierkötter and Schmidli (2017), Zhu (2017), and Liang and Palmowski (2018) considered the optimal dividend problem in the diffusion model; Højgaard (2002), Azcue and Muler (2005), Schmidli (2006), Gerber and Shiu (2006), Albrecher and Thonhauser (2008), and Azcue and Muler (2012) studied the optimal dividend strategy under the Cramér-Lundberg model. As for other risk models such as the jump-diffusion model and the Lévy risk model, recent related research can be found in Avram et al (2007Avram et al ( , 2015, Kyprianou and Palmowski (2007), Loeffen (2008Loeffen ( , 2009, Loeffen and Renaud (2010), Czarna and Palmowski (2010), Wang and Hu (2012), Hunting and Paulsen (2013), Hernandez and Junca (2015), Zhao et al (2017), Pérez et al (2018), , Wang and Zhou (2018), Wang and Zhang (2019), etc.…”

Section: Introductionmentioning

confidence: 99%

Optimal reinsurance and dividends with transaction costs and taxes under thinning structure

Chen

Yuen

Wang

2020

Preprint

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In this paper, we investigate the problem of optimal strategies of dividend and reinsurance under the Cramér-Lundberg risk model embedded with the thinningdependence structure which was firstly introduced by Wang and Yuen (2005), subject to the optimality criteria of maximizing the expected accumulated discounted dividends paid until ruin. To enhance the practical relevance of the optimal dividend and reinsurance problem, non-cheap reinsurance is considered and transaction costs and taxes are imposed on dividends, which converts our optimization problem into a mixed classical-impulse control problem. For the purpose of better mathematical tractability and neat, explicit solutions of our control problem, instead of the Cramér-Lundberg framework we study its approximated diffusion model with two thinly dependent classes of insurance businesses. Using a method of quasi-variational inequalities, we show that the optimal reinsurance follows a two-dimensional excess-of-loss reinsurance strategy, and, the optimal dividend strategy turns out to be an impulse dividend strategy with an upper and a lower barrier, i.e., every thing above the lower barrier is paid as dividends each time the surplus is above the upper barrier, otherwise no dividends are paid. Closed-form expression for the value function associated with the optimal dividend and reinsurance strategy is also given. In addition, some numerical examples are presented to illustrate the optimality results.

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Optimal Control with Restrictions for a Diffusion Risk Model Under Constant Interest Force

Cited by 5 publications

References 20 publications

Optimal investment and reinsurance with premium control

Optimal investment and reinsurance with premium control

On a Discrete Markov-Modulated Risk Model with Random Premium Income and Delayed Claims

Optimal reinsurance and dividends with transaction costs and taxes under thinning structure

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