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

Chen, Mi; Yuen, Kam Chuen; Wang, Wenyuan

doi:10.1080/03461238.2020.1824158

Cited by 11 publications

(4 citation statements)

References 52 publications

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“…Using the expected present value of dividends until ruin (the expected present value of the dividends subtracted by the discounted costs of capital injections) as the value function, [6] identified the condition under which the barrier strategy (respectively, the barrier dividend strategy together with capital injection strategy that reflects the reserve process at 0) is optimal among all admissible strategies. More results of non-impulse dividend optimization under the SNL risk processes can be found in [7,9,15,16,20,21,28,31,32,34,37,38,[45][46][47][48][49][50]53] and the references therein. The non-impulse dividends optimization under the SPL risk processes can be found in [4,5,12,13,53,55,57] and others.…”

Section: Introductionmentioning

confidence: 99%

Dividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes

Wang

Chen

et al. 2022

J Optim Theory Appl

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The optimal dividends problem has remained an active research field for decades. For an insurance company with reserve modelled by a spectrally negative Lévy process having finite first-order moment, we study the optimal impulse dividend and capital injection (IDCI) strategy for maximizing the expected accumulated discounted net dividend payment subtracted by the accumulated discounted cost of injecting capital. In this setting, the beneficiary of the dividends injects capital to ensure a non-negative risk process so that the insurer never goes bankrupt. The optimal IDCI strategy together with its value function is obtained. Besides, two numerical examples are provided to illustrate the features of the optimal strategies. The impacts of model parameters are also studied.

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Section: Introductionmentioning

confidence: 99%

Dividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes

Wang

Chen

et al. 2022

J Optim Theory Appl

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“…A recent related research can be found in [15] (see also references therein), where the problem of optimal dividends and reinsurance is formulated as a mixed classical-impulse stochastic control problem. The authors considered a fixed transaction cost when the dividends are paid out and solved the problem using the method of quasi-variational inequalities.…”

Section: Introductionmentioning

confidence: 99%

“…only q 1 is relevant because of Condition (15). q 1 ∈ (0, +∞) is a consequence of the existence of K * > 0 in Theorem 4.…”

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confidence: 99%

Optimal Reinsurance Problem under Fixed Cost and Exponential Preferences

Brachetta

Ceci

2021

Mathematics

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We investigate an optimal reinsurance problem for an insurance company taking into account subscription costs: that is, a constant fixed cost is paid when the reinsurance contract is signed. Differently from the classical reinsurance problem, where the insurer has to choose an optimal retention level according to some given criterion, in this paper, the insurer needs to optimally choose both the starting time of the reinsurance contract and the retention level to apply. The criterion is the maximization of the insurer’s expected utility of terminal wealth. This leads to a mixed optimal control/optimal stopping time problem, which is solved by a two-step procedure: first considering the pure-reinsurance stochastic control problem and next discussing a time-inhomogeneous optimal stopping problem with discontinuous reward. Using the classical Cramér–Lundberg approximation risk model, we prove that the optimal strategy is deterministic and depends on the model parameters. In particular, we show that there exists a maximum fixed cost that the insurer is willing to pay for the contract activation. Finally, we provide some economical interpretations and numerical simulations.

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“…Under common shock dependence risk model, [4] studied the minimum ruin probability problem; [19] studied the optimal dividend and excessof-loss reinsurance problem. Under thinning-dependence risk model, [21] considered stochastic optimization of the dividend strategy with reinsurance; [5] studied the optimal dividend and excess-of-loss reinsurance problem. Under the dependent risk model, the research is just beginning and very meaningful.…”

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confidence: 99%

Optimal dividend and capital injection strategies in common shock dependence model with time-inconsistent preferences

Yang

Wang

Cheng

2023

MCRF

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<p style='text-indent:20px;'>This paper discusses the optimal dividend and capital injection problems when an insurance company has two lines of business with common shock dependence. Suppose that the manager of the company has time-inconsistent preference, which can be described by a quasi-hyperbolic discount function. The value of the company is measured by the expected discounted dividend payments minus the expected discounted costs of capital injection. The goal is to find out the optimal strategies for maximizing the value of the company. By using the stochastic control techniques, we solve the problems in all cases of time-consistent preference manager, naive manager and sophisticated manager, respectively. The closed-form solutions of the value functions are presented. Our results show that the sophisticated manager is inclined to pay out dividends earlier than the naive manager, time-inconsistent preference manager is more likely to pay dividends in advance than time-consistent preference manager. Furthermore, we provide some numerical analysis to reveal the sensitivity of the optimal dividend strategies to the dependence intensity and the cost of capital injection. The results show that, as the cost of capital injection increases, sophisticated manager will give up capital injection first, followed by naive manager. In addition, we also find that: when the cost of capital injection is low, managers think that the value of the company that undertakes two kinds of insurance with high correlation is higher; while, managers have opposite evaluations, when the cost of capital injection is high.</p>

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

Cited by 11 publications

References 52 publications

Dividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes

Dividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes

Optimal Reinsurance Problem under Fixed Cost and Exponential Preferences

Optimal dividend and capital injection strategies in common shock dependence model with time-inconsistent preferences

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