Optimal dividend and capital injection strategy with a penalty payment at ruin: Restricted dividend payments

Xu, Ruijun; Woo, Jae-Kyung

doi:10.1016/j.insmatheco.2020.02.008

Cited by 12 publications

(29 citation statements)

References 31 publications

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“…Related literature. Among other papers dealing with similar topics like [17][18][19], the most related to ours is [20], which was brought to our attention only after completion of our paper. Ref.…”

Section: Remarkmentioning

confidence: 99%

Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model

Avram

Goreac

et al. 2021

Mathematics

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We investigate a control problem leading to the optimal payment of dividends in a Cramér-Lundberg-type insurance model in which capital injections incur proportional cost, and may be used or not, the latter resulting in bankruptcy. For general claims, we provide verification results, using the absolute continuity of super-solutions of a convenient Hamilton-Jacobi variational inequality. As a by-product, for exponential claims, we prove the optimality of bounded buffer capital injections (−a,0,b) policies. These policies consist in stopping at the first time when the size of the overshoot below 0 exceeds a certain limit a, and only pay dividends when the reserve reaches an upper barrier b. An exhaustive and explicit characterization of optimal couples buffer/barrier is given via comprehensive structure equations. The optimal buffer is shown never to be of de Finetti (a=0) or Shreve-Lehoczy-Gaver (a=∞) type. The study results in a dichotomy between cheap and expensive equity, based on the cost-of-borrowing parameter, thus providing a non-trivial generalization of the Lokka-Zervos phase-transition Løkka-Zervos (2008). In the first case, companies start paying dividends at the barrier b*=0, while in the second they must wait for reserves to build up to some (fully determined) b*>0 before paying dividends.

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Section: Remarkmentioning

confidence: 99%

Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model

Avram

Goreac

et al. 2021

Mathematics

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“…Let 𝜏 𝜃 := inf{𝑡 > 0, 𝑈 𝜃 𝑡 < 0} denotes the time of ruin under such controlled risk process, where inf ∅ = ∞ is assumed as usual. The following definition of the admissible dividend and capital injection strategy is borrowed from Xu and Woo [18].…”

Section: The Model and Some Preliminariesmentioning

confidence: 99%

“…ruin never occurs). Recently, Xu and Woo [18] considered both capital injections and affine penalty payments at ruin for optimal dividend problem under Cramér-Lundberg model with bounded dividend density, where capital injections are made up to the time of ruin (by forcing ruin when surplus drops below zero). The optimality of a band-type strategy for the combination of dividends and capital injections is obtained.…”

Section: Introductionmentioning

confidence: 99%

Optimal singular dividend control with capital injection and affine penalty payment at ruin

2022

Prob. Eng. Inf. Sci.

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In this paper, we extend the optimal dividend and capital injection problem with affine penalty at ruin in (Xu, R. & Woo, J.K. (2020). Insurance: Mathematics and Economics 92: 1–16) to the case with singular dividend payments. The asymptotic relationships between our value function to the one with bounded dividend density are studied, which also help to verify that our value function is a viscosity solution to the associated Hamilton–Jacob–Bellman Quasi-Variational Inequality (HJBQVI). We also show that the value function is the smallest viscosity supersolution within certain functional class. A modified comparison principle is proved to guarantee the uniqueness of the value function as the viscosity solution within the same functional class. Finally, a band-type dividend and capital injection strategy is constructed based on four crucial sets; and the optimality of such band-type strategy is proved by using fixed point argument. Numerical examples of the optimal band-type strategies are provided at the end when the claim size follows exponential and gamma distribution, respectively.

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“…In addition, in order to make the research more realistic, scholars have added various elements to the model. Such as [17], [18], [32], [31] added capital injection in the optimal dividend issues; [2], [30], [23] added transaction costs; [3], [22], [21] added reinsurance; [20], [27], [29] added ruin penalty.…”

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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 dividend and capital injection strategy with a penalty payment at ruin: Restricted dividend payments

Cited by 12 publications

References 31 publications

Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model

Equity Cost Induced Dichotomy for Optimal Dividends with Capital Injections in the Cramér-Lundberg Model

Optimal singular dividend control with capital injection and affine penalty payment at ruin

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

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