Optimal impulse and regular control strategies for proportional reinsurance problem

Rui-cheng, Yang; Liu, Kunhui; Xia, Bing

doi:10.1007/bf02936561

Cited by 8 publications

(3 citation statements)

References 13 publications

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“…The proportional reinsurance problem without considering the reinsurance transaction costs is discussed in [1]. There, the reserve R(t) is described as…”

Section: Introductionmentioning

confidence: 99%

Optimal proportional reinsurance model with transaction costs

Rui-cheng

Qin

2008

J. Appl. Math. Comput.

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Based on the mixed control strategy (regular control and impulse dividend control strategy), we formulate a proportional reinsurance model with transaction costs. For getting the maximal return function and associated mixed control strategy, using Itô calculus and classical mixed control theory, we derive the quasi-variational inequality solution to this optimal problem. Furthermore, we obtain its closed forms under some assumptions.

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“…The proportional reinsurance problem without considering the reinsurance transaction costs is discussed in [1]. There, the reserve R(t) is described as…”

Section: Introductionmentioning

confidence: 99%

Optimal proportional reinsurance model with transaction costs

Rui-cheng

Qin

2008

J. Appl. Math. Comput.

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“…The reserve of insurance companies is not changeless,but the stochastic process change over time in the combined action of various factors [1,2] .This paper mainly investigate the problem of proportional reinsurance control strategy with dividend process in insurance company, we prove the existence of optimal control strategy by variational inequality, and furthermore,we give the specific construct of optimal control strategy and the explicit structure of optimal return function are derived.…”

Section: Introductionmentioning

confidence: 99%

Control Strategy of Proportional Reinsurance with Dividend Process

Sun

Huang

Lian

2014

AMM

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“…上面描述了一个正则和脉冲的混合随机控制问题. 以往文献中也有对混合随机控制问题的研究, 例如, 文献 [17,18] 分别研究了再保和分红中的脉冲和正则混合控制问题, 而文献 [19] 考虑了 Lévy 过程下分红问题中的奇异正则随机控制问题. 注意到本文令折现因子 δ 大于零, 这意味着决策者偏好延迟注资的时间以使得成本最小.…”

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Optimal stochastic impulse and regular control for capital injections: A hybrid strategy

Li¹,

Zhou²,

Meng³

2017

Sci. Sin.-Math.

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This paper investigates an optimal capital injection problem for a large company whose cash flow is described by a drifted Brownian motion. We firstly bring forward the fact that the decision maker can choose the types of capital injection including regular or/and impulse injections in practice. The decision maker has the option to decide the capital injection rate (with a maximum restriction) of regular injection and the capital injection time and the amount of impulse injection as well. We assume that both types of capital injections have proportional costs, and an additional fixed cost occurs associated with each impulse capital injection. From the point of view of cost control, the purpose of the decision maker is to find a strategy to minimize the cost of capital injections, with the minimal requirement that the firm has a positive cash flow. It leads to a mixed stochastic impulse and regular control problem. Under this criterion, we obtain the value function and the optimal control strategy which is a hybrid type of impulse and regular capital injections. At last, we also show the sensibilities of model parameters to the optimal strategy and the value function.

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Optimal impulse and regular control strategies for proportional reinsurance problem

Cited by 8 publications

References 13 publications

Optimal proportional reinsurance model with transaction costs

Optimal proportional reinsurance model with transaction costs

Control Strategy of Proportional Reinsurance with Dividend Process

Optimal stochastic impulse and regular control for capital injections: A hybrid strategy

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