Optimal dividend and capital injection strategies in the perturbed classical risk model with transaction costs

2015 ◽  
pp. 245-248
Keyword(s):  
Transaction Costs ◽  
Risk Model ◽  
Classical Risk Model ◽  
Capital Injection ◽  
Optimal Dividend ◽  
Injection Strategies

scholarly journals Optimal Dividend and Capital Injection Strategies in the Cramér-Lundberg Risk Model

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Yan Li ◽  
Guoxin Liu
Keyword(s):  
Value Function ◽  
Risk Model ◽  
Capital Injection ◽  
Time Of Ruin ◽  
Optimal Dividend ◽  
The Time Of Ruin ◽  
Hamilton Jacobi Bellman ◽  
Injection Barrier ◽  
The Value Function ◽  
Injection Strategies

We discuss the optimal dividend and capital injection strategies in the Cramér-Lundberg risk model. The value functionV(x)is defined by maximizing the discounted value of the dividend payment minus the penalized discounted capital injection until the time of ruin. It is shown thatV(x)can be characterized by the Hamilton-Jacobi-Bellman equation. We find the optimal dividend barrierb, the optimal upper capital injection barrier 0, and the optimal lower capital injection barrier-z*. In the case of exponential claim size especially, we give an explicit procedure to obtainb,-z*, and the value functionV(x).

scholarly journals ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS

2014 ◽  
Vol 44 (3) ◽  
pp. 635-651 ◽  
Author(s):  
Chuancun Yin ◽  
Yuzhen Wen ◽  
Yongxia Zhao
Keyword(s):  
Lévy Process ◽  
Risk Model ◽  
Levy Process ◽  
Dual Model ◽  
Threshold Strategy ◽  
Classical Risk Model ◽  
Surplus Process ◽  
Optimal Dividend ◽  
Special Cases ◽  
The Classical Risk Model

AbstractIn this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Lévy process before dividends are deducted. This model includes the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to an admissible strategy whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that the optimal dividend strategy is formed by a threshold strategy.

scholarly journals On optimal periodic dividend and capital injection strategies for spectrally negative Lévy models

2018 ◽  
Vol 55 (4) ◽  
pp. 1272-1286 ◽  
Author(s):  
Kei Noba ◽  
José-Luis Pérez ◽  
Kazutoshi Yamazaki ◽  
Kouji Yano
Keyword(s):  
Arrival Time ◽  
Arrival Times ◽  
Classical Sense ◽  
Capital Injection ◽  
Dividend Payments ◽  
Poisson Arrival ◽  
Optimal Dividend ◽  
Injection Strategies

Abstract De Finetti’s optimal dividend problem has recently been extended to the case when dividend payments can be made only at Poisson arrival times. In this paper we consider the version with bail-outs where the surplus must be nonnegative uniformly in time. For a general spectrally negative Lévy model, we show the optimality of a Parisian-classical reflection strategy that pays the excess above a given barrier at each Poisson arrival time and also reflects from below at 0 in the classical sense.

scholarly journals OPTIMAL DIVIDEND AND REINSURANCE STRATEGIES WITH FINANCING AND LIQUIDATION VALUE

2016 ◽  
Vol 46 (2) ◽  
pp. 365-399 ◽  
Author(s):  
Dingjun Yao ◽  
Hailiang Yang ◽  
Rongming Wang
Keyword(s):  
Transaction Costs ◽  
Stochastic Control ◽  
Risk Model ◽  
Optimal Strategies ◽  
Proportional Reinsurance ◽  
Control Methods ◽  
Distribution Problem ◽  
Insurance Portfolio ◽  
Optimal Dividend ◽  
Dividend Distribution

AbstractThis study investigates a combined optimal financing, reinsurance and dividend distribution problem for a big insurance portfolio. A manager can control the surplus by buying proportional reinsurance, paying dividends and raising money dynamically. The transaction costs and liquidation values at bankruptcy are included in the risk model. Under the objective of maximising the insurance company's value, we identify the insurer's joint optimal strategies using stochastic control methods. The results reveal that managers should consider financing if and only if the terminal value and the transaction costs are not too high, less reinsurance is bought when the surplus increases or dividends are always distributed using the barrier strategy.

scholarly journals On a Periodic Capital Injection and Barrier Dividend Strategy in the Compound Poisson Risk Model

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 511 ◽  
Author(s):  
Wenguang Yu ◽  
Peng Guo ◽  
Qi Wang ◽  
Guofeng Guan ◽  
Qing Yang ◽  
...  
Keyword(s):  
Risk Model ◽  
Observation Interval ◽  
Claim Amount ◽  
Insurance Company ◽  
Classical Risk Model ◽  
Numerical Examples ◽  
Compound Poisson Risk Model ◽  
Capital Injection ◽  
The Classical Risk Model ◽  
Injection Function

In this paper, we assume that the reserve level of an insurance company can only be observed at discrete time points, then a new risk model is proposed by introducing a periodic capital injection strategy and a barrier dividend strategy into the classical risk model. We derive the equations and the boundary conditions satisfied by the Gerber-Shiu function, the expected discounted capital injection function and the expected discounted dividend function by assuming that the observation interval and claim amount are exponentially distributed, respectively. Numerical examples are also given to further analyze the influence of relevant parameters on the actuarial function of the risk model.

scholarly journals Optimal Dividend and Capital Injection Strategies for a Risk Model under Force of Interest

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Ying Fang ◽  
Zhongfeng Qu
Keyword(s):  
Risk Model ◽  
Risk Process ◽  
Insurance Company ◽  
Threshold Strategy ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
Optimal Injection ◽  
Force Of Interest ◽  
Capital Injections ◽  
Injection Strategies

As a generalization of the classical Cramér-Lundberg risk model, we consider a risk model including a constant force of interest in the present paper. Most optimal dividend strategies which only consider the processes modeling the surplus of a risk business are absorbed at 0. However, in many cases, negative surplus does not necessarily mean that the business has to stop. Therefore, we assume that negative surplus is not allowed and the beneficiary of the dividends is required to inject capital into the insurance company to ensure that its risk process stays nonnegative. For this risk model, we show that the optimal dividend strategy which maximizes the discounted dividend payments minus the penalized discounted capital injections is a threshold strategy for the case of the dividend payout rate which is bounded by some positive constant and the optimal injection strategy is to inject capitals immediately to make the company's assets back to zero when the surplus of the company becomes negative.

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