Optimal dividend strategy for the dual model with surplus-dependent expense

2021 ◽  
pp. 1-37
Author(s):  
Shanshan Liu ◽  
Zhaoyang Liu ◽  
Guoxin Liu
Keyword(s):  
Dual Model ◽  
Optimal Dividend ◽  
Optimal Dividend Strategy

The Optimal Dividend Problem in the Dual Model

2014 ◽  
Vol 46 (03) ◽  
pp. 746-765
Author(s):  
Erik Ekström ◽  
Bing Lu
Keyword(s):  
Fixed Point ◽  
Firm Value ◽  
Value Function ◽  
Fixed Point Method ◽  
Optimal Harvesting ◽  
Control Problems ◽  
Dual Model ◽  
Optimal Dividend ◽  
Optimal Dividend Strategy ◽  
Barrier Type

We study de Finetti's optimal dividend problem, also known as the optimal harvesting problem, in the dual model. In this model, the firm value is affected both by continuous fluctuations and by upward directed jumps. We use a fixed point method to show that the solution of the optimal dividend problem with jumps can be obtained as the limit of a sequence of stochastic control problems for a diffusion. In each problem, the optimal dividend strategy is of barrier type, and the rate of convergence of the barrier and the corresponding value function is exponential.

The Optimal Dividend Problem in the Dual Model

2014 ◽  
Vol 46 (3) ◽  
pp. 746-765 ◽  
Author(s):  
Erik Ekström ◽  
Bing Lu
Keyword(s):  
Fixed Point ◽  
Firm Value ◽  
Value Function ◽  
Fixed Point Method ◽  
Optimal Harvesting ◽  
Control Problems ◽  
Dual Model ◽  
Optimal Dividend ◽  
Optimal Dividend Strategy ◽  
Barrier Type

We study de Finetti's optimal dividend problem, also known as the optimal harvesting problem, in the dual model. In this model, the firm value is affected both by continuous fluctuations and by upward directed jumps. We use a fixed point method to show that the solution of the optimal dividend problem with jumps can be obtained as the limit of a sequence of stochastic control problems for a diffusion. In each problem, the optimal dividend strategy is of barrier type, and the rate of convergence of the barrier and the corresponding value function is exponential.

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 REFRACTION–REFLECTION STRATEGIES IN THE DUAL MODEL

2016 ◽  
Vol 47 (1) ◽  
pp. 199-238 ◽  
Author(s):  
José-Luis Pérez ◽  
Kazutoshi Yamazaki
Keyword(s):  
Additional Condition ◽  
Numerical Results ◽  
Dual Model ◽  
Maximal Rate ◽  
Absolutely Continuous ◽  
Capital Injection ◽  
Surplus Process ◽  
Optimal Dividend

AbstractWe study the dual model with capital injection under the additional condition that the dividend strategy is absolutely continuous. We consider a refraction–reflection strategy that pays dividends at the maximal rate whenever the surplus is above a certain threshold, while capital is injected so that it stays non-negative. The resulting controlled surplus process becomes the spectrally positive version of the refracted–reflected process recently studied by Pérez and Yamazaki (2015). We study various fluctuation identities of this process and prove the optimality of the refraction–reflection strategy. Numerical results on the optimal dividend problem are also given.

scholarly journals On the Optimal Dividend Strategy in a Regime-Switching Diffusion Model

2012 ◽  
Vol 44 (3) ◽  
pp. 886-906 ◽  
Author(s):  
Jiaqin Wei ◽  
Rongming Wang ◽  
Hailiang Yang
Keyword(s):  
Diffusion Model ◽  
Regime Switching ◽  
Value Function ◽  
Risk Theory ◽  
System Of Differential Equations ◽  
Arrival Times ◽  
Switching Diffusion ◽  
Optimal Dividend ◽  
Optimal Dividend Strategy ◽  
The Value Function

In this paper we consider the optimal dividend strategy under the diffusion model with regime switching. In contrast to the classical risk theory, the dividends can only be paid at the arrival times of a Poisson process. By solving an auxiliary optimal problem we show that the optimal strategy is the modulated barrier strategy. The value function can be obtained by iteration or by solving the system of differential equations. We also provide a numerical example to illustrate the effects of the restriction on the timing of the payment of dividends.

scholarly journals On the Optimal Dividend Strategy in a Regime-Switching Diffusion Model

2012 ◽  
Vol 44 (03) ◽  
pp. 886-906 ◽  
Author(s):  
Jiaqin Wei ◽  
Rongming Wang ◽  
Hailiang Yang
Keyword(s):  
Diffusion Model ◽  
Regime Switching ◽  
Value Function ◽  
Risk Theory ◽  
System Of Differential Equations ◽  
Arrival Times ◽  
Switching Diffusion ◽  
Optimal Dividend ◽  
Optimal Dividend Strategy ◽  
The Value Function

In this paper we consider the optimal dividend strategy under the diffusion model with regime switching. In contrast to the classical risk theory, the dividends can only be paid at the arrival times of a Poisson process. By solving an auxiliary optimal problem we show that the optimal strategy is the modulated barrier strategy. The value function can be obtained by iteration or by solving the system of differential equations. We also provide a numerical example to illustrate the effects of the restriction on the timing of the payment of dividends.

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