Optimal Dividend Strategy for a General Diffusion Process with Time-Inconsistent Preferences and Ruin Penalty

2018 ◽  
Vol 9 (1) ◽  
pp. 274-314 ◽  
Author(s):  
Shumin Chen ◽  
Zhongfei Li ◽  
Yan Zeng
Keyword(s):  
Diffusion Process ◽  
Optimal Dividend ◽  
Optimal Dividend Strategy ◽  
Time Inconsistent

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.

Optimal dividend strategies with time-inconsistent preferences

2014 ◽  
Vol 46 ◽  
pp. 150-172 ◽  
Author(s):  
Shumin Chen ◽  
Zhongfei Li ◽  
Yan Zeng
Keyword(s):  
Optimal Dividend ◽  
Time Inconsistent

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.

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.

scholarly journals Optimal Dividend Policy when Cash Reserves Follow a Jump-Diffusion Process Under Markov-Regime Switching

2015 ◽  
Vol 52 (1) ◽  
pp. 209-223 ◽  
Author(s):  
Zhengjun Jiang
Keyword(s):  
Diffusion Process ◽  
Regime Switching ◽  
Limited Liability ◽  
Jump Diffusion ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
Jump Diffusion Process ◽  
Finite State ◽  
Negative Exponential ◽  
Cash Reserves

In this paper we study the optimal dividend payments for a company of limited liability whose cash reserves in the absence of dividends follow a Markov-modulated jump-diffusion process with positive drifts and negative exponential jumps, where parameters and discount rates are modulated by a finite-state irreducible Markov chain. The main aim is to maximize the expected cumulative discounted dividend payments until bankruptcy time when cash reserves are nonpositive for the first time. We extend the results of Jiang and Pistorius [15] to our setup by proving that it is optimal to adopt a modulated barrier strategy at certain positive regime-dependent levels and that the value function can be explicitly characterized as the fixed point of a contraction.

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