scholarly journals Optimal dividend payments until ruin of diffusion processes when payments are subject to both fixed and proportional costs

2007 ◽  
Vol 39 (03) ◽  
pp. 669-689 ◽  
Author(s):  
Jostein Paulsen
Keyword(s):  
Optimal Policy ◽  
Value Function ◽  
Diffusion Processes ◽  
Fixed Cost ◽  
Model Parameters ◽  
Dividend Payment ◽  
Optimal Dividends ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
The Value Function

The problem of optimal dividends paid until absorbtion at zero is considered for a rather general diffusion model. With each dividend payment there is a proportional cost and a fixed cost. It is shown that there can be essentially three different solutions depending on the model parameters and the costs. (i) Whenever assets reach a barrier y *, they are reduced to y * - δ* through a dividend payment, and the process continues. (ii) Whenever assets reach a barrier y *, everything is paid out as dividends and the process terminates. (iii) There is no optimal policy, but the value function is approximated by policies of one of the two above forms for increasing barriers. A method to numerically find the optimal policy (if it exists) is presented and numerical examples are given.

scholarly journals Optimal dividend payments until ruin of diffusion processes when payments are subject to both fixed and proportional costs

2007 ◽  
Vol 39 (3) ◽  
pp. 669-689 ◽  
Author(s):  
Jostein Paulsen
Keyword(s):  
Optimal Policy ◽  
Value Function ◽  
Diffusion Processes ◽  
Fixed Cost ◽  
Model Parameters ◽  
Dividend Payment ◽  
Optimal Dividends ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
The Value Function

The problem of optimal dividends paid until absorbtion at zero is considered for a rather general diffusion model. With each dividend payment there is a proportional cost and a fixed cost. It is shown that there can be essentially three different solutions depending on the model parameters and the costs. (i) Whenever assets reach a barrier y*, they are reduced to y* - δ* through a dividend payment, and the process continues. (ii) Whenever assets reach a barrier y*, everything is paid out as dividends and the process terminates. (iii) There is no optimal policy, but the value function is approximated by policies of one of the two above forms for increasing barriers. A method to numerically find the optimal policy (if it exists) is presented and numerical examples are given.

OPTIMAL DIVIDEND–REINSURANCE WITH TWO TYPES OF PREMIUM PRINCIPLES

2015 ◽  
Vol 30 (2) ◽  
pp. 224-243 ◽  
Author(s):  
Hui Meng ◽  
Ming Zhou ◽  
Tak Kuen Siu
Keyword(s):  
Numerical Analysis ◽  
Impulse Control ◽  
Value Function ◽  
Proportional Transaction Costs ◽  
Ruin Time ◽  
Closed Form Solutions ◽  
Impulse Control Problem ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
The Value Function

A combined optimal dividend/reinsurance problem with two types of insurance claims, namely the expected premium principle and the variance premium principle, is discussed. Dividend payments are considered with both fixed and proportional transaction costs. The objective of an insurer is to determine an optimal dividend–reinsurance policy so as to maximize the expected total value of discounted dividend payments to shareholders up to ruin time. The problem is formulated as an optimal regular-impulse control problem. Closed-form solutions for the value function and optimal dividend–reinsurance strategy are obtained in some particular cases. Finally, some numerical analysis is given to illustrate the effects of safety loading on optimal reinsurance strategy.

AN OPTIMAL DIVIDEND POLICY WITH DELAYED CAPITAL INJECTIONS

2013 ◽  
Vol 55 (2) ◽  
pp. 129-150 ◽  
Author(s):  
ZHUO JIN ◽  
GEORGE YIN
Keyword(s):  
Value Function ◽  
Closed Form Solution ◽  
Form Solution ◽  
Delay Period ◽  
Programming Approach ◽  
Dividend Payment ◽  
Capital Injection ◽  
Optimal Dividend ◽  
Capital Injections ◽  
The Value Function

AbstractThis work focuses on finding optimal dividend payment and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections with delays. Starting from the classical Cramér–Lundberg process, using the dynamic programming approach, the value function obeys a quasi-variational inequality. With delays in capital injections, the company will be exposed to the risk of financial ruin during the delay period. In addition, the optimal dividend payment and capital injection strategy should balance the expected cost of the possible capital injections and the time value of the delay period. In this paper, the closed-form solution of the value function and the corresponding optimal policies are obtained. Some limiting cases are also discussed. A numerical example is presented to illustrate properties of the solution. Some economic insights are also given.

scholarly journals A note on the optimal dividends paid in a foreign currency

2016 ◽  
Vol 11 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Julia Eisenberg ◽  
Paul Krühner
Keyword(s):  
Brownian Motion ◽  
Optimal Strategy ◽  
Value Function ◽  
Foreign Currency ◽  
Initial Capital ◽  
Brownian Motion With Drift ◽  
Optimal Dividends ◽  
Surplus Process ◽  
Dividend Payments ◽  
The Value Function

AbstractWe consider an insurance entity endowed with an initial capital and a surplus process modelled as a Brownian motion with drift. It is assumed that the company seeks to maximise the cumulated value of expected discounted dividends, which are declared or paid in a foreign currency. The currency fluctuation is modelled as a Lévy process. We consider both cases: restricted and unrestricted dividend payments. It turns out that the value function and the optimal strategy can be calculated explicitly.

scholarly journals Optimal Dividend Payment in De Finetti Models: Survey and New Results and Strategies

Risks ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 96
Author(s):  
Christian Hipp
Keyword(s):  
Iteration Scheme ◽  
Dividend Payment ◽  
Monotone Iteration ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
Hamilton Jacobi Bellman Equation ◽  
De Finetti ◽  
Hamilton Jacobi Bellman ◽  
Monotone Iteration Scheme ◽  
The Value Function

We consider optimal dividend payment under the constraint that the with-dividend ruin probability does not exceed a given value α. This is done in most simple discrete De Finetti models. We characterize the value function V(s,α) for initial surplus s of this problem, characterize the corresponding optimal dividend strategies, and present an algorithm for its computation. In an earlier solution to this problem, a Hamilton-Jacobi-Bellman equation for V(s,α) can be found which leads to its representation as the limit of a monotone iteration scheme. However, this scheme is too complex for numerical computations. Here, we introduce the class of two-barrier dividend strategies with the following property: when dividends are paid above a barrier B, i.e., a dividend of size 1 is paid when reaching B+1 from B, then we repeat this dividend payment until reaching a limit L for some 0≤L≤B. For these strategies we obtain explicit formulas for ruin probabilities and present values of dividend payments, as well as simplifications of the above iteration scheme. The results of numerical experiments show that the values V(s,α) obtained in earlier work can be improved, they are suboptimal.

scholarly journals Optimal dividend strategies for two collaborating insurance companies

2017 ◽  
Vol 49 (2) ◽  
pp. 515-548 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Pablo Azcue ◽  
Nora Muler
Keyword(s):  
Value Function ◽  
Insurance Companies ◽  
Two Dimensional ◽  
Dividend Payments ◽  
Optimal Dividend ◽  
Optimal Value ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
The One ◽  
The Value Function

Abstract We consider a two-dimensional optimal dividend problem in the context of two insurance companies with compound Poisson surplus processes, who collaborate by paying each other's deficit when possible. We study the stochastic control problem of maximizing the weighted sum of expected discounted dividend payments (among all admissible dividend strategies) until ruin of both companies, by extending results of univariate optimal control theory. In the case that the dividends paid by the two companies are equally weighted, the value function of this problem compares favorably with the one of merging the two companies completely. We identify the optimal value function as the smallest viscosity supersolution of the respective Hamilton–Jacobi–Bellman equation and provide an iterative approach to approximate it numerically. Curve strategies are identified as the natural analogue of barrier strategies in this two-dimensional context. A numerical example is given for which such a curve strategy is indeed optimal among all admissible dividend strategies, and for which this collaboration mechanism also outperforms the suitably weighted optimal dividend strategies of the two stand-alone companies.

scholarly journals EVOLUTION OF AMERICAN OPTION VALUE FUNCTION ON A DIVIDEND PAYING STOCK UNDER JUMP-DIFFUSION PROCESSES

2017 ◽  
Vol 2 (3) ◽  
pp. 212-221
Author(s):  
Рехман ◽  
Nazir Rekhman ◽  
Хуссейн ◽  
Zakir Khusseyn ◽  
Али ◽  
...  
Keyword(s):  
Variational Inequalities ◽  
Value Function ◽  
Diffusion Processes ◽  
Equivalent Form ◽  
Jump Diffusion ◽  
American Option ◽  
Option Value ◽  
Jump Diffusion Processes ◽  
Hedging Strategies ◽  
The Value Function

This work is devoted to the analysis and evolution of the value function of American type options on a dividend paying stock under jump diffusion processes. An equivalent form of the value function is obtained and analyzed. Moreover, variational inequalities satisfied by this function are investigated. These results can be used to investigate the optimal hedging strategies and optimal exercise boundaries of the corresponding options.

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.

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