Optimal Dividend Strategy Research Articles

On optimal joint reflective and refractive dividend strategies in spectrally positive Lévy models

The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this context, numerous papers considered threshold (refractive) and barrier (reflective) dividend strategies. These were shown to be optimal in a number of different contexts for bounded and unbounded payout rates, respectively.In this paper, motivated by the behavior of some dividend paying stock exchange companies, we determine the optimal dividend strategy when both continuous (refractive) and lump sum (reflective) dividends can be paid at any time, and if they are subject to different transaction rates.We consider the general family of spectrally positive Lévy processes. Using scale functions, we obtain explicit formulas for the expected present value of dividends until ruin, with a penalty at ruin. We develop a verification lemma, and show that a two-layer (a,b) strategy is optimal. Such a strategy pays continuous dividends when the surplus exceeds level a>0, and all of the excess over b>a as lump sum dividend payments. Results are illustrated.

On capital injections and dividends with tax in a classical risk model

Consider the classical risk model with dividends and capital injections. In addition to the model considered by Kulenko and Schmidli (2008), tax has to be paid for dividends. Capital injections yield tax exemptions. We calculate the value function and derive the optimal dividend strategy.

Stochastic Finance of a Company Associated with Ruin, Restricted Reserve, Dividends and Dividend Strategy

In this paper a dual model of classical risk theory is considered to study the expected value of discounted dividends using imbedding method. The optimal dividend strategy is obtained in different forms. By the same technique the classical model is also analyzed. Further in the dual model expenses of a company are taken as proportional to the surplus to obtain optimal barrier strategy. We also consider a model with two components of incomes to the company in analyzing the optimal dividend strategy. In the dual model jump-diffusion is also introduced to determine the two components of dividends due to jump-gains and jump-diffusion.

Optimal dividend and equity issuance in the perturbed dual model under a penalty for ruin

ABSTRACTIn this paper, we consider the dividends and equity issuances control problem in the perturbed dual model under a penalty for ruin. Transaction costs are incurred by these business activities: dividend is taxed and fixed costs are generated by equity issuance. The objective is to maximize the expected present value of dividends minus the discounted costs of equity issuances and the discounted penalty until the ruin time. We find the joint optimal dividend and equity issuance strategy by solving the control problems of two categories of suboptimal model. Furthermore, we derive the explicit closed solutions for the value functions and the optimal strategies when the jumps are mixed exponential. In particular, we investigate the effects of the penalty, the proportional and fixed transaction costs, the expense rate and the force of interest on the optimal strategies by numerical calculations, and give some interesting economic insights.

Optimal Investment in a Dual Risk Model

Dual risk models are popular for modeling a venture capital or high tech company, for which the running cost is deterministic and the profits arrive stochastically over time. Most of the existing literature on dual risk models concentrated on the optimal dividend strategies. In this paper, we propose to study the optimal investment strategy on research and development for the dual risk models to minimize the ruin probability of the underlying company. We will also study the optimization problem when in addition the investment in a risky asset is allowed.

Optimal dividend strategies in a delayed claim risk model with dividends discounted by stochastic interest rates

We consider a discrete-time risk model with delayed claims and a dividend payment strategy. It is assumed that every main claim will induce a by-claim which may be delayed for one time period with a certain probability. In the evaluation of the expected present value of dividends, the interest rates are assumed to follow a Markov chain with finite state space. Dividends are paid to the shareholders according to an admissible strategy. The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin minus the expected discounted penalty value at ruin. We obtain some properties of the optimal dividend-payment strategy, and offer high efficiency algorithms for obtaining the optimal strategy, the optimal value function and the expectation of time of ruin under the optimal strategy. Our method is mainly to transform the value function. Numerical examples are presented to illustrate the transformation method and the impact of the penalty for ruin on the optimal strategy, the corresponding expected present value of dividends and the expectation of time of ruin.

Convexity of Ruin Probability and Optimal Dividend Strategies for a General Lévy Process.

We consider the optimal dividends problem for a company whose cash reserves follow a general Lévy process with certain positive jumps and arbitrary negative jumps. The objective is to find a policy which maximizes the expected discounted dividends until the time of ruin. Under appropriate conditions, we use some recent results in the theory of potential analysis of subordinators to obtain the convexity properties of probability of ruin. We present conditions under which the optimal dividend strategy, among all admissible ones, takes the form of a barrier strategy.

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

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).

Optimal dividend strategy in compound binomial model with bounded dividend rates

We consider the compound binomial model, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant. The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique solution of a discrete HJB equation. Moreover, we obtain some properties of the optimal payment strategy, and offer a simple algorithm for obtaining the optimal strategy. The key of our method is to transform the value function. Numerical examples are presented to illustrate the transformation method.

The Optimal Dividend Problem in the Dual Model

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

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.

Optimal dividend strategies with time-inconsistent preferences

This paper studies the optimal dividend strategies of an insurance company when the manager has time-inconsistent preferences. We consider the problem for a naive manager and a sophisticated manager, and analytically derive the optimal dividend strategies when claim sizes follow an exponential distribution. Our results show that the manager with time-inconsistent preferences tends to pay out dividends earlier than her time-consistent counterpart and that the sophisticated manager is more inclined to pay out dividends than the naive manager. Furthermore, we extend these results to the case with claim sizes following a mixed exponential distribution, and provide a numerical analysis to reveal the sensitivity of the optimal dividend strategies to changes in the premium, claims and surplus volatility.

Optimal dividend payout for classical risk model with risk constraint

In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramer-Lundberg risk model subject to both proportional and fixed transaction costs. We assume that dividend payments are prohibited unless the surplus of insurance company has reached a level b. Given fixed level b, we derive a integro-differential equation satisfied by the value function. By solving this equation we obtain the analytical solutions of the value function and the optimal dividend strategy when claims are exponentially distributed. Finally we show how the threshold b can be determined so that the expected ruin time is not less than some T. Also, numerical examples are presented to illustrate our results.

ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS

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.

Bayesian Dividend Optimization and Finite Time Ruin Probabilities

We consider the valuation problem of an (insurance) company under partial information. Therefore, we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant and observable volatility and constant but unknown drift parameter. For transforming the problem to a problem with complete information, we derive a suitable filter. The optimal value function is characterized as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. We state a numerical procedure for approximating both the optimal dividend strategy and the corresponding value function. Furthermore, threshold strategies are discussed in some detail. Finally, we calculate the probability of ruin in the uncontrolled and controlled situation.

Optimal Dividend Problem for a Compound Poisson Risk Model

In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model includes the classical risk model and the Pólya-Aeppli risk model as special cases. 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 under some conditions the optimal dividend strategy is formed by a barrier strategy. Moreover, two conjectures are proposed.

Singular optimal dividend control for the regime-switching Cramér–Lundberg model with credit and debit interest

We investigate the dividend optimization problem for a company whose surplus process is modeled by a regime-switching compound Poisson model with credit and debit interest. The surplus process is controlled by subtracting the cumulative dividends. The performance of a dividend distribution strategy which determines the timing and amount of dividend payments, is measured by the expectation of the total discounted dividends until ruin. The objective is to identify an optimal dividend strategy which attains the maximum performance. We show that a regime-switching band strategy is optimal.

An optimal dividend strategy in the discrete Sparre Andersen model with bounded dividend rates

We consider the discrete Sparre Andersen risk model and its derivative models by anew setting up the initial times, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant. The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique bounded solution of a set of discrete Hamilton–Jacobi–Bellman equations. Moreover, we introduce Bellman’s recursive algorithm and offer a simpler algorithm to obtain the optimal strategy and the optimal value functions. Our method is mainly to transform the value functions. Numerical examples are presented to illustrate the transformation method.

On the expected discounted penalty function and optimal dividend strategy for a risk model with random incomes and interclaim-dependent claim sizes

In this paper, we consider a risk model with dependence between claim sizes and interclaim arrivals. In contrast with the classical risk model where the premium process is a linear function of time, we consider a dependent risk model where the aggregate premium process is a compound Poisson process, moreover, there is a constant barrier strategy in this model. The integral equations for the expected discounted penalty function and the expected discounted dividend payments until ruin are obtained. In particular, when the individual stochastic premium amount is exponentially distributed, it is proved that both the expected discounted penalty function and the expected discounted dividend payments until ruin satisfy the Volterra integral equations. Furthermore, the representations of the solutions are derived, respectively. In addition, when the individual stochastic premium amount and claim amount are exponentially distributed, we can get the explicit expressions for the Laplace transform of the ruin time and the expected discounted dividend payments until ruin. Finally, the optimal barrier is presented under the condition of maximizing the expectation of the difference between discounted dividends until ruin and the deficit at ruin.

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

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.