Present Value Of Dividend Payments Research Articles

Nonparametric estimation of some dividend problems in the perturbed compound Poisson model

In this paper, we consider some dividend problems in the perturbed compound Poisson model under a constant barrier dividend strategy. We approximate the expected present value of dividend payments before ruin and the expected discounted penalty function based on the COS method, and construct some nonparametric estimators by using a random sample on claim number and individual claim sizes. Under a large sample size setting, we perform an error analysis of the estimators. We also provide some simulation results to verify the effectiveness of this estimation method when the sample size is finite.

On a Discrete-Time Risk Model with Random Income and a Constant Dividend Barrier

In this paper, a discrete-time risk model with random income and a constant dividend barrier is considered. Under such a dividend policy, once the insurer’s reserve hits the level b b > 0 , the excess of the reserve over b is paid off as dividends. We derive a homogeneous difference equation for the expected present value of dividend payments. Corresponding solution procedures for the difference equation are invested. Finally, we give a numerical example to illustrate the applicability of the results obtained.

A Stochastic Control Problem with Linearly Bounded Control Rates in a Brownian Model

In this paper, we consider a stochastic control problem with linearly bounded control/payment rates using a performance function given by the expected present value of dividend payments made up to ...

Statistical estimation for some dividend problems under the compound Poisson risk model

In this paper, we consider some dividend problems in the classical compound Poisson risk model under a constant barrier dividend strategy. Suppose that the Poisson intensity for the claim number process and the distribution for the individual claim sizes are both unknown. We use the COS method to study the statistical estimation for the expected present value of dividend payments before ruin and the expected discounted penalty function. The convergence rates under large sample setting are derived. Some simulation results are also given to show effectiveness of the estimators under finite sample setting.

The Erlang(n) risk model with two-sided jumps and a constant dividend barrier

In this paper, the Erlang(n) risk model with two-sided jumps and a constant dividend barrier is considered. In the analysis of the expected discounted penalty function, the downward jumps are assumed to have an arbitrary distribution function and the upward jumps are assumed to be exponentially distributed. An integro-differential equation with boundary conditions for the expected discounted penalty function is derived and the solution is provided. The defective renewal equation for the expected discounted penalty function with no barrier is derived. In the analysis of the moments of the discounted dividend payments until ruin, we assume that the inter-jump times are generalized Erlang(n) distributed. An integro-differential equation for the mth moment function of the discounted sum of dividend payments until ruin is derived. Numerical examples are also given to obtain the expressions for the expected discounted penalty function and the expected present value of dividend payments.

On a discrete-time risk model with time-dependent claims and impulsive dividend payments

A discrete-time risk model with a mathematically tractable dependence structure between interclaim times and claim sizes is considered in the presence of an impulsive dividend strategy. Under such a strategy, once the insurer's reserve upcrosses the level b, the excess of the reserve over is paid off as dividends. We derive difference equations for both the expected discounted penalty function and the expected present value of dividend payments. Solution procedures for these difference equations are provided. When the joint distribution of the interclaim time and claim size is a finite mixture of bivariate geometric distributions, closed-form expressions are given. Numerical results for several sets of parameters are also provided to illustrate the applicability of the results obtained.

OPTIMAL FINANCING AND DIVIDEND DISTRIBUTION WITH TRANSACTION COSTS IN THE CASE OF RESTRICTED DIVIDEND RATES

AbstractWe consider the optimal financing (capital injections) and dividend payment problem for a Brownian motion model in the case of restricted dividend rates. The company has no obligation to inject capitals and therefore, the bankruptcy risk is present. Capital injections, if any, will incur both fixed and proportional transaction costs and dividend payments incur proportional transaction costs. The aim is to find the optimal strategy to maximize the expected present value of dividend payments minus the total cost of capital injections up to the time of bankruptcy. The problem is formulated as a mixed impulse-regular control problem. We address the problem via studying three cases of two auxiliary functions. We derive important analytical properties of the auxiliary functions and use them to study the value function and then identify the optimal control strategy. We show that the optimal dividend control is of threshold type and the optimal financing strategy prescribes to either never inject capitals or inject capitals only when the surplus reaches 0 with a fixed lump sum amount.

The perturbed compound Poisson risk model with linear dividend barrier

In this paper, we consider a diffusion perturbed classical compound Poisson risk model in the presence of a linear dividend barrier. Partial integro-differential equations for the moment generating function and the nth moment of the present value of all dividends until ruin are derived. Moreover, explicit solutions for the nth moment of the present value of dividend payments are obtained when the individual claim size distribution is exponential. We also provided some numerical examples to illustrate the applications of the explicit solutions. Finally we derive partial integro-differential equations with boundary conditions for the Gerber–Shiu function.

Some Optimal Dividend Problems for a Surplus Process with Stochastic Interest

In this paper, some results on the dividend payments prior to ruin in the classical surplus process with stochastic interest are derived. An integro-differential equation with a boundary conditions satisfied by the expected present value of dividend payments is derived and solved. Furthermore, closed-form expressions for exponential claims are given.

Distribution of the Present Value of Dividend Payments in a Lévy Risk Model

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

Distribution of the Present Value of Dividend Payments in a Lévy Risk Model

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

Distribution of the Present Value of Dividend Payments in a Lévy Risk Model

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

Constant dividend barrier in a risk model with interclaim-dependent claim sizes

The risk model with interclaim-dependent claim sizes proposed by Boudreault et al. [Boudreault, M., Cossette, H., Landriault, D., Marceau, E., 2006. On a risk model with dependence between interclaim arrivals and claim sizes. Scand. Actur. J., 265–285] is studied in the presence of a constant dividend barrier. An integro-differential equation for some Gerber–Shiu discounted penalty functions is derived. We show that its solution can be expressed as the solution to the Gerber–Shiu discounted penalty function in the same risk model with the absence of a barrier and a combination of two linearly independent solutions to the associated homogeneous integro-differential equation. Finally, we analyze the expected present value of dividend payments before ruin in the same class of risk models. An homogeneous integro-differential equation is derived and then solved. Its solution can be expressed as a different combination of the two fundamental solutions to the homogeneous integro-differential equation associated to the Gerber–Shiu discounted penalty function.

Optimal Dividends Under a Ruin Probability Constraint

ABSTRACTWe consider a classical surplus process modified by the payment of dividends when the insurer's surplus exceeds a threshold. We use a probabilistic argument to obtain general expressions for the expected present value of dividend payments, and show how these expressions can be applied for certain individual claim amount distributions. We then consider the question of maximising the expected present value of dividend payments subject to a constraint on the insurer's ruin probability.

On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang( n) interclaim times

In this paper, we present some results on the distribution of dividend payments until ruin under a Sparre Andersen risk model with generalized Erlang( n)-distributed inter-claim times and a constant dividend barrier. An integro-differential equation for the moment-generating function of the sum of the discounted dividend payments until ruin is derived. Moreover, explicit solutions for arbitrary moments of the present value of dividend payments are obtained, when the individual claim amounts have a distribution with rational Laplace transform. Numerical illustrations of the results are given for an Erlang(2) risk model and Erlang(2)-distributed claim amounts.

Some Optimal Dividends Problems

We consider a situation originally discussed by De Finetti (1957) in which a surplus process is modified by the introduction of a constant dividend barrier. We extend some known results relating to the distribution of the present value of dividend payments until ruin in the classical risk model and show how a discrete time risk model can be used to provide approximations when analytic results are unavailable. We extend the analysis by allowing the process to continue after ruin.

Some Optimal Dividends Problems

We consider a situation originally discussed by De Finetti (1957) in which a surplus process is modified by the introduction of a constant dividend barrier. We extend some known results relating to the distribution of the present value of dividend payments until ruin in the classical risk model and show how a discrete time risk model can be used to provide approximations when analytic results are unavailable. We extend the analysis by allowing the process to continue after ruin.

Simulation methods in ruin models with non-linear dividend barriers

In this paper, a collective risk reserve process of an insurance portfolio characterized by a homogeneous Poisson claim number process, a constant premium flow and independent and identically distributed claims is considered. In the presence of a non-linear dividend barrier strategy and interest on the free reserve we derive equations for the probability of ruin and the expected present value of dividend payments which give rise to several numerical number-theoretic solution techniques. For various claim size distributions and a parabolic barrier numerical tests and comparisons of these techniques are performed. In particular, the efficiency gain obtained by implementing low-discrepancy sequences instead of pseudo-random sequences is investigated.