Optimal dividend payments in the classical risk model when payments are subject to both transaction costs and taxes

In this paper, we study optimal dividend problem in the classical risk model. Transaction costs and taxes are required when dividends occur. The problem is formulated as a stochastic impulse control problem. By solving the corresponding quasi-variational inequality, we obtain the analytical solutions of the optimal return function and the optimal dividend strategy when claims are exponentially distributed. We also find a formula for the expected time between dividends. The results show that, as the dividend tax rate decreases, it is optimal for the shareholders to receive smaller but more frequent dividend payments.     

On capital injections and dividends with tax in a diffusion approximation

We consider a diffusion approximation to a risk process with dividends and capital injections. Tax has to be paid on dividends, but capital injections lead to an exemption from tax. That is, tax is only paid for the aggregate excess of dividends over the capital injections. The value of a strategy is the expected value of the discounted dividend payments after tax minus the discounted capital injections. We solve the problem and show that the optimal dividend strategy is a barrier strategy.     

Optimal dividend strategy with transaction costs for an upward jump model

In this paper, we consider the optimal dividend problem with transaction costs when the incomes of a company can be described by an upward jump model. Both fixed and proportional costs are considered in the problem. The value function is defined as the expected total discounted dividends up to the time of ruin. Although the same problem has already been studied in the pure diffusion model and the spectrally negative Lévy process, the optimal dividend problem in an upward jump model has two different aspects in determining the optimal dividends barrier and in the property of the value function. First, the value function is twice continuous differentiable in the diffusion case, but it is not in the jump model. Second, under the spectrally negative Lévy process, downward jumps will not cause any payment actions; however, it might trigger dividend payments when there are upward jumps. In deriving the optimal barriers, we show that the value function is bounded by a linear function. Using this property, we establish the verification theorem for the value function. By solving the quasi-variational inequalities associated with this problem, we obtain the closed-form solution to the value function and hence the optimal dividend strategy when the income sizes follow a common exponential distribution. In the presence of a fixed transaction cost, it is shown that the optimal strategy is a two-barrier policy, and the optimal barriers are only dependent on the fixed cost and not the proportional cost. A numerical example is used to illustrate how the fixed cost plays a significant role in the optimal dividend strategy and also the value function. Moreover, an increased fixed cost results in larger but less frequent dividend payments.     

Semiparametric estimation in the optimal dividend barrier for the classical risk model

In the context of an insurance portfolio which provides dividend income for the insurance company’s shareholders, an important problem in risk theory is how the premium income will be paid to the shareholders as dividends according to a barrier strategy until the next claim occurs whenever the surplus attains the level of ‘barrier’. In this paper, we are concerned with the estimation of optimal dividend barrier, defined as the level of the barrier that maximizes the expected discounted dividends until ruin, under the widely used compound Poisson model as the aggregate claims process. We propose a semi-parametric statistical procedure for estimation of the optimal dividend barrier, which is critically needed in applications. We first construct a consistent estimator of the objective function that is complexly related to the expected discounted dividends and then the estimated optimal dividend barrier as the minimizer of the estimated objective function. In theory, we show that the constructed estimator of the optimal dividend barrier is statistically consistent. Numerical experiments by both simulated and real data analyses demonstrate that the proposed estimators work reasonably well with an appropriate size of samples.     

Optimal dividend control for a generalized risk model with investment incomes and debit interest

This paper investigates dividend optimization of an insurance corporation under a more realistic model, which takes into consideration refinancing or capital injections. The model follows the compound Poisson framework with credit interest for positive reserve and debit interest for negative reserve. Ruin occurs when the reserve drops below the critical value. The company controls the dividend pay-out dynamically with the objective to maximize the expected total discounted dividends until ruin. We show that the optimal strategy, is a band strategy and it is optimal to pay no dividends when the reserve is negative.     

Optimal dividend policy and growth option

We analyse the interaction between the dividend policy and the decision on investment in a growth opportunity of a liquidity constrained firm. This leads us to study a mixed singular control/optimal stopping problem for a diffusion that we solve quasi-explicitly by establishing a connection with an optimal stopping problem. We characterize situations where it is optimal to postpone the distribution of dividends in order to invest at a subsequent date in the growth opportunity. We show that uncertainty and liquidity shocks have an ambiguous effect on the investment decision.      

Morgan Stanley Roundtable on Capital Structure and Payout Policy

A group of finance academics and practitioners discusses a number of topical issues in corporate financial management: Is there such a thing as an optimal, or value‐maximizing, capital structure for a given company? What proportion of a firm's current earnings should be distributed to the firm's shareholders? And under what circumstances should such distributions take the form of stock repurchases rather than dividends? The consensus that emerged was that a company's financing and payout policies should be designed to support its business strategy. For growth companies, the emphasis is on preserving financial fl exibility to carry out the business plan, which means heavy reliance on equity financing and limited payouts. But for companies in mature industries with few major investment opportunities, more aggressive use of debt and higher payouts can add value by reducing taxes and controlling the corporate “free cash flow problem.” Both leveraged financing and cash distributions through dividends and stock buybacks represent a commitment by management to shareholders that the firm's excess cash will not be wasted on projects that produce growth at the expense of profitability. As for the choice between dividends and stock repurchases, dividends appear to provide a stronger commitment to pay out excess cash than open market repurchase programs. Stock buybacks, at least of the open market variety, preserve a higher degree of managerial fl exibility for companies that want to be able to capitalize on unpredictable investment opportunities. But, as with the debt‐equity decision, there is an optimal level of financial fl exibility; too little can mean lost investment opportunities but too much can lead to overinvestment.     

Optimal Dynamic Premium Control in Non-life Insurance. Maximizing Dividend Pay-outs

In this paper we consider the problem of finding optimal dynamic premium policies in non-life insurance. The reserve of a company is modeled using the classical Cramér-Lundberg model with premium rates calculated via the expected value principle. The company controls dynamically the relative safety loading with the possibility of gaining or loosing customers. It distributes dividends according to a 'barrier strategy' and the objective of the company is to find an optimal premium policy and dividend barrier maximizing the expected total, discounted pay-out of dividends. In the case of exponential claim size distributions optimal controls are found on closed form, while for general claim size distributions a numerical scheme for approximations of the optimal control is derived. Based on the idea of De Vylder going back to the 1970s, the paper also investigates the possibilities of approximating the optimal control in the general case by using the closed form solution of an approximating problem with exponential claim size distributions.     

MORGAN STANLEY ROUNDTABLE ON Capital Structure and Payout Policy

A group of distinguished finance academics and practitioners discuss a number of topical issues in corporate financial management: Is there such a thing as an optimal, or value‐maximizing, capital structure for a given company? What proportion of a firm's current earnings should be distributed to the firm's shareholders? And under what circumstances should such distributions take the form of stock repurchases rather than dividends? The consensus that emerges is that a company's financing and payout policies should be designed to support its business strategy. For growth companies, the emphasis is on preserving financial flexibility to carry out the business plan, which means heavy reliance on equity financing and limited payouts. But for companies in mature industries with few major investment opportunities, more aggressive use of debt and higher payouts can add value both by reducing taxes and controlling the corporate free cash flow problem. In such cases, both leveraged financing and cash distributions through dividends and stock buybacks signal management's commitment to its shareholders that the firm's excess cash will not be wasted on projects that produce low‐return growth that comes at the expense of profitability. As for the choice between dividends and stock repurchases, dividends provide a stronger commitment to pay out excess cash than open market repurchase programs. Stock buybacks, at least of the open market variety, preserve more flexibility for companies that want to be able to capitalize on unpredictable investment opportunities. But, as with the debt‐equity decision, there is an optimal level of financial flexibility: too little can mean lost investment opportunities, but too much can lead to overinvestment.     

Geometric Brownian Motion Models for Assets and Liabilities: From Pension Funding to Optimal Dividends

Abstract

In this paper asset and liability values are modeled by geometric Brownian motions. In the first part of the paper we consider a pension plan sponsor with the funding objective that the pension asset value is to be within a band that is proportional to the pension liability value. Whenever the asset value is about to fall below the lower barrier or boundary of the band, the sponsor will provide sufficient funds to prevent this from happening. If, on the other hand, the asset value is about to exceed the upper barrier of the band, the assets are reduced by the potential overflow and returned to the sponsor. This paper calculates the expected present value of the payments to be made by the sponsor as well as that of the refunds to the sponsor. In particular we are interested in situations where these two expected values are equal. In the second part of the paper the refunds at the upper barrier are interpreted as the dividends paid to the shareholders of a company according to a barrier strategy. However, if the (modified) asset value ever falls to the liability value, which is the lower barrier, “ruin” takes place, and no more dividends can be paid. We derive an explicit expression for the expected discounted dividends before ruin. From this we find an explicit expression for the proportionality constant of the upper barrier that maximizes the expected discounted dividends. If the initial asset value is the optimal upper barrier, there is a particularly simple and intriguing expression for the expected discounted dividends, which can be interpreted as the present value of a deterministic perpetuity with exponentially growing payments.     

Moments of Discounted Dividends for a Threshold Strategy in the Compound Poisson Risk Model

Abstract

We consider a compound Poisson risk model in which part of the premium is paid to the shareholders as dividends when the surplus exceeds a specified threshold level. In this model we are interested in computing the moments of the total discounted dividends paid until ruin occurs. However, instead of employing the traditional argument, which involves conditioning on the time and amount of the first claim, we provide an alternative probabilistic approach that makes use of the (defective) joint probability density function of the time of ruin and the deficit at ruin in a classical model without a threshold. We arrive at a general formula that allows us to evaluate the moments of the total discounted dividends recursively in terms of the lower-order moments. Assuming the claim size distribution is exponential or, more generally, a finite shape and scale mixture of Erlangs, we are able to solve for all necessary components in the general recursive formula. In addition to determining the optimal threshold level to maximize the expected value of discounted dividends, we also consider finding the optimal threshold level that minimizes the coefficient of variation of discounted dividends. We present several numerical examples that illustrate the effects of the choice of optimality criterion on quantities such as the ruin probability.     

The valuation of warrants: Implementing a new approach

The option pricing model developed by Black and Scholes and extended by Merton gives rise to partial differential equations governing the value of an option. When the underlying stock pays no dividends – and in some very restrictive cases when it does – a closed form solution to the differential equation subject to the appropriate boundary conditions, has been obtained. But, in some relevant cases such as the one in which the stock pays discrete dividends, no closed form solution has been found. This paper shows how to solve these equations by numerical methods. In addition, the optimal strategy for exercising American options is derived. A numerical illustration of the procedure is also presented.     

Signaling, Free Cash Flow and "Nonmonotonic" Dividends

Many argue that dividends signal future earnings or dispose of excess cash. Empirical support is inconclusive, potentially because no model combines both rationales. This paper does. Higher quality firms pay dividends to eliminate the free cash-flow problem, while firms that outsiders perceive as lower quality pay dividends to signal future earnings and reduce the free cash-flow problem. In equilibrium, dividends are nonmonotonic with respect to the signal observed by outsiders; the highest quality firms pay smaller dividends than lower perceived quality firms. The model reconciles the existing literature and generates new empirical predictions that are tested and supported.     

Do non-financial factors influence corporate dividend policies? Evidence from business strategy

In this paper, we examine the influence of business strategy on dividend policy. We find that firms following an innovation-oriented strategy (prospectors) pay significantly lower dividends than those following an efficiency-oriented strategy (defenders). Our cross-sectional analyses show that such association is more pronounced among firms with greater investment opportunities and superior performance. Further analysis reveals that prospectors make significantly more capital investment, consistent with prospectors paying fewer dividends to finance their investment activities. Moreover, we address potential endogeneity concerns by implementing (i) a triple-difference analysis (DiDiD) that exploits an exogenous shock that hinders innovation through curbing the supply of highly skilled employees and (ii) an instrumental variable approach. Our results are robust to a propensity-score-matched (PSM) analysis, the inclusion of individual business strategy components, and the use of alternative measures of the dependent variables. Overall, our findings highlight business strategy as an inherent and non-financial determinant of dividend policies.     

Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest

Abstract

In the absence of investment and dividend payments, the surplus is modeled by a Brownian motion. But now assume that the surplus earns investment income at a constant rate of credit interest. Dividends are paid to the shareholders according to a barrier strategy. It is shown how the expected discounted value of the dividends and the optimal dividend barrier can be calculated; Kummer’s confluent hypergeometric differential equation plays a key role in this context. An alternative assumption is that business can go on after ruin, as long as it is profitable. When the surplus is negative, a higher rate of debit interest is applied. Several numerical examples document the influence of the parameters on the optimal dividend strategy.     

Financial Contracting and Leverage Induced Over- and Under-Investment Incentives

This paper investigates the effects of seniority rules and restrictive dividend convenants on the over- and under-investment incentives associated with risky debt. We show that increasing seniority of new debt decreases the incidence of under-investment but increases over-investment, and vice versa. Under symmetric information, the optimal seniority rule is to give new debtholders first claim on a new project without recourse to existing assets (i.e., project financing). Under asymmetric information, the optimal debt contract requires equating the expected return to new debtholders in the default state to the new project's cash flow in the same rate. If this is not possible, the optimal seniority rule calls for strict subordination of new debt if the expected cash flow in default is small and full seniority if it is large. With regard to dividend convenants, we show that their effect depends on whether or not dividend payments are conditioned on future investments. When they are unconditioned, allowing more dividends increases the under-investment incentive. In contrast, conditional dividends decrease the underinvestment incentive and increase the over-investment incentive.     

American options: the EPV pricing model

Summary We explicitly solve the pricing problem for perpetual American puts and calls, and provide an efficient semi-explicit pricing procedure for options with finite time horizon. Contrary to the standard approach, which uses the price process as a primitive, we model the price process as the expected present value of a stream, which is a monotone function of a Lévy process. Certain processes exhibiting mean-reverting, stochastic volatility and/or switching features can be modeled this way. This specification allows us to consider assets that pay no dividends at all when the level of the underlying stochastic factor is too low, assets that pay dividends at a fixed rate when the underlying stochastic process remains in some range, or capped dividends.The authors are grateful to the anonymous referees for valuable comments and suggestions.     

Inside shareholders’ effective tax rates and dividends

Using information collected from the Swedish tax authorities, we calculate insiders’ actual effective tax rates on dividends. With this unique dataset, we find a significant negative cross-sectional relationship between insiders’ effective tax rates and dividend payout. This result is consistent with a tax-induced clientele effect for dividends. We also look at the impact of large block trades on dividends. We find that when insiders with zero effective taxes sell blocks, subsequent dividend payments are significantly more likely to decrease. This provides evidence that large shareholders are adjusting dividends for their individual tax situations.     

Optimal dividend policy,debt policy and the level of investment within a multi-period DCF framework

This paper simultaneously analyses optimal dividend, debt and investment policy within a conventional multi-period DCF framework, and takes account of differential personal taxation over both investors and types of income, the effect of dividends and interest on the level of share issues and hence share issue costs, and the effect of dividends and interest on the level of internally-financed investment. Application of the model to three distinct tax regimes reveals that the value benefit from debt is small at best whilst the value benefit from dividends is substantial even in a regime without dividend imputation.