Dividend Strategy Research Articles

On the bailout dividend problem with periodic dividend payments for spectrally negative Markov additive processes

This paper studies the bailout optimal dividend problem with regime switching under the constraint that dividend payments can be made only at the arrival times of an independent Poisson process while capital can be injected continuously in time. We show the optimality of the regime-modulated Parisian-classical reflection strategy when the underlying risk model follows a general spectrally negative Markov additive process. In order to verify the optimality, first we study an auxiliary problem driven by a single spectrally negative Lévy process with a final payoff at an exponential terminal time and characterize the optimal dividend strategy. Then, we use the dynamic programming principle to transform the global regime-switching problem into an equivalent local optimization problem with a final payoff up to the first regime switching time. The optimality of the regime modulated Parisian-classical barrier strategy can be proven by using the results from the auxiliary problem and approximations via recursive iterations.

On the dual risk model with Parisian implementation delays under a mixed dividend strategy

AbstractIn this paper, we consider a mixed dividend strategy in a dual risk model. The mixed dividend strategy is the combination of a threshold dividend and a Parisian implementation delays dividend under periodic observation. Given a series of discrete observation points, when the surplus level is larger than the predetermined bonus barrier at observation point, the Parisian implementation delays dividend is immediately carried out, and the threshold dividend is performed continuously during the delayed period. We study the Gerber-Shiu expected discounted penalty function and the expected discounted dividend payments before ruin in such a dual risk model. Numerical illustrations are given to study the influence of relevant parameters on the ruin-related quantities and the selection of the optimal dividend barrier for a given initial surplus level.

Influence of economic factors on the share’s value through the concepts of the life cycle: The case of Indonesia

The article aimed to substantiate the differentiated impact of critical internal factors of the economic activities on the market value of shares for joint-stock companies accounting for the organizational development cycle. Using the Company’s Financial Statements in the Automotive and Component subsectors listed on the Indonesia Stock Exchange for 2008-2021, the Chow test, path analysis, and t-criterion, we determined the features of the relationship between the share price and the economic performance indicators of joint-stock companies are determined. We used path analysis for modeling to assess the relationship between the price of shares and the number of dividend payments per share, asset turnover, and net profit per share built. A differentiated nature of the relationship between the indicators depending on the accounting company’s life cycle has been established. Knowing the stage of the business, the company can develop the most effective dividend strategy and determine the appropriate management method.

A refracted Lévy process with delayed dividend pullbacks

ABSTRACT The threshold dividend strategy, under which dividends are paid only when the insurer's surplus exceeds a pre-determined threshold, has received considerable attention in risk theory. However, in practice, it seems rather unlikely that an insurer will immediately pull back the dividend payments as soon as its surplus level drops below the dividend threshold. Hence, in this paper, we propose a refracted Lévy risk model with delayed dividend pullbacks triggered by a certain Poissonian observation scheme. Leveraging the extensive literature on fluctuation identities for spectrally negative Lévy processes, we obtain explicit expressions for two-sided exit identities of the proposed insurance risk process. Also, penalties are incorporated into the analysis of dividend payouts as a mechanism to penalize for the volatility of the dividend policy and account for an investor's typical preference for more stable cash flows. An explicit expression for the expected (discounted) dividend payouts net of penalties is derived. The criterion for the optimal threshold level that maximizes the expected dividend payouts is also discussed. Finally, several numerical examples are considered to assess the impact of dividend delays on ruin-related quantities. We numerically show that dividend strategies with more steady dividend payouts can be preferred (over the well-known threshold dividend strategy) when penalty fee become too onerous.

Optimal dividend and capital injection strategies in common shock dependence model with time-inconsistent preferences

<p style='text-indent:20px;'>This paper discusses the optimal dividend and capital injection problems when an insurance company has two lines of business with common shock dependence. Suppose that the manager of the company has time-inconsistent preference, which can be described by a quasi-hyperbolic discount function. The value of the company is measured by the expected discounted dividend payments minus the expected discounted costs of capital injection. The goal is to find out the optimal strategies for maximizing the value of the company. By using the stochastic control techniques, we solve the problems in all cases of time-consistent preference manager, naive manager and sophisticated manager, respectively. The closed-form solutions of the value functions are presented. Our results show that the sophisticated manager is inclined to pay out dividends earlier than the naive manager, time-inconsistent preference manager is more likely to pay dividends in advance than time-consistent preference manager. Furthermore, we provide some numerical analysis to reveal the sensitivity of the optimal dividend strategies to the dependence intensity and the cost of capital injection. The results show that, as the cost of capital injection increases, sophisticated manager will give up capital injection first, followed by naive manager. In addition, we also find that: when the cost of capital injection is low, managers think that the value of the company that undertakes two kinds of insurance with high correlation is higher; while, managers have opposite evaluations, when the cost of capital injection is high.</p>

A Lévy risk model with ratcheting and barrier dividend strategies

<p style='text-indent:20px;'>The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this paper, we consider the two-layer <inline-formula><tex-math id="M1">\begin{document}$ (a, b) $\end{document}</tex-math></inline-formula> dividend strategy when the risk process is modeled by a spectrally negative Lévy process, such a strategy has an increasing dividend rate when the surplus exceeds level <inline-formula><tex-math id="M2">\begin{document}$ a>0 $\end{document}</tex-math></inline-formula>, and all of the excess over <inline-formula><tex-math id="M3">\begin{document}$ b>a $\end{document}</tex-math></inline-formula> as lump sum dividend payments. Using fluctuation identities and scale functions, we obtain explicit formulas for the expected net present value of dividends until ruin and the Laplace transform of the time to ruin. Finally, numerical illustrations are present to show the impacts of parameters on the expected net present value.</p>

Numerical Method for a Perturbed Risk Model with Proportional Investment

In this paper, we study the perturbed risk model with a threshold dividend strategy and proportional investment. The insurance companies are allowed to invest their surplus in a financial market consisting of a risk-free asset and a risky asset in fixed proportions; the risky assets are modeled by the jump-diffusion process. Firstly, using the theory of the stochastic process and stochastic analysis, we obtained the integro-differential equations satisfied by the expected discounted dividend payments and the discounted penalty function. Secondly, we obtained the numerical approximate solutions of the integro-differential equations through the sinc method, since the analytical solutions of them are not easy to obtain, and we found that the error is within a manageable range. Finally, we considered some numerical examples where the claim sizes follow an exponential distribution, a mixture of two exponential distributions or the lognormal distribution in detail, and explored how perturbations and proportional investment affect dividends and ruin probability. Moreover, sensitive analysis showed that the proportion of the risky investment, the diffusion coefficient, the distribution of the claims and the positive jump in the risky assets investment all have explicit impacts on dividends and ruin probability.

Recursive Approaches for Multi-Layer Dividend Strategies in a Phase-Type Renewal Risk Model

In this paper we consider a risk model with two independent classes of insurance risks in the presence of a multi-layer dividend strategy. We assume that both of the claim number processes are renewal processes with phase-type inter-arrival times. By analysing the Markov chains associated with the two given phase-type distributions of the inter-arrival times, algorithmic schemes for the determination of explicit expressions for the Gerber–Shiu expected discounted penalty function, as well as the expected discounted dividend payments are derived, using two different approaches.

Optimal dividend bands revisited: a gradient-based method and evolutionary algorithms

We reconsider the study of optimal dividend strategies in the Cramér-Lundberg risk model. It is well-known that the solution of the classical dividend problem is in general a band strategy. However, the numerical techniques for the identification of the optimal bands available in the literature are very hard to implement and explicit numerical results are known for very few cases only. In this paper we put a gradient-based method into place which allows to determine optimal bands in more general situations. In addition, we adapt an evolutionary algorithm to this dividend problem, which is not as fast, but applicable in considerable generality, and can serve for providing a competitive benchmark. We illustrate the proposed methods in concrete examples, reproducing earlier results in the literature as well as establishing new ones for claim size distributions that could not be studied before.

Some optimisation problems in insurance with a terminal distribution constraint

In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time T follows a normal distribution with a given mean and a given variance. In both cases, the surplus of the insurance company is assumed to follow a Brownian motion with drift. First, we allow the insurance company to pay dividends and seek to maximise the expected discounted dividend payments or to minimise the ruin probability under the terminal distribution constraint. Here, we find explicit expressions for the optimal strategies in both cases, when the dividend strategy is updated at discrete points in time and continuously in time. Second, we let the insurance company buy a reinsurance contract for a pool of insured or a branch of business. We set the initial capital to zero in order to verify whether the premia are sufficient to buy reinsurance and to manage the risk of incoming claims in such a way that the desired risk characteristics are achieved at some terminal time without external help (represented, for instance, by a positive initial capital). We only allow for piecewise constant reinsurance strategies producing a normally distributed terminal surplus, whose mean and variance lead to a given Value at Risk or Expected Shortfall at some confidence level α. We investigate the question which admissible reinsurance strategy produces a smaller ruin probability, if the ruin-checks are due at discrete deterministic points in time.

Approximating the classical risk process by stable Lévy motion

The classical Cramér–Lundberg risk process is commonly used to model the surplus of an insurer; it characterizes the claim arrival process and the claim size random variable Y through a compound Poisson process, along with a constant rate of premium income. When , the process can be approximated by a diffusion process, but that requirement eliminates many heavy-tailed claim models, such as the Pareto with . In this paper, we generalize the well known diffusion approximation by assuming that Y lies in the domain of attraction of an α-stable random variable, for . Then, we construct a sequence of classical Cramér–Lundberg risk processes and show that the sequence converges to an α-stable Lévy motion in the Skorokhod -topology. We prove this convergence by proving the pointwise convergence of the corresponding Laplace exponents of our processes, which to our knowledge, is a new result. To apply this convergence result, we show the convergence of a sequence of Gerber–Shiu distributions of exponential Parisian ruin, and we show the convergence of a sequence of payoff functions for barrier dividend strategies. Both of these applications provide new proofs of the stated limits.

Optimal excess of loss reinsurance-barrier dividend strategies with investment

The optimal barrier dividend problem under excess of loss reinsurance strategy has rarely been studied so far. We combine the risk factors such as market friction and terminal residual value with risk investment and risk control strategy, and study the resulting optimal investment-excess of loss reinsurance-barrier dividend problem. Based on the dynamic programming principle, we establish the Hamilton-Jacobi-Bellman equation, and obtain the explicit solutions for the optimal investment-excess of loss reinsurance strategy. The optimal dividend function is solved by the differential-integral method. The existence and uniqueness of the optimal dividend boundary is proved.

On the surplus management of funds with assets and liabilities in presence of solvency requirements

In this paper, we consider a company whose assets and liabilities evolve according to a correlated bivariate geometric Brownian motion, such as in Gerber and Shiu [(2003). Geometric Brownian motion models for assets and liabilities: From pension funding to optimal dividends. North American Actuarial Journal 7(3), 37–56]. We determine what dividend strategy maximises the expected present value of dividends until ruin in two cases: (i) when shareholders won't cover surplus shortfalls and a solvency constraint [as in Paulsen (2003). Optimal dividend payouts for diffusions with solvency constraints. Finance and Stochastics 7(4), 457–473] is consequently imposed and (ii) when shareholders are always to fund any capital deficiency with capital (asset) injections. In the latter case, ruin will never occur and the objective is to maximise the difference between dividends and capital injections. Developing and using appropriate verification lemmas, we show that the optimal dividend strategy is, in both cases, of barrier type. Both value functions are derived in closed form. Furthermore, the barrier is defined on the ratio of assets to liabilities, which mimics some of the dividend strategies that can be observed in practice by insurance companies. The existence and uniqueness of the optimal strategies are shown. Results are illustrated.

Revealing the impact of a water-economy nexus-based joint tax management policy on the environ-economic system: An advanced exploration of double dividend strategies and multi-scale response mechanisms

Economic growth is constrained by water scarcity, and a unified policy analysis framework is required to enhance the coordinated development of the environ-economic system from the perspective of wastewater management. Thus, a multi-scale water-economic double dividend mechanism model (MWED) is first developed to (i) derive strategies for simultaneously achieving water scarcity mitigation and economic increase through compounding wastewater tax (WT) policies and reduced value-added tax (RVT) policies; (ii) explore the internal response mechanisms at the sectoral scale in the central region; and (iii) reveal the responses of economic output and multiple water resources in external regions under the cascading effects. This integrated approach of a computable general equilibrium model, an ecological network analysis, and a multi-regional input-output analysis is applied to Shanxi Province, China, a representative water-scarce region. The double dividend strategies of WT_6 yuan/ton*RVT_2%, WT_8 yuan/ton*RVT_2.5%, and WT_10 yuan/ton*RVT_3% were conducive to alleviating water scarcity and stimulating economic growth by adjusting the production structures or upgrading treatment technologies to reduce wastewater discharge, reducing the use of water-intensive energy sources to condense direct water consumption, and enhancing the connection between low water consumption sectors and advantageous economic sectors to optimize the virtual water network structure. Based on complex inter-regional relationships, these cascading effects can stimulate the economic output of other provinces and alleviate prevailing water scarcities by increasing virtual water inflows in economically developed regions and decreasing direct water consumption in economically undeveloped regions. The ability of water-rich regions to reconcile differences in water resource endowments can be further strengthened.

Determinants of Dividend Payout in The Utilities Sector among Malaysian Public Listed Companies

The issue of dividend payout in certain companies called the dividend puzzle raises a number of research issues that can be studied in detail at various levels. However, this study aims to determine the factors affecting determinants of dividend payout in the utilities sector such as debt, cash flows, investment, and growth. A total of 12 listed companies’ data over 3 years of 2017-2019 is used and analysed using a fixed-effect model. The findings underline the significant role of the independent variables in deciding the amount of dividend payout in the utilities sector. It demonstrated that only three variables are significant to the dividend payout; cash flow, investment, and growth. The results might provide a company’s board of directors and management team with appropriate dividend strategies that influence the shareholders’ investment decisions. This research provides empirical evidence on the study related to factors influencing dividend policy, which is currently considered inconclusive.

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.

Spectrally negative Lévy risk model under mixed ratcheting-periodic dividend strategies

In this article, we consider the mixed ratcheting-periodic dividend strategies for spectrally negative Lévy risk model, in which dividend payments can both be made continuously without falling and discretely at the jump times of an independent Poisson process. The expected net present value of dividends paid up to ruin and the Laplace transform of the ruin time are obtained by using Lévy fluctuation theory. All the results are expressed in terms of scale functions. Finally, numerical results for Brownian motion with drift are given.

Optimal Ratcheting of Dividends in a Brownian Risk Model

We study the problem of optimal dividend payout from a surplus process governed by Brownian motion with drift under the additional constraint of ratcheting, i.e., the dividend rate can never decrease. We solve the resulting two-dimensional optimal control problem, identifying the value function to be the unique viscosity solution of the corresponding Hamilton--Jacobi--Bellman equation. For finitely many admissible dividend rates we prove that threshold strategies are optimal, and for any closed interval of admissible dividend rates we establish the $\varepsilon$-optimality of curve strategies. This work is a counterpart of [H. Albrecher, P. Azcue, and N. Muler, SIAM J. Control Optim., 58 (2020) pp. 1822--1845], where the ratcheting problem was studied for a compound Poisson surplus process with drift. In the present Brownian setup, calculus of variation techniques allow us to obtain a much more explicit analysis and description of the optimal dividend strategies. We also give some numerical illustrations of the optimality results.

Moment-constrained optimal dividends: precommitment and consistent planning

AbstractA moment constraint that limits the number of dividends in an optimal dividend problem is suggested. This leads to a new type of time-inconsistent stochastic impulse control problem. First, the optimal solution in the precommitment sense is derived. Second, the problem is formulated as an intrapersonal sequential dynamic game in line with Strotz’s consistent planning. In particular, the notions of pure dividend strategies and a (strong) subgame-perfect Nash equilibrium are adapted. An equilibrium is derived using a smooth fit condition. The equilibrium is shown to be strong. The uncontrolled state process is a fairly general diffusion.

Optimal Dividend Strategies with Reinsurance under Contagious Systemic Risk

This paper studies the multidimensional mixed singular-regular stochastic control problems subject to reduced-form default driven by contagious intensities. The dynamic process of surplus is given by a system of diffusion processes with two controls, and the intensity of the reduced-form model increases when defaults occur. We derive the recursive Hamilton--Jacobi--Bellman variational inequalities by the dynamic programming principle and present analytical and recursive solutions. We prove that the solutions are classical and recursively associated with each other by the default states. The verification theorem is presented.