ON DE FINETTI'S OPTIMAL IMPULSE DIVIDEND CONTROL PROBLEM UNDER CHAPTER 11 BANKRUPTCY

Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S.Chapter 11 bankruptcy.We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments.Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem,and hence computations and proofs that are distinct from[44]are needed.To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy,the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching.Some explicit expressions of the expected net present values under a double barrier dividend strategy,new to the literature,are established in terms of scale functions.With the help of these expressions,we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies.When the tail of the Lévy measure is log-convex,this optimal double barrier dividend strategy is then verified as the optimal dividend strategy,solving our optimal impulse control problem.

“China Shock”or China Dividend?-China GVC Participation’s Effects on Trading Partners’Technological Progress

This paper explores the effects of China’s global value chain(GVC)participation on technological progress in trading-partner countries based on estimated data on value-added trade between China and 52 trading partners.We find that,first,although China’s exports lowered the total factor productivity(TFP)of its trading partners(competitive effect),its imports greatly increased trading partners’TFP(effect of scale).This implies that China’s GVC participation is beneficial to its trading partners’technological progress in the form of a considerable technology dividend effect.Second,China’s export dividend effect compensates for the negative effect of Chinese competition on trading partners’technological progress;the innovation effects attributable to China’s imports reinforce the positive effects of scale on technological progress.When innovation is factored in,the China dividend thus becomes further reinforced.Third,China’s merchandise imports have a diminishing positive effect on technological progress in trading partners as geographical distance increases,but trade in services transcends geographical boundaries,and the positive technological progress effect of China’s service imports do not diminish as distance increases.We find that the“China dividend”from China’s GVC participation is a significant contributor to technological progress in partner nations,and China’s imports are conducive to innovation and technological progress in developed countries in the long run.

Equilibrium dividend strategies in the dual model with a random time horizon

This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.

Transition from Demographic Dividend to Reform Dividend:——Simulation of China's Potential Growth Rate

Due to diminishing demographic dividend characterized by a falling workingage population and rising dependency ratio, China's long-term potential growth rates will keep declining, likely to be a mere 6.6% during the 13 th Five-Year Plan period(2016-2020). China's economic growth sustainability hinges upon its transition from the previous dependence on demographic dividend to the future reform dividend. In the growth accounting equation, we have simulated various reform initiatives and arrived at the following findings. First, although both the labor participation rate and TFP can increase China's potential growth rate, the former will only achieve a short-term growth effect, which will diminish in the long run. By contrast, the growth effect of TFP demonstrates the tendency of continuous increase. This further indicates that China's economic growth will increasingly rely on TFP improvement instead of traditional factor input. Second, different from the diminishing growth effect of enrolment rate, training may play a pivotal role in human capital development to significantly enhance potential growth rates. Third, if all reform initiatives can achieve their expected effects, integrated reform dividends may reach one or two percentage points of China's potential growth rate.

EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME

In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.

ON THE EXPECTED DISCOUNTED PENALTY FUNCTION IN A MARKOV-DEPENDENT RISK MODEL WITH CONSTANT DIVIDEND BARRIER

This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.

CLASSICAL RISK MODEL WITH THRESHOLD DIVIDEND STRATEGY

In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.

The compound Poisson risk model with dependence under a multi-layer dividend strategy

In this paper, a compound Poisson risk model with time-dependent claims is studiedunder a multi-layer dividend strategy. A piecewise integro-differential equation for the Gerber- Shiu function is derived and solved. Asymptotic formulas of the ruin probability are obtained when the claim size distributions are heavy-tailed.

A BLACK－SCHOLES FORMULA FOR OPTIONPRICINGWITHDIVIDENDS

We obtain a Black Scholes formula for the arbitrage free pricing of European Call options with constant coefficients when the underlying stock generates dividends. To hedge the Call option, we will always borrow money form bank. We see the influence of the dividend term on the option pricing via the comparison theorem of BSDE(backward stochastic differential equation,). We also consider the option pricing problem in terms of the borrowing rate R which is not equal to the interest rate r. The corresponding Black Scholes formula is given. We notice that it is in fact the borrowing rate that plays the role in the pricing formula.

ON THE RENEWAL RISK MODEL WITH INTEREST AND DIVIDEND

We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.

Optimal proportional reinsurance and dividend payments with transaction costs and internal competition

We study the dividend optimization problem for an insurance company under the consideration of internal competition between different units inside company and transaction costs when dividends occur. The management of the company controls the reinsurance rate, the timing and the amount of dividends paid out to maximize the expected total dividends paid out to the shareholders until ruin time. By solving the corresponding quasi-variational inequality, we obtain the optimal return function and the optimal strategy.

OPTIMAL PROPORTIONAL REINSURANCE WITH CONSTANT DIVIDEND BARRIER

In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.

Future demographic dividend——tapping the source of China’s economic growth

This paper presents a review of the demographic dividend in China’s economic growth or the contribution of the demographic factor to China’s rapid economic growth over the past 30 years. Based on this review, it explores how China has sustained high-speed economic growth in the midst of a slowdown in working age population growth, surplus labor depletion and population aging. This study intends to demonstrate that the second demographic dividend may still arise after the decline and even disappearance of the first demographic dividend to avoid demographic debt by boosting labor productivity through the furtherance of education, extending the competitive advantage of China’s industry, tapping new sources of savings through institutional arrangements of pension security, and expanding labor resource and human capital stock in the aging era through the institutional arrangements in the labor market.

Optimal dividend and capital injection problem with a random time horizon and a ruin penalty in the dual model

In the dual risk model, we consider the optimal dividend and capital injection problem, which involves a random time horizon and a ruin penalty. Both fixed and proportional costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends, and the penalized discounted both capital injections and ruin penalty during the horizon, which is described by the minimum of the time of ruin and an exponential random variable. The explicit solutions for optimal strategy and value function are obtained, when the income jumps follow a hyper-exponential distribution.Besides, some numerical examples are presented to illustrate our results.

Effect of family control on corporate dividend policy of firms in Pakistan

This study examines the impact of family control on the dividend policy of firms in Pakistan,covering the period from 2009 to 2016.It also investigates whether family control moderates the impact of firm-specific factors on the dividend policy.The GMM model for panel data estimation is used.The mean difference univariate analysis shows that family firms differ from nonfamily firms based on financial characteristics.The multivariate analysis shows that family firms pay lower dividends than nonfamily firms.Besides,firm size inversely affects the dividend policy,whereas tangibility positively affects it.Moreover,family control does not moderate the impact of all firm-specific factors on the dividend policy.Overall,family control,size,and tangibility are found to be the main determinants of the dividend policy in Pakistan.

On two actuarial quantities for the compound Poisson risk model with tax and a threshold dividend strategy

In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.

ASYMPTOTIC THEORY FOR A RISK PROCESS WITH A HIGH DIVIDEND BARRIER

A modified classical model with a dividend barrier is considered. It is shown that there is a simple approximation formula for the time of ruin when the level of dividend barrier is high and the claim sizes have a distribution that belongs to S（γ） with γ 〉0.

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.

Periodic dividends and capital injections for a spectrally negative Lévy risk process under absolute ruin

The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the absolute ruin,the expected discounted dividends and the expected discounted capital injections are discussed.We also study the joint Laplace transforms including the absolute ruin time and the total dividends or the total capital injections.All the results are expressed in scale functions.

The Expected Discounted Tax Payments on Dual Risk Model under a Dividend Threshold

In this paper, we consider the dual risk model in which periodic taxation are paid according to a loss-carry-forward system and dividends are paid under a threshold strategy. We give an analytical approach to derive the expression of gδ(u) (i.e. the Laplace transform of the first upper exit time). We discuss the expected discounted tax payments for this model and obtain its corresponding integro-differential equations. Finally, for Erlang (2) inter-innovation distribution, closedform expressions for the expected discounted tax payments are given.