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...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.展开更多
In recent years,the research focus in insurance risk theory has shifted towards multi-type mixed dividend strategies.However,the practical factors and constraints in financial market transactions,such as interest rate...In recent years,the research focus in insurance risk theory has shifted towards multi-type mixed dividend strategies.However,the practical factors and constraints in financial market transactions,such as interest rates,tax rates,and transaction fees,inevitably impact these strategies.By incorporating appropriate constraints,a multi-type mixed strategy can better simulate real-world transactions.Following the approach of Liu et al.[28],we examine a classical compound Poisson risk model that incorporates the constraints of constant interest rates and a periodic-threshold mixed dividend strategy.In this model,the surplus process of insurance companies is influenced by several factors.These factors include constant interest rates,continuously distributed dividends within intervals(threshold dividend strategy),and dividends at discrete time points(periodic dividend strategy).We derive the piecewise integro-differential equations(IDEs)that describe the expected present value of dividends(EPVDs)until ruin time and the Gerber-Shiu expected discounted penalty function.Furthermore,we provide explicit solutions to these IDEs using an alternative method based on the inverse Laplace transform combined with the Dickson-Hipp operator.This enables us to obtain explicit expressions for the dividend and Gerber-Shiu functions.Additionally,we present examples to illustrate the application of our results.展开更多
We derive some results on the dividend payments prior to ruin in the classical surplus process with interest.An integro-differential equation with a boundary conditions satisfied by the expected present value of divid...We derive some results on the dividend payments prior to ruin in the classical surplus process with interest.An integro-differential equation with a boundary conditions satisfied by the expected present value of dividend payments is derived and solved.Furthermore,we derive an integro-differential equation for the moment generating function,through which we analyze the higher moment of the present value of dividend payments.Finally,closed-form expressions for exponential claims are given.展开更多
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...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.展开更多
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 gi...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.展开更多
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 stro...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.展开更多
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-...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.展开更多
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 ge...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.展开更多
Yunnan Baoshan Industrial Park,with the joint effort of the government of Myanmar,has been playing its leading role in constructing investment of Baoshan-Mandalay Miuda Industrial Park ever since the Belt and Road Ini...Yunnan Baoshan Industrial Park,with the joint effort of the government of Myanmar,has been playing its leading role in constructing investment of Baoshan-Mandalay Miuda Industrial Park ever since the Belt and Road Initiative.展开更多
基金the financial support from the National Natural Science Foundation of China(12171405 and 11661074)the Program for New Century Excellent Talents in Fujian Province University+2 种基金the financial support from the Characteristic&Preponderant Discipline of Key Construction Universities in Zhejiang Province(Zhejiang Gongshang University-Statistics)Collaborative Innovation Center of Statistical Data Engineering Technology&ApplicationDigital+Discipline Construction Project(SZJ2022B004)。
文摘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.
基金supported by the National Natural Science Foundation of China(12361095)the Jiangxi Provincial Natural Science Foundation(20232BAB201028)。
文摘In recent years,the research focus in insurance risk theory has shifted towards multi-type mixed dividend strategies.However,the practical factors and constraints in financial market transactions,such as interest rates,tax rates,and transaction fees,inevitably impact these strategies.By incorporating appropriate constraints,a multi-type mixed strategy can better simulate real-world transactions.Following the approach of Liu et al.[28],we examine a classical compound Poisson risk model that incorporates the constraints of constant interest rates and a periodic-threshold mixed dividend strategy.In this model,the surplus process of insurance companies is influenced by several factors.These factors include constant interest rates,continuously distributed dividends within intervals(threshold dividend strategy),and dividends at discrete time points(periodic dividend strategy).We derive the piecewise integro-differential equations(IDEs)that describe the expected present value of dividends(EPVDs)until ruin time and the Gerber-Shiu expected discounted penalty function.Furthermore,we provide explicit solutions to these IDEs using an alternative method based on the inverse Laplace transform combined with the Dickson-Hipp operator.This enables us to obtain explicit expressions for the dividend and Gerber-Shiu functions.Additionally,we present examples to illustrate the application of our results.
文摘We derive some results on the dividend payments prior to ruin in the classical surplus process with interest.An integro-differential equation with a boundary conditions satisfied by the expected present value of dividend payments is derived and solved.Furthermore,we derive an integro-differential equation for the moment generating function,through which we analyze the higher moment of the present value of dividend payments.Finally,closed-form expressions for exponential claims are given.
基金supported by the NSFC(11171101)Doctoral Fund of Education Ministry of China(20104306110001)the Graduate Research and Innovation Fund of Hunan Province(CX2011B197)
文摘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.
基金supported in part by Hubei Normal University Post-graduate Foundation(2007D59 and 2007D60)the Science and Technology foundation of Hubei(D20092207)the National Natural Science Foundation of China(10671149)
文摘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.
基金the National Natural Science Foundation of China(10571092)the major program of Key Research Institute of HumanitiesSocial Sciences at Universities(04JJD790006).
文摘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.
文摘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.
基金Supported in part by the National Natural Science Foun-dation of China and the Ministry of Education of China
文摘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.
文摘Yunnan Baoshan Industrial Park,with the joint effort of the government of Myanmar,has been playing its leading role in constructing investment of Baoshan-Mandalay Miuda Industrial Park ever since the Belt and Road Initiative.
