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 ...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.展开更多
Numerous researchers have applied the martingale approach for models driven by L¶evy processes to study optimal investment problems.This paper considers an insurer who wants to maximize the expected utility of te...Numerous researchers have applied the martingale approach for models driven by L¶evy processes to study optimal investment problems.This paper considers an insurer who wants to maximize the expected utility of terminal wealth by selecting optimal investment and proportional reinsurance strategies.The insurer's risk process is modeled by a L¶evy process and the capital can be invested in a security market described by the standard Black-Scholes model.By the martingale approach,the closed-form solutions to the problems of expected utility maximization are derived.Numerical examples are presented to show the impact of model parameters on the optimal strategies.展开更多
In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are o...In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.展开更多
This paper considers a model of an insurance company which is allowed to invest a risky asset and to purchase proportional reinsurance. The objective is to find the policy which maximizes the expected total discounted...This paper considers a model of an insurance company which is allowed to invest a risky asset and to purchase proportional reinsurance. The objective is to find the policy which maximizes the expected total discounted dividend pay-out until the time of bankruptcy and the terminal value of the company under liquidity constraint. We find the solution of this problem via solving the problem with zero terminal value. We also analyze the influence of terminal value on the optimal policy.展开更多
We consider an optimization problem of an insurance company in the diffusion setting, which controls the dividends payout as well as the capital injections. To maximize the cumulative expected discounted dividends min...We consider an optimization problem of an insurance company in the diffusion setting, which controls the dividends payout as well as the capital injections. To maximize the cumulative expected discounted dividends minus the penalized discounted capital injections until the ruin time, there is a possibility of (cheap or non-cheap) proportional reinsurance. We solve the control problems by constructing two categories of suboptimal models, one without capital injections and one with no bankruptcy by capital injection. Then we derive the explicit solutions for the value function and totally characterize the optimal strategies. Particularly, for cheap reinsurance, they axe the same as those in the model of no bankruptcy.展开更多
In this paper,the authors analyze the optimal reinsurance and dividend problem with model uncertainty for an insurer.Here the model uncertainty represents possible deviations between the real market and the assumed mo...In this paper,the authors analyze the optimal reinsurance and dividend problem with model uncertainty for an insurer.Here the model uncertainty represents possible deviations between the real market and the assumed model.In addition to the incorporation of model uncertainty into the traditional diffusion surplus process,the authors include a penalty function in the objective function.The proposed goal is to find the optimal reinsurance and dividend strategy that maximizes the expected discounted dividend before ruin in the worst case of all possible scenarios,namely,the worst market.Using a dynamic programming approach,the problem is reduced to solving a Hamilton-Jacob-Bellman-Isaac(HJBI)equation with singular control.This problem is more difficult than the traditional robust control or singular control problem.Here,the authors prove that the value function is the unique solution to this HJBI equation with singular control.Moreover,the authors present a verification theorem when a smooth solution can be found,and derive closed-form solution when the function in the objective function is specified.展开更多
In this paper, under the criterion of maximizing the expected exponential utility of terminal wealth, we study the optimal proportional reinsurance and investment policy for an insurer with the compound Poisson claim ...In this paper, under the criterion of maximizing the expected exponential utility of terminal wealth, we study the optimal proportional reinsurance and investment policy for an insurer with the compound Poisson claim process. We model the price process of the risky asset to the constant elasticity of variance (for short, CEV) model, and consider net profit condition and variance reinsurance premium principle in our work. Using stochastic control theory, we derive explicit expressions for the optimal policy and value function. And some numerical examples are given.展开更多
In this paper,we consider an optimal investment and proportional reinsurance problem with delay,in which the insurer’s surplus process is described by a jump-diffusion model.The insurer can buy proportional reinsuran...In this paper,we consider an optimal investment and proportional reinsurance problem with delay,in which the insurer’s surplus process is described by a jump-diffusion model.The insurer can buy proportional reinsurance to transfer part of the insurance claims risk.In addition to reinsurance,she also can invests her surplus in a financial market,which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility(SV)model.Considering the performance-related capital flow,the insurer’s wealth process is modeled by a stochastic differential delay equation.The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth.We explicitly derive the optimal strategy and the value function.Finally,we provide some numerical examples to illustrate our results.展开更多
This paper considers the dividend optimization problem for an insurance company under the consideration of internal competition between different units inside the company. The objective is to find a reinsurance policy...This paper considers the dividend optimization problem for an insurance company under the consideration of internal competition between different units inside the company. The objective is to find a reinsurance policy and a dividend payment scheme so as to maximize the expected discounted value of the dividend payment, and the expected present value of an amount which the insurer earns until the time of ruin. By solving the corresponding constrained Hamilton-Jacobi-Bellman (HJB) equation, we obtain the value function and the optimal reinsurance policy and dividend payment.展开更多
基金Supported by the National Natural Science Foundation of China(11371284)
文摘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.
基金the National Natural Science Foundation of China(71471081)Teaching Reform Project of Nanjing University of Finance and Economics(JGY034)Degree and Graduate Education Project of Nanjing University of Finance and Economics(Y18005).
文摘Numerous researchers have applied the martingale approach for models driven by L¶evy processes to study optimal investment problems.This paper considers an insurer who wants to maximize the expected utility of terminal wealth by selecting optimal investment and proportional reinsurance strategies.The insurer's risk process is modeled by a L¶evy process and the capital can be invested in a security market described by the standard Black-Scholes model.By the martingale approach,the closed-form solutions to the problems of expected utility maximization are derived.Numerical examples are presented to show the impact of model parameters on the optimal strategies.
基金the National Natural Science Foundation of China(No.10571092)
文摘In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.
基金Supported by Doctor Foundation of Xinjiang Universitythe National Natural Science Foundation of China
文摘This paper considers a model of an insurance company which is allowed to invest a risky asset and to purchase proportional reinsurance. The objective is to find the policy which maximizes the expected total discounted dividend pay-out until the time of bankruptcy and the terminal value of the company under liquidity constraint. We find the solution of this problem via solving the problem with zero terminal value. We also analyze the influence of terminal value on the optimal policy.
基金Supported by the National Basic Research Program of China (973 Program) (Grant No. 2007CB814905)the National Natural Science Foundation of China (NSFC Grant No. 10871102)
文摘We consider an optimization problem of an insurance company in the diffusion setting, which controls the dividends payout as well as the capital injections. To maximize the cumulative expected discounted dividends minus the penalized discounted capital injections until the ruin time, there is a possibility of (cheap or non-cheap) proportional reinsurance. We solve the control problems by constructing two categories of suboptimal models, one without capital injections and one with no bankruptcy by capital injection. Then we derive the explicit solutions for the value function and totally characterize the optimal strategies. Particularly, for cheap reinsurance, they axe the same as those in the model of no bankruptcy.
基金supported by the National Natural Science Foundation of China under Grant No. 11771466Program for Innovation Research under Grant No. 20170074the Emerging Interdisciplinary Project of CUFE
文摘In this paper,the authors analyze the optimal reinsurance and dividend problem with model uncertainty for an insurer.Here the model uncertainty represents possible deviations between the real market and the assumed model.In addition to the incorporation of model uncertainty into the traditional diffusion surplus process,the authors include a penalty function in the objective function.The proposed goal is to find the optimal reinsurance and dividend strategy that maximizes the expected discounted dividend before ruin in the worst case of all possible scenarios,namely,the worst market.Using a dynamic programming approach,the problem is reduced to solving a Hamilton-Jacob-Bellman-Isaac(HJBI)equation with singular control.This problem is more difficult than the traditional robust control or singular control problem.Here,the authors prove that the value function is the unique solution to this HJBI equation with singular control.Moreover,the authors present a verification theorem when a smooth solution can be found,and derive closed-form solution when the function in the objective function is specified.
基金Supported by the NNSF of China(Grant Nos.11471165,61304065)the QinLan Project of Nanjing Normal University
文摘In this paper, under the criterion of maximizing the expected exponential utility of terminal wealth, we study the optimal proportional reinsurance and investment policy for an insurer with the compound Poisson claim process. We model the price process of the risky asset to the constant elasticity of variance (for short, CEV) model, and consider net profit condition and variance reinsurance premium principle in our work. Using stochastic control theory, we derive explicit expressions for the optimal policy and value function. And some numerical examples are given.
基金This research was supported by the National Natural Science Foundation of China(No.71801186)the Science Foundation of Ministry of Education of China(No.18YJC630001)the Natural Science Foundation of Guangdong Province of China(No.2017A030310660).
文摘In this paper,we consider an optimal investment and proportional reinsurance problem with delay,in which the insurer’s surplus process is described by a jump-diffusion model.The insurer can buy proportional reinsurance to transfer part of the insurance claims risk.In addition to reinsurance,she also can invests her surplus in a financial market,which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility(SV)model.Considering the performance-related capital flow,the insurer’s wealth process is modeled by a stochastic differential delay equation.The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth.We explicitly derive the optimal strategy and the value function.Finally,we provide some numerical examples to illustrate our results.
基金Supported by the National Natural Science Foundation of China(No.10971157)the Natural Science Foundation of Xinjiang University(No.BS100102)
文摘This paper considers the dividend optimization problem for an insurance company under the consideration of internal competition between different units inside the company. The objective is to find a reinsurance policy and a dividend payment scheme so as to maximize the expected discounted value of the dividend payment, and the expected present value of an amount which the insurer earns until the time of ruin. By solving the corresponding constrained Hamilton-Jacobi-Bellman (HJB) equation, we obtain the value function and the optimal reinsurance policy and dividend payment.