This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the prob...This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.展开更多
Based on the Lie symmetry method,we derive the explicit optimal invest strategy for an investor who seeks to maximize the expected exponential(CARA)utility of the terminal wealth in a defined-contribution pension plan...Based on the Lie symmetry method,we derive the explicit optimal invest strategy for an investor who seeks to maximize the expected exponential(CARA)utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model.We examine the point symmetries of the Hamilton-Jacobi-Bellman(HJB)equation associated with the portfolio optimization problem.The symmetries compatible with the terminal condition enable us to transform the(2+1)-dimensional HJB equation into a(1+1)-dimensional nonlinear equation which is linearized by its infinite-parameter Lie group of point transformations.Finally,the ansatz technique based on variables separation is applied to solve the linear equation and the optimal strategy is obtained.The algorithmic procedure of the Lie symmetry analysis method adopted here is quite general compared with conjectures used in the literature.展开更多
In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and the...In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.展开更多
This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the ...This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term＇s explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained.展开更多
An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is...An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.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
To analyze the stress wave propagation associated with the vortex-induced vibration（VIV） of a marine riser, this paper employed a multi-signal complex exponential method. This method is an extension of the classical...To analyze the stress wave propagation associated with the vortex-induced vibration（VIV） of a marine riser, this paper employed a multi-signal complex exponential method. This method is an extension of the classical Prony＇s method which decomposes a complicated signal into a number of complex exponential components. Because the proposed method processes multiple signals simultaneously, it can estimate the “global” dominating frequencies（poles） shared by those signals.The complex amplitude（residues） corresponding to the estimated frequencies for those signals is also obtained in the process. As the signals were collected at different locations along the axial direction of a marine riser, the phenomena of the stress wave propagation could be analyzed through the obtained residues of those signals. The Norwegian Deepwater Program（NDP） high mode test data were utilized in the numerical studies, including data sets in both the in-line（IL） and cross-flow（CF） directions. It was found that the most dominant component in the IL direction has its stress wave propagation along the riser being dominated by a standing wave, while that in the CF direction dominated by a traveling wave.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, the surplus process is assumed to be a periodic risk model and the insurer is allowed to invest in multiple risky assets described by the Black-Scholes market model. Under shortselling prohibition, the ...In this paper, the surplus process is assumed to be a periodic risk model and the insurer is allowed to invest in multiple risky assets described by the Black-Scholes market model. Under shortselling prohibition, the authors consider the optimal investment from an insurer＇s point of view by maximizing the adjustment coefficent and the expected exponential utility of wealth at one period, respectively. It is shown that the optimal strategies of both of optimization problems are to invest a fixed amount of money in each risky asset.展开更多
Baton and Lemaire(Astin Bull 12:57–71,1981)proved the nonemptiness of the core of a reinsurance market in which the risks of companies are independent.However,cases involving dependent risks have received increasing ...Baton and Lemaire(Astin Bull 12:57–71,1981)proved the nonemptiness of the core of a reinsurance market in which the risks of companies are independent.However,cases involving dependent risks have received increasing concerns in modern actuarial science.In this paper,we investigate the nonemptiness of the core of a reinsurance market where the risks of different companies may be dependent.When the exponential utility function is employed,we find an important property on risk premium and show that the core of the market is always nonempty.展开更多
This paper investigates the optimal reinsurance and investment in a hidden Markov financial market consisting of non-risky （bond） and risky （stock） asset. We assume that only the price of the risky asset can be ob...This paper investigates the optimal reinsurance and investment in a hidden Markov financial market consisting of non-risky （bond） and risky （stock） asset. We assume that only the price of the risky asset can be observed from the financial market. Suppose that the insurance company can adopt proportional reinsurance and investment in the hidden Markov financial market to reduce risk or increase profit. Our objective is to maximize the expected exponential utility of the terminal wealth of the surplus of the insurance company. By using the filtering theory, we establish the separation principle and reduce the problem to the complete information case. With the help of Girsanov change of measure and the dynamic programming approach, we characterize the value function as the unique solution of a linear parabolic partial differential equation and obtain the Feynman-Kac representation of the value function.展开更多
基金Supported by the Key Grant Project of Chinese Ministry of Education (NO.309018)National Natural Science Foundation of China (NO.70973104,NO.11171304)Zhejiang Provincial Natural Science Foundation of China (NO.Y6110023)
文摘This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.
基金supported in part by the 13th Five-Year National Key Research and Development Program of China(Grant No.2016YFCO401407)the National Natural Science Foundation of China(Grant No.72071076)+1 种基金the Beijing NaturalScience Foundation(Grant No.Z200001)the Fundamental Research Funds of the Central Universities(Grant Nos.2019MS050,2020MS043).
文摘Based on the Lie symmetry method,we derive the explicit optimal invest strategy for an investor who seeks to maximize the expected exponential(CARA)utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model.We examine the point symmetries of the Hamilton-Jacobi-Bellman(HJB)equation associated with the portfolio optimization problem.The symmetries compatible with the terminal condition enable us to transform the(2+1)-dimensional HJB equation into a(1+1)-dimensional nonlinear equation which is linearized by its infinite-parameter Lie group of point transformations.Finally,the ansatz technique based on variables separation is applied to solve the linear equation and the optimal strategy is obtained.The algorithmic procedure of the Lie symmetry analysis method adopted here is quite general compared with conjectures used in the literature.
基金supported by the National Natural Science Foundation of China(Grant No.12301603).
文摘In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.
文摘This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term＇s explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained.
基金National Natural Science Foundation of China(No.62073071)Fundamental Research Funds for the Central Universities and Graduate Student Innovation Fund of Donghua University,China(No.CUSF-DH-D-2021045)。
文摘An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.
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financially supported by the National Natural Science Foundation of China(Grant Nos.51490675,51379197 and 51522906)
文摘To analyze the stress wave propagation associated with the vortex-induced vibration（VIV） of a marine riser, this paper employed a multi-signal complex exponential method. This method is an extension of the classical Prony＇s method which decomposes a complicated signal into a number of complex exponential components. Because the proposed method processes multiple signals simultaneously, it can estimate the “global” dominating frequencies（poles） shared by those signals.The complex amplitude（residues） corresponding to the estimated frequencies for those signals is also obtained in the process. As the signals were collected at different locations along the axial direction of a marine riser, the phenomena of the stress wave propagation could be analyzed through the obtained residues of those signals. The Norwegian Deepwater Program（NDP） high mode test data were utilized in the numerical studies, including data sets in both the in-line（IL） and cross-flow（CF） directions. It was found that the most dominant component in the IL direction has its stress wave propagation along the riser being dominated by a standing wave, while that in the CF direction dominated by a traveling wave.
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supported by National Basic Research Program of China(973 Program) under Grant No. 2007CB814905the Natural Science Foundation of China under Grant No.11171164
文摘In this paper, the surplus process is assumed to be a periodic risk model and the insurer is allowed to invest in multiple risky assets described by the Black-Scholes market model. Under shortselling prohibition, the authors consider the optimal investment from an insurer＇s point of view by maximizing the adjustment coefficent and the expected exponential utility of wealth at one period, respectively. It is shown that the optimal strategies of both of optimization problems are to invest a fixed amount of money in each risky asset.
基金Jia-Hua Zhang’s research is supported by Fudan University Student Growth Fund Scholarship.Shu-Cherng Fang’s research is supported by US ARO Grant(No.W911NF-15-1-0223)Yi-Fan Xu’s research is supported by the National Natural Science Foundation of China(Nos.71372113,71531005)Join Funding of Fudan University&Taiwan University.
文摘Baton and Lemaire(Astin Bull 12:57–71,1981)proved the nonemptiness of the core of a reinsurance market in which the risks of companies are independent.However,cases involving dependent risks have received increasing concerns in modern actuarial science.In this paper,we investigate the nonemptiness of the core of a reinsurance market where the risks of different companies may be dependent.When the exponential utility function is employed,we find an important property on risk premium and show that the core of the market is always nonempty.
基金Supported by National Natural Science Foundation of China(NSFC grant No.11371020,71302156)
文摘This paper investigates the optimal reinsurance and investment in a hidden Markov financial market consisting of non-risky （bond） and risky （stock） asset. We assume that only the price of the risky asset can be observed from the financial market. Suppose that the insurance company can adopt proportional reinsurance and investment in the hidden Markov financial market to reduce risk or increase profit. Our objective is to maximize the expected exponential utility of the terminal wealth of the surplus of the insurance company. By using the filtering theory, we establish the separation principle and reduce the problem to the complete information case. With the help of Girsanov change of measure and the dynamic programming approach, we characterize the value function as the unique solution of a linear parabolic partial differential equation and obtain the Feynman-Kac representation of the value function.
