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
In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows ...In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.展开更多
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
The Goodgrant Foundation is a charitable organization that wants to improve education performance of undergraduates attending colleges and universities in the US. So the foundation plans to contribute a total of US 50...The Goodgrant Foundation is a charitable organization that wants to improve education performance of undergraduates attending colleges and universities in the US. So the foundation plans to contribute a total of US 50 million for a suitable team of schools per year under the condition of avoiding repeated other large grant organizations’ investment. The DEA (Data Estimate Analysis) model is developed to determine an optimal investment strategy for the Goodgrant Foundation. In this paper, two questions were solved: how to choose a suitable team of schools and how to allocate the investment. Before the establishment of the model, the EXCEL software is used to preprocess data. Then the DEA model which includes two models in the paper is developed. For the first question, the CCR model is established to rank schools which used efficiency from DEAP 2.1. For the second question, the resource allocation model is established to allocate investment amount by weights of allocation from MATLAB software. Accordingly, the optimal investment strategy is received for the Goodgrant Foundation. Through the analysis above, 23 from 293 schools are selected to invest. Then the schools are ranked and the investment of US 50 million for 23 schools is allocated.展开更多
We devise a model for security investment that reflects dynamic interaction between a defender, who faces uncertainty, and an attacker, who repeatedly targets the weakest link. Using the model, we derive and compare o...We devise a model for security investment that reflects dynamic interaction between a defender, who faces uncertainty, and an attacker, who repeatedly targets the weakest link. Using the model, we derive and compare optimal security investment over multiple periods, exploring the delicate balance between proactive and reactive security investment. We show how the best strategy depends on the defender’s knowledge about prospective attacks and the recoverability of costs when upgrading defenses reactively. Our model explains why security under-investment is sometimes rational even when effective defenses are available and can be deployed independently of other parties’ choices. Finally, we connect the model to real-world security problems by examining two case studies where empirical data are available: computers compromised for use in online crime and payment card security.展开更多
This study focuses on investigating the optimal investment strategy for an optimization problem with delay using the uncertainty theory. The financial market is composed of a risk-free asset and a risk asset with an u...This study focuses on investigating the optimal investment strategy for an optimization problem with delay using the uncertainty theory. The financial market is composed of a risk-free asset and a risk asset with an uncertain price process described by an uncertain differential equation. An optimization problem is assumed that its objective is a nonlinear function of decision variable. By deriving the equation of optimality, an analytical solution is obtained for the optimal delay investment strategy, and the optimal delay value function. Finally, an economic analysis and numerical sensitivity analysis are conducted to evaluate the research results.展开更多
This paper mainly studies the optimal investment problem of defined contribution(DC)pension under the self-protection and minimum security.First,we apply Ito?theorem to obtain the differential equation of the real sto...This paper mainly studies the optimal investment problem of defined contribution(DC)pension under the self-protection and minimum security.First,we apply Ito?theorem to obtain the differential equation of the real stock price after discounting inflation.Then,under the constraint of external guarantee of DC pension terminal wealth,self-protection is introduced to study the maximization of the expected utility of terminal wealth at retirement time and any time before retirement.The explicit solution of the optimal investment strategy of DC pension at retirement time and any time before retirement should be derived by martingale method.Finally,the influence of selfprotection on the optimal investment strategy of DC pension is numerically analyzed.展开更多
The investment problem of oilfield development is to trade off the investment exploration investment and development investment.With low return on investment got by using the existing method to solve this problem,we c...The investment problem of oilfield development is to trade off the investment exploration investment and development investment.With low return on investment got by using the existing method to solve this problem,we construct an optimal model to improve it based on Data Envelopment Analysis(DEA)method and the relations about investment and proven reserves,investment and output as well as production cost.Data Envelopment Analysis(DEA)method is used to present a method to determine the optimal scale of productivity construction investment in unit production.The relation between total cumulated proven reserves and cumulative exploration investment is denoted as an exponential model.The relation among productions and remaining recoverable reserves as well as production cost may be described as an exponential operational cost function.Based on above two relation models and investment effectiveness coefficients of every block,we establish an optimal model whose objective function is net present value(NPV)profit maximum,whose constrain conditions include investment,reserve/production ratio,production and some equality constraints under the mode of sustainable development.It can be solved by genetic algorithms.The result of case study shows that this optimal investment of oilfield development has multi-stage investment structure under given conditions;the model can provide scientific basic theory for oil companies to make a long-term strategic program and investment plan in oil exploration and development,may decrease the subjective blindness in the investment and bring about a reasonable and orderly exploration and development of oil resources.展开更多
In this paper, the surplus of an insurance company is modeled by a Markovian regime- switching diffusion process. The insurer decides the proportional reinsurance and investment so as to increase revenue. The regime-s...In this paper, the surplus of an insurance company is modeled by a Markovian regime- switching diffusion process. The insurer decides the proportional reinsurance and investment so as to increase revenue. The regime-switching economy consists of a fixed interest security and several risky shares. The optimal proportional reinsurance and investment strategies with no short-selling constraints for maximizing an exponential utility on terminal wealth are obtained.展开更多
In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by...In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross (CIR) model. For the stock price process, we consider both the case of constant volatility (driven by an O U process) and the case of stochastic volatility (driven by a CIR model). In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.展开更多
This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynami...This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution to the HJB equation in the full information case. Some numerical illustrations are also provided.展开更多
In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to deri...In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to derive analytical expressions for the optimal portfolio policy and the mean-variance efficient frontier under certain conditions. We illustrate these results by an numerical example.展开更多
Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distr...Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distribution of extended regular variation, starting from an integro-differential equation for the maximal survival probability, we find that the corresponding ruin probability as a function of the initial surplus is also extended regular variation.展开更多
The author studies the optimal investment stopping problem in both continuous and discrete cases, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the ...The author studies the optimal investment stopping problem in both continuous and discrete cases, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth.Based on the work of Hu et al.(2018) with an additional stochastic payoff function,the author characterizes the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equations(BSDEs for short) with unbounded terminal condition. In regard to the discrete problem, she gets the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provides some useful a priori estimates about the solutions with the help of an auxiliary forward-backward SDE system and Malliavin calculus. Finally, she obtains the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization.展开更多
This paper studies a problem of optimal investment and consumption with early retirement option under constant elasticity variation(CEV)model with finite horizon.Two risky assets are involved in the model with one fol...This paper studies a problem of optimal investment and consumption with early retirement option under constant elasticity variation(CEV)model with finite horizon.Two risky assets are involved in the model with one following geometric Brownian motion and the other a CEV model.This problem is a kind of two dimensional mixed control and optimal stopping problems with finite horizon.The existence and continuity of the optimal retirement threshold surfaces are proved and the working and retirement regions are characterized theoretically.Least-squares Monte-Carlo methods are developed to solve this mixed control and optimal stopping problem.The algorithms are well implemented and the optimal retirement threshold surfaces,optimal investment strategies and the optimal consumptions are drawn via examples.展开更多
We develop a fractional-degree expectation dependence which is the generalization of the first-degree and second-degree expectation dependence.The motivation for introducing such a dependence notion is to conform with...We develop a fractional-degree expectation dependence which is the generalization of the first-degree and second-degree expectation dependence.The motivation for introducing such a dependence notion is to conform with the preferences of decision makers who are mostly risk averse but would be risk seeking at some wealth levels.We investigate some tractable equivalent properties for this new dependence notion,and explore its properties,including the invariance under increasing and concave transformations,and the invariance under convolution.We also extend our results to a combined fractional-degree expectation dependence notion includingε-almost firstdegree expectation dependence.Two applications on portfolio diversification problem and optimal investment in the presence of a background risk illustrate the usefulness of the approaches proposed in the present paper.展开更多
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Supported by the National Natural Science Foundation of Tianjin (07JCYBJC05200)the Young Scholar Program of Tianjin University of Finance and Economics (TJYQ201201)
文摘In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.
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.
文摘The Goodgrant Foundation is a charitable organization that wants to improve education performance of undergraduates attending colleges and universities in the US. So the foundation plans to contribute a total of US 50 million for a suitable team of schools per year under the condition of avoiding repeated other large grant organizations’ investment. The DEA (Data Estimate Analysis) model is developed to determine an optimal investment strategy for the Goodgrant Foundation. In this paper, two questions were solved: how to choose a suitable team of schools and how to allocate the investment. Before the establishment of the model, the EXCEL software is used to preprocess data. Then the DEA model which includes two models in the paper is developed. For the first question, the CCR model is established to rank schools which used efficiency from DEAP 2.1. For the second question, the resource allocation model is established to allocate investment amount by weights of allocation from MATLAB software. Accordingly, the optimal investment strategy is received for the Goodgrant Foundation. Through the analysis above, 23 from 293 schools are selected to invest. Then the schools are ranked and the investment of US 50 million for 23 schools is allocated.
文摘We devise a model for security investment that reflects dynamic interaction between a defender, who faces uncertainty, and an attacker, who repeatedly targets the weakest link. Using the model, we derive and compare optimal security investment over multiple periods, exploring the delicate balance between proactive and reactive security investment. We show how the best strategy depends on the defender’s knowledge about prospective attacks and the recoverability of costs when upgrading defenses reactively. Our model explains why security under-investment is sometimes rational even when effective defenses are available and can be deployed independently of other parties’ choices. Finally, we connect the model to real-world security problems by examining two case studies where empirical data are available: computers compromised for use in online crime and payment card security.
文摘This study focuses on investigating the optimal investment strategy for an optimization problem with delay using the uncertainty theory. The financial market is composed of a risk-free asset and a risk asset with an uncertain price process described by an uncertain differential equation. An optimization problem is assumed that its objective is a nonlinear function of decision variable. By deriving the equation of optimality, an analytical solution is obtained for the optimal delay investment strategy, and the optimal delay value function. Finally, an economic analysis and numerical sensitivity analysis are conducted to evaluate the research results.
基金Supported by the National Social Science Foundation of China(20BTJ048)Anhui University Humanities and Social Science Research Major Project(SK2021ZD0043)。
文摘This paper mainly studies the optimal investment problem of defined contribution(DC)pension under the self-protection and minimum security.First,we apply Ito?theorem to obtain the differential equation of the real stock price after discounting inflation.Then,under the constraint of external guarantee of DC pension terminal wealth,self-protection is introduced to study the maximization of the expected utility of terminal wealth at retirement time and any time before retirement.The explicit solution of the optimal investment strategy of DC pension at retirement time and any time before retirement should be derived by martingale method.Finally,the influence of selfprotection on the optimal investment strategy of DC pension is numerically analyzed.
文摘The investment problem of oilfield development is to trade off the investment exploration investment and development investment.With low return on investment got by using the existing method to solve this problem,we construct an optimal model to improve it based on Data Envelopment Analysis(DEA)method and the relations about investment and proven reserves,investment and output as well as production cost.Data Envelopment Analysis(DEA)method is used to present a method to determine the optimal scale of productivity construction investment in unit production.The relation between total cumulated proven reserves and cumulative exploration investment is denoted as an exponential model.The relation among productions and remaining recoverable reserves as well as production cost may be described as an exponential operational cost function.Based on above two relation models and investment effectiveness coefficients of every block,we establish an optimal model whose objective function is net present value(NPV)profit maximum,whose constrain conditions include investment,reserve/production ratio,production and some equality constraints under the mode of sustainable development.It can be solved by genetic algorithms.The result of case study shows that this optimal investment of oilfield development has multi-stage investment structure under given conditions;the model can provide scientific basic theory for oil companies to make a long-term strategic program and investment plan in oil exploration and development,may decrease the subjective blindness in the investment and bring about a reasonable and orderly exploration and development of oil resources.
基金supported by National Natural Science Foundation of China (Grant No.11001139)Fundamental Research Funds for the Central Universities (Grant No.65010771)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP Grant No.20100031120002)the second author is supported by the Discovery Grant from the Australian Research Council (ARC) (Project No.DP1096243)
文摘In this paper, the surplus of an insurance company is modeled by a Markovian regime- switching diffusion process. The insurer decides the proportional reinsurance and investment so as to increase revenue. The regime-switching economy consists of a fixed interest security and several risky shares. The optimal proportional reinsurance and investment strategies with no short-selling constraints for maximizing an exponential utility on terminal wealth are obtained.
基金Supported by National Basic Research Program of China (973 Program, Grant No. 2007CB814905)National Natural Science Foundation of China (Grant No. 10871102)
文摘In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross (CIR) model. For the stock price process, we consider both the case of constant volatility (driven by an O U process) and the case of stochastic volatility (driven by a CIR model). In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.
基金supported by National Key R&D Program of China under Grant No.2018YFB1305400the National Natural Science Foundations of China under Grant Nos.11971266,11831010,11571205Shandong Provincial Natural Science Foundations under Grant Nos.ZR2020ZD24,ZR2019ZD42。
文摘This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution to the HJB equation in the full information case. Some numerical illustrations are also provided.
基金Supported by the Natural Science Foundation of China(No.71071071,11101205)Ministry of Education Social Science Research Fund Planning Project,China Postdoctoral Science Foundation(No.200902507,20080431079)+1 种基金Nanjing University of Finance&Economics Science Research Foundation(2012Y1204)the Natural Sciences and Engineering Research Council of Canada(NSERC)
文摘In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to derive analytical expressions for the optimal portfolio policy and the mean-variance efficient frontier under certain conditions. We illustrate these results by an numerical example.
基金Supported by the National Natural Science Foundation of China(No.10571167,No.70501028)Beijing Sustentation Fund for Elitist(Grant No.20071D1600800421)National Social Science Foundation of China(Grant No.05&ZD008).
文摘Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distribution of extended regular variation, starting from an integro-differential equation for the maximal survival probability, we find that the corresponding ruin probability as a function of the initial surplus is also extended regular variation.
基金This work was supported by the China Scholarship Councilthe National Science Foundation of China(No.11631004)the Science and Technology Commission of Shanghai Municipality(No.14XD1400400)。
文摘The author studies the optimal investment stopping problem in both continuous and discrete cases, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth.Based on the work of Hu et al.(2018) with an additional stochastic payoff function,the author characterizes the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equations(BSDEs for short) with unbounded terminal condition. In regard to the discrete problem, she gets the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provides some useful a priori estimates about the solutions with the help of an auxiliary forward-backward SDE system and Malliavin calculus. Finally, she obtains the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization.
基金supported by the National Natural Science Foundation of China(Grant No.12071373)by the Fundamental Research Funds for the Central Universities of China(Grant No.JBK1805001)+1 种基金The work of J.Xing was supported by the National Natural Science Foundation of China(Grant No.12101151)by the Guizhou Key Laboratory of Big Data Statistical Analysis(Grant No.[2019]5103).
文摘This paper studies a problem of optimal investment and consumption with early retirement option under constant elasticity variation(CEV)model with finite horizon.Two risky assets are involved in the model with one following geometric Brownian motion and the other a CEV model.This problem is a kind of two dimensional mixed control and optimal stopping problems with finite horizon.The existence and continuity of the optimal retirement threshold surfaces are proved and the working and retirement regions are characterized theoretically.Least-squares Monte-Carlo methods are developed to solve this mixed control and optimal stopping problem.The algorithms are well implemented and the optimal retirement threshold surfaces,optimal investment strategies and the optimal consumptions are drawn via examples.
文摘We develop a fractional-degree expectation dependence which is the generalization of the first-degree and second-degree expectation dependence.The motivation for introducing such a dependence notion is to conform with the preferences of decision makers who are mostly risk averse but would be risk seeking at some wealth levels.We investigate some tractable equivalent properties for this new dependence notion,and explore its properties,including the invariance under increasing and concave transformations,and the invariance under convolution.We also extend our results to a combined fractional-degree expectation dependence notion includingε-almost firstdegree expectation dependence.Two applications on portfolio diversification problem and optimal investment in the presence of a background risk illustrate the usefulness of the approaches proposed in the present paper.