In this paper, we are concerned with Re?ected Geometric Brownian Motion (RGBM) with two barriers. And the stationary distribution of RGBM is derived by Markovian in?nitesimal Generator method. Consequently the ?rst pa...In this paper, we are concerned with Re?ected Geometric Brownian Motion (RGBM) with two barriers. And the stationary distribution of RGBM is derived by Markovian in?nitesimal Generator method. Consequently the ?rst passage time of RGBM is also discussed.展开更多
The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independe...The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independent standard Brownian motions. Conditions are given such that the solution is positive if the initial condition is positive. The equation the most probable path must satisfy is also derived and applied to a mathematical finance problem.展开更多
Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the...Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the others before, and it has a broad applying background and important theoretical significance in financial control and management of investment.This paper generalizes substantially the above stochastic control models under quite extensive conditions and describes the models more exactly under more normal theoretical system of stochastic process.By establishing a set of proper variational equations and proving the existence of its solution, and applying the means of stochastic analysis, this paper proves that the generalized stochastic control models have optimal controls.Meanwhile, we also analyze the structure of optimal controls carefully.Besides, we study the solution function of variational equations in a relatively deep-going way, which constitutes the value function of control models to some extent.Because the analysis methods of this paper are greatly different from those of original reference, this paper possesses considerable originality to some extent.In addition, this paper gives the strict proof to the part of original reference which is not fairly well-knit in analyses, and makes analyses and discussions of the model have the exactitude of mathematical sense.展开更多
研究了更新风险模型中的渐近破产概率,其中允许保险公司将其资产按常数比例投资于满足几何布朗运动的股票市场,其余部分投资于非负利率的债券市场.对此模型假定索赔额满足正则分布且两两拟渐近独立,根据伊藤公式,给出保险公司资产的表达...研究了更新风险模型中的渐近破产概率,其中允许保险公司将其资产按常数比例投资于满足几何布朗运动的股票市场,其余部分投资于非负利率的债券市场.对此模型假定索赔额满足正则分布且两两拟渐近独立,根据伊藤公式,给出保险公司资产的表达式,并最后给出了有限时间和无限时间的破产概率.当更新过程的特殊情况即复合泊松过程且索赔额独立同分布时,得出最终破产概率简洁的渐近表达式,与文献[Gaier J,Grandits P.Ruin probabilities and investment underinterest force in the presence of regularly varying tails.Scand Actuarial J,2004(4):256-278]中得到结果一样,并给出了模拟的结果.展开更多
文摘In this paper, we are concerned with Re?ected Geometric Brownian Motion (RGBM) with two barriers. And the stationary distribution of RGBM is derived by Markovian in?nitesimal Generator method. Consequently the ?rst passage time of RGBM is also discussed.
基金the General Research Fund of the University of Kansas.
文摘The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independent standard Brownian motions. Conditions are given such that the solution is positive if the initial condition is positive. The equation the most probable path must satisfy is also derived and applied to a mathematical finance problem.
基金Supported by the National Natural Science Foundation of China (Grant No 19671004)
文摘Recently, international academic circles advanced a class of new stochastic control models of a geometric Brownian motion which is an important kind of impulse control models whose cost structure is different from the others before, and it has a broad applying background and important theoretical significance in financial control and management of investment.This paper generalizes substantially the above stochastic control models under quite extensive conditions and describes the models more exactly under more normal theoretical system of stochastic process.By establishing a set of proper variational equations and proving the existence of its solution, and applying the means of stochastic analysis, this paper proves that the generalized stochastic control models have optimal controls.Meanwhile, we also analyze the structure of optimal controls carefully.Besides, we study the solution function of variational equations in a relatively deep-going way, which constitutes the value function of control models to some extent.Because the analysis methods of this paper are greatly different from those of original reference, this paper possesses considerable originality to some extent.In addition, this paper gives the strict proof to the part of original reference which is not fairly well-knit in analyses, and makes analyses and discussions of the model have the exactitude of mathematical sense.
文摘研究了更新风险模型中的渐近破产概率,其中允许保险公司将其资产按常数比例投资于满足几何布朗运动的股票市场,其余部分投资于非负利率的债券市场.对此模型假定索赔额满足正则分布且两两拟渐近独立,根据伊藤公式,给出保险公司资产的表达式,并最后给出了有限时间和无限时间的破产概率.当更新过程的特殊情况即复合泊松过程且索赔额独立同分布时,得出最终破产概率简洁的渐近表达式,与文献[Gaier J,Grandits P.Ruin probabilities and investment underinterest force in the presence of regularly varying tails.Scand Actuarial J,2004(4):256-278]中得到结果一样,并给出了模拟的结果.
