Consider a storage model fed by a Markov modulated Brownian motion. We prove that the stationary distribution of the model exits and that the running maximum of the storage process over the interval [0, t] grows asymp...Consider a storage model fed by a Markov modulated Brownian motion. We prove that the stationary distribution of the model exits and that the running maximum of the storage process over the interval [0, t] grows asymptotically like log t as t→∞.展开更多
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
This paper is concerned with the pricing problem of the discrete arithmetic average Asian call option while the discrete dividends follow geometric Brownian motion. The volatility of the dividends model depends on the...This paper is concerned with the pricing problem of the discrete arithmetic average Asian call option while the discrete dividends follow geometric Brownian motion. The volatility of the dividends model depends on the Markov-Modulated process. The binomial tree method, in which a more accurate factor has been used, is applied to solve the corresponding pricing problem. Finally, a numerical example with simulations is presented to demonstrate the effectiveness of the proposed method.展开更多
Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions,which find applications in many areas including queueing theory and mathematical finance.In this paper,we focus on stati...Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions,which find applications in many areas including queueing theory and mathematical finance.In this paper,we focus on stationary distributions for sticky Brownian motions.Main results obtained here include tail asymptotic properties in the marginal distributions and joint distributions.The kernel method,copula concept and extreme value theory are the main tools used in our analysis.展开更多
在证券市场,布林带作为流行的技术分析工具被广泛的运用.到目前为止有许多模型被建立用来预测证券的价格,因此研究这些模型是否具有布林带性质是一个重要的问题.Liu,Huang and Zheng(2006)和Liu and Zheng(2006)分别讨论了Black-Schole...在证券市场,布林带作为流行的技术分析工具被广泛的运用.到目前为止有许多模型被建立用来预测证券的价格,因此研究这些模型是否具有布林带性质是一个重要的问题.Liu,Huang and Zheng(2006)和Liu and Zheng(2006)分别讨论了Black-Scholes模型和随机波动率模型作为真实的股票市场的布林带,并且证明了相应的统计量的平稳性和大数定律成立.本文我们将上述结果推广到马氏调制的几何布朗运动模型.展开更多
In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expans...In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expansion for the transition density, we prove the existence and uniqueness of both quasi-stationary distribution (qsd) and mean ratio quasi-stationary distribution (mrqsd). The later is shown to be closely related to laws of large numbers (LLN) and to quasi-ergodicity. We further show that the mrqsd is the unique stationary distribution of a certain limiting ergodic diffusion process of the BM conditioned on not having been killed. We also show that a phase transition occurs from mrqsd to qsd. On the other hand, we study the large deviation behavior related to the above problems. A key observation is that the mrqsd is the unique minimum of certain large deviation rate function. We further prove that the limiting diffusion process also satisfies a large deviation principle with the rate function attaining its unique minimum at the mrqsd. These give interpretations of the mrqsd from different points of view, and establish some intrinsic connections among the above topics. Some general results concerning Yaglom limit, moment convergence and LLN are also obtained.展开更多
基金the National Natural Science Foundation of China (No. 10131040).
文摘Consider a storage model fed by a Markov modulated Brownian motion. We prove that the stationary distribution of the model exits and that the running maximum of the storage process over the interval [0, t] grows asymptotically like log t as t→∞.
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.
文摘This paper is concerned with the pricing problem of the discrete arithmetic average Asian call option while the discrete dividends follow geometric Brownian motion. The volatility of the dividends model depends on the Markov-Modulated process. The binomial tree method, in which a more accurate factor has been used, is applied to solve the corresponding pricing problem. Finally, a numerical example with simulations is presented to demonstrate the effectiveness of the proposed method.
基金supported by the Shandong Provincial Natural Science Foundation of China(Grtant No.ZR2019MA035)the Natural Sciences and Engineering Research Council(NSERC)of Canadasupported by the China Scholarship Council(Grant No.201708370006)。
文摘Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions,which find applications in many areas including queueing theory and mathematical finance.In this paper,we focus on stationary distributions for sticky Brownian motions.Main results obtained here include tail asymptotic properties in the marginal distributions and joint distributions.The kernel method,copula concept and extreme value theory are the main tools used in our analysis.
基金Research partially supported by N.S.F.C.Grant 10371074 and 10671072by"Shu Guang"project(04SG27)of Shanghai Municipal Education Commission and Shanghai Education Development Foundationby Doctoral Program Foundation of the Ministry of Education of China(20060269016)by Anhui Province university young teacher scientific research funds 2006jq1045.
文摘在证券市场,布林带作为流行的技术分析工具被广泛的运用.到目前为止有许多模型被建立用来预测证券的价格,因此研究这些模型是否具有布林带性质是一个重要的问题.Liu,Huang and Zheng(2006)和Liu and Zheng(2006)分别讨论了Black-Scholes模型和随机波动率模型作为真实的股票市场的布林带,并且证明了相应的统计量的平稳性和大数定律成立.本文我们将上述结果推广到马氏调制的几何布朗运动模型.
基金supported by National Natural Science Foundation of China(Grant No. 10971253)
文摘In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expansion for the transition density, we prove the existence and uniqueness of both quasi-stationary distribution (qsd) and mean ratio quasi-stationary distribution (mrqsd). The later is shown to be closely related to laws of large numbers (LLN) and to quasi-ergodicity. We further show that the mrqsd is the unique stationary distribution of a certain limiting ergodic diffusion process of the BM conditioned on not having been killed. We also show that a phase transition occurs from mrqsd to qsd. On the other hand, we study the large deviation behavior related to the above problems. A key observation is that the mrqsd is the unique minimum of certain large deviation rate function. We further prove that the limiting diffusion process also satisfies a large deviation principle with the rate function attaining its unique minimum at the mrqsd. These give interpretations of the mrqsd from different points of view, and establish some intrinsic connections among the above topics. Some general results concerning Yaglom limit, moment convergence and LLN are also obtained.
