The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also pr...The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved.展开更多
The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of soluti...The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.展开更多
In this paper we consider the problem of determining the optimal time to buy an asset in a position of an uptrend or downtrend in the financial market and currency market as well as other markets. Asset price is model...In this paper we consider the problem of determining the optimal time to buy an asset in a position of an uptrend or downtrend in the financial market and currency market as well as other markets. Asset price is modeled as a geometric Brownian motion with drift being a two-state Markov chain. Based on observations of asset prices, investors want to detect the change points of price trends as accurately as possible, so that they can make the decision to buy. Using filtering techniques and stochastic analysis, we will develop the optimal boundary at which investors implement their decisions when the posterior probability process reaches a certain threshold.展开更多
Suppose that C is a finite collection of patterns. Observe a Markov chain until one of the patterns in C occurs as a run. This time is denoted by τ. In this paper, we aim to give an easy way to calculate the mean wai...Suppose that C is a finite collection of patterns. Observe a Markov chain until one of the patterns in C occurs as a run. This time is denoted by τ. In this paper, we aim to give an easy way to calculate the mean waiting time E(τ) and the stopping probabilities P(τ = τA)with A ∈ C, where τA is the waiting time until the pattern A appears as a run.展开更多
Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time ts of this flow is still not well understood. Especi...Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time ts of this flow is still not well understood. Especially, there exist a series of jumps on the ts-λ. curve. In this paper we introduce a normalized mechanical energy by mode decomposition and mathematical analogy to describe the start-up process. An improved definition of start-up time is presented based on the normalized mechanical energy. It is proved that the ts-λ. curve contains a series of jumps if λ is larger than a critical value. The exact positions of the jumps are determined and the physical reason of the jumps is discussed.展开更多
Assume that we want to shell an asset with unknown drift but known that the drift is a two value random variable, and the initial distribution can be estimated. As time goes by, this distribution is updated and base o...Assume that we want to shell an asset with unknown drift but known that the drift is a two value random variable, and the initial distribution can be estimated. As time goes by, this distribution is updated and base on the probability of the drift takes the small one gives us the stopping rule. Research results show that the optimal strategy to sell the asset is if the initial probability that the drift receives a small value greater than a certain threshold then liquidates the asset immediately, otherwise the asset holder will wait until the probability of the drift receives a small value passing a certain threshold, it is the optimal time to liquidate the asset.展开更多
In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and th...In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and this probability distribution behavior changes chronologically. The result of finding the optimal strategy to sell the asset is the first time asset price falling into deterministic time-dependent boundary. Moreover, the boundary is represented by an increasing and continuous monotone function satisfying a nonlinear integral equation. We also conduct to find the empirical optimization boundary and simulate the asset price process.展开更多
In this paper,we prove the existence and uniqueness for Backward Stochastic Differential Equations with stopping time as time horizon under the hypothesis that the generator is bounded.We first prove for the stopping ...In this paper,we prove the existence and uniqueness for Backward Stochastic Differential Equations with stopping time as time horizon under the hypothesis that the generator is bounded.We first prove for the stopping time with finite values and for the general stopping time we prove the result taking limit.We suggest a new approach to generalize the results for the case of constant time horizon to the case of stopping time horizon.展开更多
Objective: Study the influence of the stop time in winter, times of plateau on the index in early days for plateau constructors meet;Method:Is it participate in plateau construction of 2002-2004 to choose,enter into t...Objective: Study the influence of the stop time in winter, times of plateau on the index in early days for plateau constructors meet;Method:Is it participate in plateau construction of 2002-2004 to choose,enter into the plateau again of 2003-2005 practise clothes finish to mate 326 materials “physical examination in front of the worker",which is passed in Nanshankou Hospital in early days, divided into 3 groups according to the difference of year for the physical examination, examine by leaning towards relevant analytical methods;Result: （1） In the situation of day controlling about the stop time in winter, times of garrison in plateau and blood and oxygen saturation lever （SaO2）, the systolic pressure （sBP） is presented and shouldered relevantly winter to control. Present positive correlation with the value of hemoglobin （Hb）;（2） It is stopped that in case of controlling and is garrisoned in the number of times of plateau in winter day and blood and oxygen saturation lever （SaO2） to present positive correlation. Present and shoulder with the hemoglobin （Hb） relevantly.Conclusion: In order to ensure the health of plateau constructors to the maximum extent, should try one’s best to reduce the number of times of returning to the plateau in possible cases. At the same time each one constructs for year and returns to the time that the hinterland concentrates rest should be on above 90 days.展开更多
AS a foreigner anywhere, it is important to make an effort to experience the cultural heritage of the city you are in. In Paris you should visit Montmartre, in London you can＇t miss Buckingham Palace, and before you ...AS a foreigner anywhere, it is important to make an effort to experience the cultural heritage of the city you are in. In Paris you should visit Montmartre, in London you can＇t miss Buckingham Palace, and before you leave Sydney, a trip to the Blue Mountains is essential, For Beiiing, the unquestionable birthplace of Chinese culture is buried deep within the city＇s ancient hutongs.展开更多
基金This work was supported by the National Natural Science Foundation of China (10001022 and 10371067)the Excellent Young Teachers Program and the Doctoral program Foundation of MOE and Shandong Province,P.R.C.
文摘The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved.
文摘The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.
文摘In this paper we consider the problem of determining the optimal time to buy an asset in a position of an uptrend or downtrend in the financial market and currency market as well as other markets. Asset price is modeled as a geometric Brownian motion with drift being a two-state Markov chain. Based on observations of asset prices, investors want to detect the change points of price trends as accurately as possible, so that they can make the decision to buy. Using filtering techniques and stochastic analysis, we will develop the optimal boundary at which investors implement their decisions when the posterior probability process reaches a certain threshold.
基金Supported by the National Natural Science Foundation of China(11771286,11371317)the Zhejiang Provincial Natural Science Foundation of China(LQ18A010007)
文摘Suppose that C is a finite collection of patterns. Observe a Markov chain until one of the patterns in C occurs as a run. This time is denoted by τ. In this paper, we aim to give an easy way to calculate the mean waiting time E(τ) and the stopping probabilities P(τ = τA)with A ∈ C, where τA is the waiting time until the pattern A appears as a run.
文摘Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time ts of this flow is still not well understood. Especially, there exist a series of jumps on the ts-λ. curve. In this paper we introduce a normalized mechanical energy by mode decomposition and mathematical analogy to describe the start-up process. An improved definition of start-up time is presented based on the normalized mechanical energy. It is proved that the ts-λ. curve contains a series of jumps if λ is larger than a critical value. The exact positions of the jumps are determined and the physical reason of the jumps is discussed.
文摘Assume that we want to shell an asset with unknown drift but known that the drift is a two value random variable, and the initial distribution can be estimated. As time goes by, this distribution is updated and base on the probability of the drift takes the small one gives us the stopping rule. Research results show that the optimal strategy to sell the asset is if the initial probability that the drift receives a small value greater than a certain threshold then liquidates the asset immediately, otherwise the asset holder will wait until the probability of the drift receives a small value passing a certain threshold, it is the optimal time to liquidate the asset.
文摘In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and this probability distribution behavior changes chronologically. The result of finding the optimal strategy to sell the asset is the first time asset price falling into deterministic time-dependent boundary. Moreover, the boundary is represented by an increasing and continuous monotone function satisfying a nonlinear integral equation. We also conduct to find the empirical optimization boundary and simulate the asset price process.
文摘In this paper,we prove the existence and uniqueness for Backward Stochastic Differential Equations with stopping time as time horizon under the hypothesis that the generator is bounded.We first prove for the stopping time with finite values and for the general stopping time we prove the result taking limit.We suggest a new approach to generalize the results for the case of constant time horizon to the case of stopping time horizon.
文摘Objective: Study the influence of the stop time in winter, times of plateau on the index in early days for plateau constructors meet;Method:Is it participate in plateau construction of 2002-2004 to choose,enter into the plateau again of 2003-2005 practise clothes finish to mate 326 materials “physical examination in front of the worker",which is passed in Nanshankou Hospital in early days, divided into 3 groups according to the difference of year for the physical examination, examine by leaning towards relevant analytical methods;Result: （1） In the situation of day controlling about the stop time in winter, times of garrison in plateau and blood and oxygen saturation lever （SaO2）, the systolic pressure （sBP） is presented and shouldered relevantly winter to control. Present positive correlation with the value of hemoglobin （Hb）;（2） It is stopped that in case of controlling and is garrisoned in the number of times of plateau in winter day and blood and oxygen saturation lever （SaO2） to present positive correlation. Present and shoulder with the hemoglobin （Hb） relevantly.Conclusion: In order to ensure the health of plateau constructors to the maximum extent, should try one’s best to reduce the number of times of returning to the plateau in possible cases. At the same time each one constructs for year and returns to the time that the hinterland concentrates rest should be on above 90 days.
文摘AS a foreigner anywhere, it is important to make an effort to experience the cultural heritage of the city you are in. In Paris you should visit Montmartre, in London you can＇t miss Buckingham Palace, and before you leave Sydney, a trip to the Blue Mountains is essential, For Beiiing, the unquestionable birthplace of Chinese culture is buried deep within the city＇s ancient hutongs.
