His fundamental contributions to stochastic control include establishing a relation between maximum principle and dynamic programming via the viscosity solution theory , and introducing and developing the indefinite stochastic lq control theory 他应用粘性解理论建立了最大值原理与动态规划之间的本质关系,并开创及发展了不定随机lq控制理论。这些都是随机控制论领域中的重大贡献。
The study of backward stochastic differential equation ( bsde ) come from the research of stochastic control and finance etc . ; on the contrary , the results of the equation theory applied to the control , finance and pde etc . fields of math 倒向随机微分方程( bsde )的研究源于随机控制和金融等问题的研究;反过来方程理论的研究成果在控制、金融领域,偏微分方程等数学领域有着重要的应用。
So far , bsdes have 2 types : one is ito integral type bsde driven by brown motion which come directly from stochastic control and it is applied to financial problem later ; the other is bsde with conditional expectation which come directly from financial problem )型倒向随机微分方程,直接源自于随机控制的研究,后来被应用于金融问题的研究;第二类是带有条件期望的倒向随机微分方程,它直接源自于金融问题的研究。
The analysis involves martingale theory , optimal stopping , stochastic control problem and convex analysis . as for the general incomplete financial market , the upper - and lower - hedging prices of arbitrage - free interval are obtained . the quisimartingales decomposition has been proved 借助于鞅论,最优停时,随机控制和凸分析等理论与方法,就一般的非完备金融市场,未定权益的估值得以研究,并且我们求出了上、下保值价格。
This paper discusses a variation equation problem in a class of singular stochastic control with stopping time , gives its solution under two different conditions , which is a one order continuous differentiable and concave function , and gives the exact form 摘要讨论了一类带停时的奇异型随机控制问题中的一个变分方程问题,并且在两种不同的情况下给出了该变分方程的解,即为一阶连续可导凹函数,并在两种情况下给出了此函数的具体形式。
Stochastic control or stochastic optimal control is a subfield of control theory which deals with the existence of uncertainty either in observations of the data or in the things that drive the evolution of the data. The designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability distribution affects the evolution and observation of the state variables.