共查询到20条相似文献,搜索用时 15 毫秒
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Shao Lin JI Zhen WU 《数学学报(英文版)》2007,23(12):2189-2204
The authors get a maximum principle for one kind of stochastic optimization problem motivated by dynamic measure of risk. The dynamic measure of risk to an investor in a financial market can be studied in our framework where the wealth equation may have nonlinear coefficients. 相似文献
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本文讨论不完全市场中股票收益率不确定时的动态风险度量问题和一个相关的随机对策问题。该动态风险度量可表示为一个随机最优控制问题的值函数,以倒向随机微分方程为工具我们给出了最优目标具有的形式,并给出随机对策问题上值与下值相等的充分条件和鞍点的存在性。 相似文献
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倒向随机微分方程及其应用 总被引:43,自引:1,他引:42
本文将介绍一类新的议程:倒向随机微分方程,为了便于理解,我们将首先通过与常微分方程和经典的随机微分方程的对比,并通过数理经济和数学金融学中的一个典型的例子来引入倒向随机微分方程。 相似文献
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Feng Hu 《数学学报(英文版)》2013,29(4):815-832
In this paper, we study dynamically consistent nonlinear evaluations in Lp(1p2). One of our aim is to obtain the following result: under a domination condition, an Ft-consistent evaluation is an Eg-evaluation in Lp . Furthermore, without the assumption that the generating function g(t, ω, y, z) is continuous with respect to t, we provide some useful characterizations of an Eg-evaluation by g and give some applications. These results include and extend some existing results. 相似文献
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Rainer BUCKDAHN 《应用数学学报(英文版)》2011,27(4):647-678
In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory
of Reflected Backward Stochastic Differential Equations (RBSDEs). We will establish the dynamic programming principle for
the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward
way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper
and the lower Hamilton-Jacobi-Bellman-Isaacs equations with obstacles, respectively. The method differs significantly from
those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove
a new estimate for RBSDEs being sharper than that in the paper of El Karoui, Kapoudjian, Pardoux, Peng and Quenez (1997),
which turns out to be very useful because it allows us to estimate the L
p
-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution
to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs
equation with obstacle. 相似文献
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本文研究伊藤-泊松型随机微分方程的线性二次控制问题,利用动态规划方法、伊藤公式等技巧,通过解HJB方程,我们得到了随机Riccati方程及另外两个微分方程,求出控制变量,解决了线性二次最优控制最优问题. 相似文献
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Zhenxin Liu 《数学研究通讯:英文版》2023,39(3):476-500
The limit distribution for homogeneous Markov processes is studied extensively and well understood, but it is not the case for inhomogeneous
Markov processes. In this paper, we review some recent results on inhomogeneous Markov processes generated by non-autonomous stochastic (partial)
differential equations (SDE in short). Under some suitable conditions, we show
that the distribution of recurrent solutions of SDEs constitutes the limit distribution of the corresponding inhomogeneous Markov processes. 相似文献
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本文建立了油气田开采动态系统的随机微分方程数学模型,在对模型求解的基础上,给出了各状态变量的均值函数与方差函数的估计。 相似文献
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路慧芹 《数学物理学报(A辑)》2002,22(3):386-390
该文利用锥理论和Banach 压缩映象原理讨论了一类含参数的非线性算子方程,证明了这类方程解的存在唯一性及其解对参数的连续相依性定理,并给出了对Banach 空间中含参数的一阶积-微分方程初值问题的应用. 相似文献
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The paper presents a valuation model of futures options trading at exchanges with initial margin requirements and daily price limit, and this result gives an academic guidance to design trading rules at exchanges. Unlike the leading work of Black, certain trading rules are considered so as to be more fit for practical futures markets. The paper prices futures options with initial margin requirements and daily price limit by duplicating them with the help of the theory of backward stochastic differential equations (BSDEs, for short). Furthermore, an explicit expression of the price Of the call (or the put) futures option is given and also is shown to be the unique solution of the associated nonlinear partial differential equation. 相似文献
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We consider a class of nonlinear integro-differential equations involving a fractional power of the Laplacian and a nonlocal quadratic nonlinearity represented by a singular integral operator. Initially, we introduce cut-off versions of this equation, replacing the singular operator by its Lipschitz continuous regularizations. In both cases we show the local existence and global uniqueness in L1Lp. Then we associate with each regularized equation a stable-process-driven nonlinear diffusion; the law of this nonlinear diffusion has a density which is a global solution in L1 of the cut-off equation. In the next step we remove the cut-off and show that the above densities converge in a certain space to a solution of the singular equation. In the general case, the result is local, but under a more stringent balance condition relating the dimension, the power of the fractional Laplacian and the degree of the singularity, it is global and gives global existence for the original singular equation. Finally, we associate with the singular equation a nonlinear singular diffusion and prove propagation of chaos to the law of this diffusion for the related cut-off interacting particle systems. Depending on the nature of the singularity in the drift term, we obtain either a strong pathwise result or a weak convergence result.
Mathematics Subject Classifications (2000) 60K35, 35S10. 相似文献
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On optimal solutions of general continuous-singular stochastic control problem of McKean-Vlasov type
Lina Guenane Mokhtar Hafayed Shahlar Meherrem Syed Abbas 《Mathematical Methods in the Applied Sciences》2020,43(10):6498-6516
In this paper, we establish general necessary optimality conditions for stochastic continuous-singular control of McKean-Vlasov type equations. The coefficients of the state equation depend on the state of the solution process as well as of its probability law and the control variable. The coefficients of the system are nonlinear and depend explicitly on the absolutely continuous component of the control. The control domain under consideration is not assumed to be convex. The proof of our main result is based on the first- and second-order derivatives, with respect to measure in Wasserstein space of probability measures, and by using variational method. 相似文献
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《Stochastic Processes and their Applications》2019,129(10):4009-4050
We study ergodic backward stochastic differential equations (EBSDEs), for which the underlying diffusion is assumed to be multiplicative and of linear growth. The fact that the forward process has an unbounded diffusion is balanced with an assumption of weak dissipativity for its drift. Moreover, the forward equation is assumed to be non-degenerate. We study the existence and uniqueness of EBSDEs and we apply our results to an ergodic optimal control problem. In particular, we show the large time behaviour of viscosity solution of Hamilton–Jacobi–Bellman equation with an exponential rate of convergence when the underlying diffusion is multiplicative and unbounded. 相似文献
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Starting from the theory of porous materials, the nonlinear theory of dry friction, and the model of a bent slender beam, a nonlinear constitutive equation for elastic porous metal rubbers is constructed. Static compressive experiments were carried out on hollow cylinders of such a rubber, from which relations between all coefficients of the constitutive equation and the material density were determined. Based on the data obtained, the constitutive equation of the material was predicted successfully. The effect of density of the metal rubber on its stiffness and on the nonlinear constitutive equation was revealed by experiments.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 449–460, July–August, 2005. 相似文献
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In this paper, we consider the problem to find a market portfolio that minimizes the convex risk measure of the terminal wealth in a jump diffusion market. We formulate the problem as a two player (zero-sum) stochastic differential game. To help us find a solution, we prove a theorem giving the Hamilton–Jacobi–Bellman–Isaacs (HJBI) conditions for a general zero-sum stochastic differential game in a jump diffusion setting. We then use the theorem to study particular risk minimization problems. Finally, we extend our approach to cover general stochastic differential games (not necessarily zero-sum), and we obtain similar HJBI equations for the Nash equilibria of such games. 相似文献
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The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Recently, techniques from applied mathematics have been utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. It was shown that dyad and multiplicative triad interactions combine with the climatological linear operator interactions to produce a normal form with both strong nonlinear cubic dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. The probability distribution functions (PDFs) of low frequency climate variables exhibit small but significant departure from Gaussianity but have asymptotic tails which decay at most like a Gaussian. Here, rigorous upper bounds with Gaussian decay are proved for the invariant measure of general normal form stochastic models. Asymptotic Gaussian lower bounds are also established under suitable hypotheses. 相似文献