Multidimensional quadratic and subquadratic BSDEs with special structure

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2013-09-26 DOI:10.1080/17442508.2015.1013959

Patrick Cheridito, Kihun Nam

引用次数: 53

Abstract

We study multidimensional BSDEs of the formwith bounded terminal conditions and drivers that grow at most quadratically in . We consider three different cases. In the first case, the BSDE is Markovian, and a solution can be obtained from a solution to a related FBSDE. In the second case, the BSDE becomes a one-dimensional quadratic BSDE when projected to a one-dimensional subspace, and a solution can be derived from a solution of the one-dimensional equation. In the third case, the growth of the driver in is strictly subquadratic, and the existence and uniqueness of a solution can be shown by first solving the BSDE on a short time interval and then extending it recursively.

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具有特殊结构的多维二次和次二次BSDEs

我们研究了具有有界末端条件和最多二次增长的驱动的多维BSDEs的形式。我们考虑三种不同的情况。在第一种情况下，BSDE是马尔可夫的，可以从相关FBSDE的解中得到解。在第二种情况下，当将BSDE投影到一维子空间时，BSDE变成了一维二次BSDE，并且可以从一维方程的解中得到解。在第三种情况下，驱动器的增长是严格次二次的，通过先在短时间区间上求解BSDE，然后递归扩展它，可以证明解的存在唯一性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.