Infinite Interval Backward Stochastic Differential Equations in the Plane

Infinite Interval Backward Stochastic Differential Equations in the Plane This paper studies the existence and uniqueness of solution of infinite interval backward stochastic differential equation (BSDE) in the plane driven by a Brownian sheet. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Infinite Interval Backward Stochastic Differential Equations in the Plane

Infinite Interval Backward Stochastic Differential Equations in the Plane

Acta Mathematicae Applicatae Sinica, English Series Vol. 19, No. 3 (2003) 485–490 Infinite Interval Backward Stochastic Differential Equations in the Plane Yan-ling Gu School of Mathematics and System Sciences, Shandong University, Jinan 250100, China (E-mail: guyl@math.sdu.edu.cn) Abstract This paper studies the existence and uniqueness of solution of infinite interval backward stochastic differential equation (BSDE) in the plane driven by a Brownian sheet. Keywords Two-parameter mixed type BSDE 2000 MR Subject Classification 60H10 1 Introduction Nonlinear backward stochastic differential equation (BSDE) has been independently introduced [4] [3] by Pardoux, Peng and by Duffie, Epstein . These authors proved the existence and unique- ness of an adapted pair of square integrable processes (Y ,Z ) satisfying t t t∈[0,T ] T T Y = ξ + f (s, Y ,Z )ds − Z dW,t ∈ [t, T ], t s s s s t t where W = {W ,t ∈ [0,T ]} is a standard d-dimensional Brownian motion defined on a com- plete probability space (Ω ,F , P), and let {F } denote its nature filtration, ξ is an F t 0≤t≤T T -measurable square integrable random variable and f (ω, t, y, z) is an adapted function which is [2] Lipschitz in (y, z). Later Chen, Wang extended this result to the infinite time interval BSDE whose Lipschitz coefficients can be unbounded and gave some applications. The theory provides a useful framework for formulating problems in mathematical finance and this motivates the work presented here. Backward stochastic differential equation in the plane driven by a two-parameter Brownian [8] motion is a new subject. Zaidi, Nualart first studied this kind of equation, but in their paper there is a stringent condition imposed on the Lipschitzian constants. This paper purports to give a sufficient condition on the coefficients of a class of infinite interval BSDE, under which the infinite interval BSDE has a unique solution for any given square...
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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2003 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
D.O.I.
10.1007/s10255-003-0124-0
Publisher site
See Article on Publisher Site

Abstract

This paper studies the existence and uniqueness of solution of infinite interval backward stochastic differential equation (BSDE) in the plane driven by a Brownian sheet.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 3, 2017

References

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