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On Forward–Backward Stochastic Differential Equations in a Domination-Monotonicity Framework.
- Source :
-
Applied Mathematics & Optimization . Feb2022, Vol. 85 Issue 1, p1-46. 46p. - Publication Year :
- 2022
-
Abstract
- In this paper, inspired by various stochastic linear-quadratic (LQ, for short) problems, we develop the method of continuation to study nonlinear forward–backward stochastic differential equations (FBSDEs, for short) in a kind of domination-monotonicity frameworks. The coupling of FBSDEs is in a general form, i.e., it not only appears in integral terms and terminal terms, but also in initial terms. By virtue of introducing various matrices, matrix-valued random variables and matrix-valued stochastic processes, we present the domination-monotonicity framework carefully and rigorously. A unique solvability result and a pair of estimates for coupled FBSDEs are obtained (see Theorem 3.5 in the case of simple domination-monotonicity conditions and Theorem 5.2 in the case of multi-level self-similar domination-monotonicity structures). As applications of theoretical results, the related stochastic Hamiltonian systems of several LQ problems are discussed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00954616
- Volume :
- 85
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 155153267
- Full Text :
- https://doi.org/10.1007/s00245-022-09841-8