Preprint1993

Solvability of forward-backward SDEs and the nodal set of Hamilton-Jacobi-Bellman Equations

43 citations0/0 files stored

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Stochastic processes and financial applications Nonlinear Differential Equations Analysis Nonlinear Partial Differential Equations

Abstract

. In this paper, the solvability of a class of forward-backward stochastic differential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. We design a stochastic relaxed control problem, with both drift and diffusion all being controlled, so that the solvability problem is converted to a problem of finding the nodal set of the viscosity solution to a certain Hamilton-Jacobi-Bellman equation. Our method overcomes the fatal difficulty encountered in the traditional contraction mapping theorem approach to the existence theorem of such SDEs. Keywords. forward-backward stochastic differential equations, stochastic control, relaxed control, viscosity solutions, nodal set. AMS Mathematics subject classification. 35K15, 49L20, 49L25, 60H10, 93E20. 1 Department of Mathematics, Purdue University, West Lafayette, IN 47907. 2 IMA, University of Minnesota, Minneapolis, MN 55455; on leave from Department of Mathematics, Fudan University, Shanghai 200433, China. ...

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 43 citations exist upstream.

References

2007Brownian Motion and Stochastic Calculus 2005Stochastic Integration and Differential Equations 1990Adapted solution of a backward stochastic differential equation 1978An Introductory Approach to Duality in Optimal Stochastic Control 1990Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems

Cited by

2019Backward stochastic Volterra integral equations—Representation of adapted solutions 2017Dynamic approaches for some time-inconsistent optimization problems 2008Weak solutions for forward–backward SDEs—a martingale problem approach 2000Forward–backward stochastic differential equations with nonsmooth coefficients

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.