Forward-backward stochastic differential equations and their applications in finance

Author

Ma, Jin

Author_Institution

Dept. of Math., Purdue Univ., West Lafayette, IN, USA

Volume

4

fYear

1995

fDate

13-15 Dec 1995

Firstpage

3354

Abstract

In this paper we present some results concerning the solvability of the adapted solutions to a class of forward-backward stochastic differential equations over an arbitrarily prescribed time duration, and several applications of such equations in mathematical finance. In particular, we introduce a direct scheme (called “four step scheme”) initiated by Ma-Protter-Yong (1994), which enables one to derive the explicit relations between the forward and backward components of the adapted solutions. Using the extensions of such a scheme in different directions, we then study some problems in finance including a console rate problem, a problem of hedging options for a large investor, and a stochastic Black-Scholes formula

Keywords

computability; differential equations; finance; partial differential equations; probability; stochastic processes; console rate proble; forward-backward stochastic differential equations; four step scheme; hedging options; mathematical finance; option pricing; probability; solvability; stochastic Black-Scholes formula; Differential equations; Filtration; Finance; Forward contracts; Infinite horizon; Integral equations; Mathematics; Pricing; Stochastic processes;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1995., Proceedings of the 34th IEEE Conference on

Conference_Location

New Orleans, LA

ISSN

0191-2216

Print_ISBN

0-7803-2685-7

Type

conf

DOI

10.1109/CDC.1995.479005

Filename

479005