Applications of the asymptotic expansion approach based on Malliavin-Watanabe calculus in financial problems. (English) Zbl 1191.91057
Akahori, Jiro (ed.) et al., Stochastic processes and applications to mathematical finance. Proceedings of the Ritsumeikan international symposium, Kusatsu, Shiga, Japan, March 5–9, 2003. River Edge, NJ: World Scientific (ISBN 981-238-778-1/hbk). 195-232 (2004).
Summary: This paper reviews the asymptotic expansion approach based on Malliavin-Watanabe Calculus in Mathematical Finance. We give the basic formulation of the asymptotic expansion approach and discuss its power and usefulness to solve important problems arisen in finance. As illustrations we use three major problems in finance and give some useful formulae and new results including numerical analyses.
For the entire collection see [Zbl 1065.91001].
For the entire collection see [Zbl 1065.91001].
MSC:
| 91G10 | Portfolio theory |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 60H07 | Stochastic calculus of variations and the Malliavin calculus |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 91G80 | Financial applications of other theories |
