紹介
Numerical Methods in Finance has emerged as a discipline at the intersection of probability theory, finance and numerical analysis. This book, based on lectures given at the Newton Institute as part of a broader programme, describes a wide variety of numerical methods used in financial analysis: computation of option prices, especially of American option prices, by finite difference and other methods; numerical solution of portfolio management strategies; statistical procedures; identification of models; Monte Carlo methods; and numerical implications of stochastic volatilities. Articles have been written in a pedagogic style and made reasonably self-contained, covering both mathematical matters and practical issues in numerical problems. Thus the book has something to offer economists, probabilists and applied mathematicians working in finance.
目次
Introduction
1. Convergence of numerical schemes for degenerate parabolic equations arising in finance theory G. Barles
2. Continuous-time Monte Carlo methods and variance reduction Nigel J. Newton
3. Recent advances in numerical methods for pricing derivative securities M. Broad and J. Detemple
4. American options: a comparison of numerical methods F. AitSahlia and P. Carr
5. Fast, accurate and inelegant valuation of American options Adriaan Joubert and L. C. G. Rogers
6. Valuation of American options in a jump-diffusion model Xiao Lan Zhang
7. Some nonlinear methods for studying far-from-the-money contingent claims E. Fournie, J. M. Lasry and P.-L. Lions
8. Stochastic volatility models E. Fournie, J. M. Lasry and N. Touzi
9. Dynamic optimisation for a mixed portfolio with transaction costs Agnes Sulem
10. Imperfect markets and backward stochastic differential equations N. El Karoui and M. C. Quenez
11. Numerical methods for backward stochastic differential equations D. Chevance
12. Viscosity solutions and numerical schemes for investment/consumption models with transaction costs Agnes Tourin and Thaleia Zariphopoulou
13. Does volatility jump or just diffuse? A statistical approach Renzo G. Avesani and Pierre Bertrand
14. Martingale-based hedge error control Peter Bossaerts and Bas Werker
15. The use of second order stochastic dominance to bound European call prices: theory and results Claude Henin and Nathalie Pistre.
