Analysis, Geometry, and Modeling in Finance

Produktbeschreibung

This book offers new ways of solving financial problems using techniques found in physics and mathematics. Through the problem of option pricing, it demonstrates how differential geometry, spectral decomposition, and supersymmetry can be used as new tools in finance. The author covers practical issues from the industry, such as the calibration of stochastic volatility models and stochastic Libor market models. He uses Mathematica® and C++ for numerical implementations and provides end-of-chapter problems, including some based on recently published research papers. 

Inhaltsverzeichnis

Introduction. A Brief Course in Financial Mathematics. Smile Dynamics and
Pricing of Exotic Options. Differential Geometry and Heat Kernel Expansion.
Local Volatility Models and Geometry of Real Curves. Stochastic Volatility
Models and Geometry of Complex Curves. Multi-Asset European Option and Flat
Geometry. Stochastic Volatility Libor Market Models and Hyperbolic Geometry.
Solvable Local and Stochastic Volatility Models. Schrödinger Semigroups
Estimates and Implied Volatility Wings. Analysis on Wiener Space with
Applications. Portfolio Optimization and Bellman-Hamilton-Jacobi Equation.
Appendices. References. Index. 

Autoreninfo

Pierre Henry-Labordere