A Benchmark Approach to Quantitative Finance [electronic resource] / by Eckhard Platen, David Heath.

Preliminaries from Probability Theory -- Statistical Methods -- Modeling via Stochastic Processes -- Diffusion Processes -- Martingales and Stochastic Integrals -- The Itô Formula -- Stochastic Differential Equations -- to Option Pricing -- Various Approaches to Asset Pricing -- Continuous Financial Markets -- Portfolio Optimization -- Modeling Stochastic Volatility -- Minimal Market Model -- Markets with Event Risk -- Numerical Methods -- Solutions for Exercises.

The benchmark approach provides a general framework for financial market modeling, which extends beyond the standard risk neutral pricing theory. It permits a unified treatment of portfolio optimization, derivative pricing, integrated risk management and insurance risk modeling. The existence of an equivalent risk-neutral pricing measure is not required. Instead, it leads to pricing formulae with respect to the real world probability measure. This yields important modeling freedom which turns out to be necessary for the derivation of realistic, parsimonious market models. The first part of the book describes the necessary tools from probability theory, statistics, stochastic calculus and the theory of stochastic differential equations with jumps. The second part is devoted to financial modeling under the benchmark approach. Various quantitative methods for the fair pricing and hedging of derivatives are explained. The general framework is used to provide an understanding of the nature of stochastic volatility. The book is intended for a wide audience that includes quantitative analysts, postgraduate students and practitioners in finance, economics and insurance. It aims to be a self-contained, accessible but mathematically rigorous introduction to quantitative finance for readers that have a reasonable mathematical or quantitative background. Finally, the book should stimulate interest in the benchmark approach by describing some of its power and wide applicability.