Stochastic Analytical Models in Mathematical Finance

Chapter
Part of the Mathematics for Industry book series (MFI, volume 5)

Abstract

Stochastic analysis is a key tool in the recent study of Mathematical Finance. Stochastic analytical models in Mathematical Finance are classified into two types. One is a discrete model, in which the trading time is restricted to the set of natural numbers, and moreover the underlying probability space is often a finite set. The other is a continuous model, which admits the trading time to be any non-negative real number. In a lot of continuous models, stochastic differential equations govern the time evolution of the models. A short survey on these two models will be given.

Keywords

Equivalent martingale measure Pricing formula CRR model Trinomial model Stochastic integral Black-Scholes model Implied volatility Stochastic volatility model Single-factor model 

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Faculty of Arts and ScienceKyushu UniversityNishi-kuJapan

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