Introduction to Stochastic Finance

ISBN-13: 9789811316562 / Angielski / Miękka / 2018 / 403 str.

Jia-An Yan

Opis

This book gives a systematic introduction to the basic theory of financial mathematics, with an emphasis on applications of martingale methods in pricing and hedging of contingent claims, interest rate term structure models, and expected utility maximization problems.

Recenzje

"The monograph is a wonderful text for graduate courses in mathematical finance and related fields. ... The materials presented in the monograph are organised in a thoughtful way." (Tak Kuen Siu, zbMATH 1420.91001, 2019)

Spis treści

Foundation of Probability Theory and Discrete-time Martingales.- Portfolio Selection Theory in Discrete Time.- Financial Markets in Discrete Time.- Martingale Theory and Itˆo Stochastic Analysis.- The Black-Scholes Model and Its Modifications.- Pricing and Hedging of Exotic Options.- Itˆo Process and Diffusion Models.- Term Structure Models For Interest Rates.- Optimal Investment-Consumption Strategies in Diffusion Models.- Static Risk Measures.- Stochastic Calculus and Semimartingale Model.- Optimal Investment in Incomplete Markets.- Martingale Method for Utility Maximization.- Optimal Growth Portfolios

and Option Pricing

O autorze

Professor Jia-An Yan is a Professor of Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences. He is a Member of the Chinese Academy of Sciences and he has served as Editor-in-Chief of Acta Mathematicae Applicatae Sinica and members of several editorial boards. His main research area is stochastic analysis and mathematical finance.

Blurb

This book gives a systematic introduction to the basic theory of financial mathematics, with an emphasis on applications of martingale methods in pricing and hedging of contingent claims, interest rate term structure models, and expected utility maximization problems. The general theory of static risk measures, basic concepts and results on markets of semimartingale model,  and a numeraire-free and original probability based framework for financial markets are also included. The basic theory of probability and Ito's theory of stochastic analysis, as preliminary knowledge, are presented.