"Introductory Stochastic Analysis for Finance and Insurance" by X. Sheldon Lin

Introductory Stochastic Analysis for Finance and Insurance introduces readers to the topics needed to master and use basic stochastic analysis techniques for mathematical finance. The author presents the theories of stochastic processes and stochastic calculus and provides the necessary tools for modeling and pricing in finance and insurance. Practical in focus, the book's emphasis is on application, intuition, and computation, rather than theory.

Incorporates the many tools needed for modeling and pricing in finance and insurance



Consequently, the text is of interest to graduate students, researchers, and practitioners interested in these areas. While the text is self-contained, an introductory course in probability theory is beneficial to prospective readers.

This book evolved from the author's experience as an instructor and has been thoroughly classroom-tested.
Following an introduction, the author sets forth the fundamental information and tools needed by researchers and practitioners working in the financial and insurance industries:
* Overview of Probability Theory
* Discrete-Time stochastic processes
* Continuous-time stochastic processes
* Stochastic calculus: basic topics

CONTENTS
List of Figures
List of Tables
Preface
1 Introduction
2 Overview of Probability Theory
2.1 Probability Spaces and Information Structures
2.2 Random Variables, Moments and Transforms
2.3 Multivariate Distributions
2.4 Conditional Probability and Conditional Distributions
2.5 Conditional Expectation
2.6 The Central Limit Theorem
3 Discrete-Time Stochastic Processes
3.1 Stochastic Processes and Information Structures
3.2 Random Walks
3.3 Discrete-Time Markov Chains
3.4 Martingales and Change of Probability Measure
3.5 Stopping Times
3.6 Option Pricing with Binomial Models
4 Continuous-Time Stochastic Processes
4.1 General Description of Continuous-Time Stochastic Processes
4.2 Brownian Motion
4.3 The Reflection Principle and Barrier Hitting Probabilities
4.4 The Poisson Process and Compound Poisson Process
4.5 Martingales
4.6 Stopping Times and the Optional Sampling Theorem
5 Stochastic Calculus: Basic Topics
5.1 Stochastic (lto) Integration
5.2 Stochastic Differential Equations
5.3 One-Dimensional Ito's Lemma
5.4 Continuous-Time Interest Rate Models
5.5 The Black-Scholes Model and Option Pricing Formula
5.6 The Stochastic Version of Integration by Parts
5.7 Exponential Martingales
5.8 The Martingale Representation Theorem
6 Stochastic Calculus: Advanced Topics
6.1 The Feynman-Kac Formula
6.2 The Black-Scholes Partial Differential Equation
6.3 The Girsanov Theorem
6.4 The Forward Risk Adjusted Measure and Bond Option Pricing
6.5 Barrier Hitting Probabilities Revisited
6.6 Two-Dimensional Stochastic Differential Equations
7 Applications in Insurance
7.1 Deferred Variable Annuities and Equity-Indexed Annuities
7.2 Guaranteed Annuity Options
7.3 Universal Life
References
Topic Index