Stochastic Analysis With Financial Applications Hong Kong 2009 1st edition by Arturo Kohatsu Higa,Nicolas Privault,Shuenn Jyi Sheu ISBN 3034800967 978-3034800969

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ISBN 10: 3034800967
ISBN 13: 978-3034800969
Author: Arturo Kohatsu Higa,Nicolas Privault,Shuenn Jyi Sheu

Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. The book also covers the areas of backward stochastic differential equations via the (non-linear) G-Brownian motion and the case of jump processes. Concerning the applications to finance, many of the articles deal with the valuation and hedging of credit risk in various forms, and include recent results on markets with transaction costs.

Stochastic Analysis With Financial Applications: Hong Kong 2009 1st Table of contents:

• Introduction to Stochastic Processes in Finance

  • Basic Concepts of Stochastic Processes
  • Role of Stochastic Processes in Financial Modeling
  • Review of Probability Theory and Random Variables

• Foundations of Stochastic Calculus

  • Brownian Motion and Geometric Brownian Motion
  • Itô’s Lemma and Stochastic Differential Equations (SDEs)
  • Stochastic Integration and Differential Equations

• Pricing Financial Derivatives

  • Black-Scholes Model and Its Derivation
  • Option Pricing and Hedging Strategies
  • Interest Rate Models and Bond Pricing

• Applications of Stochastic Models in Financial Markets

  • Volatility Modeling and Forecasting
  • Stochastic Models for Asset Prices
  • Risk Neutral Valuation and Arbitrage Pricing

• Numerical Methods for Stochastic Modeling

  • Monte Carlo Simulation
  • Finite Difference Methods for Option Pricing
  • Approximation Techniques for SDEs

• Advanced Topics in Stochastic Finance

  • Stochastic Control and Optimal Stopping Problems
  • Portfolio Optimization in Stochastic Environments
  • Stochastic Volatility Models and Their Applications

• Modeling Market Microstructure

  • Price Formation and Market Dynamics
  • Limit Order Books and Order Flow
  • High-Frequency Trading and Stochastic Models

• Financial Risk Management

  • Risk Measures: Value at Risk (VaR) and Conditional VaR
  • Stress Testing and Scenario Analysis
  • Applications in Credit Risk, Liquidity Risk, and Market Risk

• Empirical Applications of Stochastic Models

  • Estimating Parameters for Stochastic Models
  • Fitting Models to Financial Data
  • Case Studies in Financial Markets

• Conclusion and Future Directions

  • Emerging Trends in Stochastic Analysis for Finance
  • The Role of Machine Learning and AI in Financial Applications
  • Challenges and Opportunities in Stochastic Financial Modeling

• Appendices

  • Mathematical Background for Stochastic Processes
  • Software and Tools for Financial Modeling
  • Glossary of Key Terms in Stochastic Finance

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