Stochastic Finance An Introduction in Discrete Time 3rd Edition by Hans Föllmer, Alexander Schied ISBN ‎ 3110218046 978-3110218046

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ISBN 10: ‎ 3110218046

ISBN 13: 978-3110218046

Author: Hans Föllmer, Alexander Schied

 This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This third revised and extended edition now contains more than one hundred exercises. It also includes new material on risk measures and the related issue of model uncertainty, in particular a new chapter on dynamic risk measures and new sections on robust utility maximization and on efficient hedging with convex risk measures.

Stochastic Finance An Introduction in Discrete Time 3rd Table of contents:

• Introduction to Stochastic Finance

  • Overview of Stochastic Processes in Finance
  • The Role of Mathematical Models in Financial Markets
  • Basic Principles of Asset Pricing and Investment
  • Discrete-Time Models: A Historical Perspective

• Fundamentals of Probability and Stochastic Processes

  • Probability Theory Basics: Events, Probability Spaces, and Conditional Probability
  • Random Variables and Distributions
  • Stochastic Processes: Definition and Types
  • Markov Chains and Their Applications

• Arbitrage and Market Efficiency

  • The Concept of Arbitrage in Financial Markets
  • No-Arbitrage Conditions and Their Importance
  • Market Efficiency and the Role of Information
  • The Fundamental Theorem of Asset Pricing

• Discrete-Time Asset Pricing Models

  • Single-Period Models: Introduction to Simple Pricing Models
  • Multi-Period Models: Generalizing the Single-Period Case
  • Binomial Model: Discrete-Time Representation of Stock Prices
  • Martingales and Their Role in Asset Pricing

• Risk and Return in Stochastic Finance

  • Defining Risk and Return in Financial Contexts
  • Expected Return and Risk Metrics
  • The Role of Risk Aversion in Investment Decisions
  • The Concept of Portfolio Theory in Discrete Time

• Optimal Portfolio Selection

  • Markowitz Portfolio Theory: Discrete-Time Version
  • The Efficient Frontier and Capital Allocation Line
  • Risk-Free Assets and the Tangency Portfolio
  • Dynamic Portfolio Selection: Rebalancing in Discrete Time

• The Concept of Dynamic Hedging

  • Hedging Strategies in Discrete-Time Models
  • The Role of Dynamic Hedging in Risk Management
  • Continuous and Discrete-Time Hedging
  • Applications to Options and Derivatives

• Derivatives Pricing in Discrete Time

  • Introduction to Derivatives and Financial Contracts
  • Binomial Options Pricing Model
  • The Black-Scholes Model: A Discrete-Time Approximation
  • Put and Call Options, Futures, and Forward Contracts

• Stochastic Control and Optimization

  • Introduction to Stochastic Control in Finance
  • Dynamic Optimization of Investment and Consumption
  • Value Function and Bellman Equation
  • Applications of Stochastic Control to Portfolio Management

• Interest Rate Models and Bond Pricing

  • Introduction to Interest Rates and Bonds
  • Discrete-Time Models of Interest Rates
  • Pricing Bonds and Derivatives Based on Interest Rates
  • Term Structure Models and Yield Curves

• Numerical Methods in Stochastic Finance

  • Monte Carlo Simulation for Pricing and Risk Assessment
  • Binomial Trees and Trinomial Trees in Option Pricing
  • Numerical Methods for Solving Stochastic Differential Equations
  • Implementing Stochastic Finance Models in Practice

• Applications of Stochastic Finance

  • Applications to Equity Markets, Commodities, and Foreign Exchange
  • Risk Management in Stochastic Financial Models
  • Insurance and Actuarial Models
  • Real-World Financial Applications: Case Studies

• Conclusion and Future Directions

  • The Future of Stochastic Finance and Emerging Trends
  • Continuing Advances in Financial Mathematics and Computational Finance
  • Challenges in Real-World Financial Modeling
  • Key Concepts and Tools for Future Research

• Appendices

  • Mathematical Background: Probability Theory, Linear Algebra, and Calculus
  • Useful Tables and Formulas for Financial Modeling
  • Suggested Reading and Resources
  • Index

 

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Hans Föllmer,Alexander Schied,Stochastic Finance,Discrete Time