Advanced Mathematical Methods for Finance 1st Edition by Julia Di Nunno, Bernt Oksendal ISBN 3642435513 9783642435515

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ISBN 10: 3642435513 
ISBN 13: 9783642435515
Author: Julia Di Nunno, Bernt Oksendal

This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.

 Advanced Mathematical Methods for Finance 1st Table of contents:

• Basic Mathematical Concepts for Finance

  • Review of Linear Algebra
  • Probability Theory and Statistics in Finance
  • Calculus and Optimization Techniques
  • Differential Equations

• Stochastic Processes in Finance

  • Random Variables and Probability Distributions
  • Brownian Motion and Wiener Processes
  • Markov Processes and Their Applications
  • Stochastic Calculus: Itô’s Lemma

• Time Value of Money and Discounting

  • Present Value and Future Value Concepts
  • Discounting Techniques
  • Bond Pricing and Yield Calculations

• Risk and Return Models

  • Portfolio Theory and the Efficient Frontier
  • Capital Asset Pricing Model (CAPM)
  • Arbitrage Pricing Theory
  • Volatility and Risk Measures

• Derivatives Pricing

  • Introduction to Derivatives (Options, Futures, Swaps)
  • Black-Scholes Model
  • Binomial Option Pricing Model
  • Pricing of Other Derivatives

• Interest Rate Models

  • Fixed Income Securities
  • Term Structure Models
  • Heath-Jarrow-Morton Model
  • Interest Rate Derivatives and Hedging

• Numerical Methods in Finance

  • Monte Carlo Simulation
  • Finite Difference Methods
  • Numerical Optimization Techniques
  • Solving Stochastic Differential Equations

• Risk Management Techniques

  • Value at Risk (VaR)
  • Credit Risk Models
  • Hedging Strategies
  • Stress Testing and Scenario Analysis

• Advanced Topics in Financial Mathematics

  • Market Microstructure and Order Flow
  • Portfolio Optimization Under Constraints
  • Dynamic Hedging and Stochastic Control
  • Financial Engineering and Structured Products

• Applications and Case Studies

  • Real-World Examples of Mathematical Finance
  • Practical Issues in Derivatives Markets
  • Risk Management in Banks and Hedge Funds

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