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Financial Mathematics

  • 1st Edition - January 25, 2016
  • Latest edition
  • Author: Yuliya Mishura
  • Language: English

Finance Mathematics is devoted to financial markets both with discrete and continuous time, exploring how to make the transition from discrete to continuous time in option pr… Read more

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Description

Finance Mathematics is devoted to financial markets both with discrete and continuous time, exploring how to make the transition from discrete to continuous time in option pricing. This book features a detailed dynamic model of financial markets with discrete time, for application in real-world environments, along with Martingale measures and martingale criterion and the proven absence of arbitrage.

With a focus on portfolio optimization, fair pricing, investment risk, and self-finance, the authors provide numerical methods for solutions and practical financial models, enabling you to solve problems both from mathematical and from financial point of view.

Key features

  • Calculations of Lower and upper prices, featuring practical examples
  • The simplest functional limit theorem proved for transition from discrete to continuous time
  • Learn how to optimize portfolio in the presence of risk factors

Readership

Academics, researchers, and practitioners in quantitative finance, financial risk management, economics and other areas of math, science and engineering

Table of contents

Chapter 1. Financial Markets with Discrete Time1.1. General description of a market model with discrete time1.2. Arbitrage opportunities, martingale measures and martingale1.3. Contingent claims: complete and incomplete markets1.4. The Cox–Ross–Rubinstein approach to option pricing1.5. The sequence of the discrete-time markets as an intermediate1.6. American contingent claimsChapter 2. Financial Markets with Continuous Time2.1. Transition from discrete to continuous time2.2. Black–Scholes formula for the arbitrage-free price of the2.3. Arbitrage theory for the financial markets with continuous time2.4. American contingent claims in continuous time2.5. Exotic derivatives in the model with continuous time

Product details

  • Edition: 1
  • Latest edition
  • Published: February 1, 2016
  • Language: English

About the author

YM

Yuliya Mishura

Yuliya Mishura is Professor and Head of the Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Ukraine. Her research interests include stochastic analysis, theory of stochastic processes, stochastic differential equations, numerical schemes, financial mathematics, risk processes, statistics of stochastic processes, and models with long-range dependence.
Affiliations and expertise
Head, Department of Probability, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko Kyiv National University, Kiev, Ukraine

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