Financial Mathematics

Inbunden, Engelska, 2016

Av Yuliya Mishura, Ukraine) Mishura, Yuliya (Head, Department of Probability, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko Kyiv National University, Kiev

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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.

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

Produktinformation

Utgivningsdatum2016-01-25
Mått152 x 229 x 16 mm
Vikt330 g
FormatInbunden
SpråkEngelska
Antal sidor194
FörlagElsevier Science
ISBN9781785480461

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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.

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