Advanced Mathematical Methods for Finance

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Advanced Mathematical Methods for Finance

Format:  Hardcover,

536 pages

Edition: Edition.

Publisher: Springer

Publish Date: Mar 2011

ISBN-13: 9783642184116

ISBN-10: 3642184111

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Book Information

The following content was provided by the publisher.
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, L vy 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.

Specifications

Editor:
Editor:
Publisher: Springer
Publish Date: Mar 2011
ISBN-13: 9783642184116
ISBN-10: 3642184111
Format: Hardcover
Number of Pages: 536
Shipping Weight (in pounds): 1.6
Product in Inches (L x W x H): 6.5 x 0.9 x 9.4
Walmart No.: 9783642184116

Chapter outline

Dynamic Risk Measuresp. 1
Ambit Processes and Stochastic Partial Differential Equationsp. 35
Fractional Processes as Models in Stochastic Financep. 75
Credit Contagion in a Long Range Dependent Macroeconomic Factor Modelp. 105
Modelling Information Flows in Financial Marketsp. 133
An Overview of Comonotonicity and Its Applications in Finance and Insurancep. 155
A General Maximum Principle for Anticipative Stochastic Control and Applications to Insider Tradingp. 181
Analyticity of the Wiener-Hopf Factors and Valuation of Exotic Options in Lvy Modelsp. 223
Optimal Liquidation of a Pairs Tradep. 247
A PDE-Based Approach for Pricing Mortgage-Backed Securitiesp. 257
Nonparametric Methods for Volatility Density Estimationp. 293
Fractional Smoothness and Applications in Financep. 313
Liquidity Models in Continuous and Discrete Timep. 333
Some New BSDE Results for an Infinite-Horizon Stochastic Control Problemp. 367
Functionals Associated with Gradient Stochastic Flows and Nonlinear SPDEsp. 397
Pricing and Hedging of Rating-Sensitive Claims Modeled by F-doubly Stochastic Markov Chainsp. 417
Exotic Derivatives under Stochastic Volatility Models with Jumpsp. 455
Asymptotics of HARA Utility from Terminal Wealth under Proportional Transaction Costs with Decision Lag or Execution Delay and Obligatory Diversificationp. 509

Book description

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, L Dy 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.

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