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Presents new models, new methods and new results in quantitative finance
Includes an analysis of new financial products such as exotic derivatives and liquidity models
Shows an application-oriented presentation of mathematical finance
Covers hot topics such as pricing and hedging
Develops models of risk and risk contagion
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.
Content Level »Research
Keywords »Calculus of variations - Comonotonicity applied in finance - Fractional processes in finance - Mathematical finance reviewed - Modeling of long and short range dependence - Pricing and hedging - Quantitative finance - Stochastic control with finite and infinite horizon - Stochastic finance - Stochastic modeling in finance - Stochastic partial differential equations