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 andjump diffusions. Moreover, fractional Brownian motion and ambit processes arealso 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 innew methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance. Presents new models, new methods and new results in quantitative financeIncludes an analysis of new financial products such as exotic derivatives and liquidity modelsShows an application-oriented presentation of mathematical financeCovers hot topics such as pricing and hedgingDevelops models of risk and risk contagion INDICE: Dynamic risk measures. Ambit processes and stochastic partial differential equations. Fractional processes as models in stochastic finance. Credit contagion in a long range dependent macroeconomic factor model. Modeling information flows in financial markets. An overview of comonotonicity and its applications in finance and insurance. A general maximum principle for anticipative stochastic control and applications to insider trading. Analyticity of theWiener-Hopf factors and valuation of exotic options in Levy models. Optimal liquidation of a pairs trade. A PDE-based approach or pricing mortgage-backed securities. Nonparametric methods for volatility density estimation. Fractionalsmoothness and applications in finance. Liquidity models in continuous and discrete times. Some new BSDE results for an infinite-horizon stochastic controlproblem. Functionals associated with gradient stochastic flows and nonlinear SPDEs. Fractional smoothness and applications in Finance modeled by F-doubly stochastic Markov chains. Exotic derivatives under stochastic volatility modelswith jumps. Asymptotics of HARA utility from terminal wealth under proportional transaction costs with decision lag or execution delay and obligatory diversification.
- ISBN: 978-3-642-18411-6
- Editorial: Springer Berlin Heidelberg
- Encuadernacion: Cartoné
- Páginas: 350
- Fecha Publicación: 01/04/2011
- Nº Volúmenes: 1
- Idioma: Inglés