Financial Markets in Continuous Time

In modern financial practice, asset prices are modelled by means of stochastic processes, and continuous-time stochastic calculus thus plays a central role in financial modelling. This approach has its roots in the foundational work of the Nobel laureates

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Editorial Board M. Avellaneda G. Barone-Adesi M. Broadie M.H.A. Davis E. Derman C. Klüppelberg E. Kopp W. Schachermayer

Springer Finance Springer Finance is a programme of books aimed at students, academics and practitioners working on increasingly technical approaches to the analysis of financial markets. It aims to cover a variety of topics, not only mathematical finance but foreign exchanges, term structure, risk management, portfolio theory, equity derivatives, and financial economics. Ammann M., Credit Risk Valuation: Methods, Models, and Application (2001) Back K., A Course in Derivative Securities: Introduction to Theory and Computation (2005) Barucci E., Financial Markets Theory. Equilibrium, Efficiency and Information (2003) Bielecki T.R. and Rutkowski M., Credit Risk: Modeling, Valuation and Hedging (2002) Bingham N.H. and Kiesel R., Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives (1998, 2nd ed. 2004) Brigo D. and Mercurio F., Interest Rate Models: Theory and Practice (2001, 2nd ed. 2006) Buff R., Uncertain Volatility Models-Theory and Application (2002) Carmona R.A. and Tehranchi M.R., Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective (2006) Dana R-A. and Jeanblanc M., Financial Markets in Continuous Time (2003) Deboeck G. and Kohonen T. (Editors), Visual Explorations in Finance with Self-Organizing Maps (1998) Delbaen F. and Schachermayer W., The Mathematics of Arbitrage (2005) Elliott R.J. and Kopp P.E., Mathematics of Financial Markets (1999, 2nd ed. 2005) Fengler M.R., Semiparametric Modeling of Implied Volatility (2005) Geman H., Madan D., Pliska S.R. and Vorst T. (Editors), Mathematical Finance–Bachelier Congress 2000 (2001) Gundlach M., Lehrbass F. (Editors), CreditRisk+ in the Banking Industry (2004) Jondeau E., Financial Modeling Under Non-Gaussian Distributions (2007) Kellerhals B.P., Asset Pricing (2004) Külpmann M., Irrational Exuberance Reconsidered (2004) Kwok Y.-K., Mathematical Models of Financial Derivatives (1998) Malliavin P. and Thalmaier A., Stochastic Calculus of Variations in Mathematical Finance (2005) Meucci A., Risk and Asset Allocation (2005) Pelsser A., Efficient Methods for Valuing Interest Rate Derivatives (2000) Prigent J.-L., Weak Convergence of Financial Markets (2003) Schmid B., Credit Risk Pricing Models (2004) Shreve S.E., Stochastic Calculus for Finance I (2004) Shreve S.E., Stochastic Calculus for Finance II (2004) Yor M., Exponential Functionals of Brownian Motion and Related Processes (2001) Zagst R., Interest-Rate Management (2002) Zhu Y.-L., Wu X., Chern I.-L., Derivative Securities and Difference Methods (2004) Ziegler A., Incomplete Information and Heterogeneous Beliefs in Continuous-time Finance (2003) Ziegler A., A Game Theory Analysis of Options (2004)

Rose-Anne Dana · Monique Jeanblanc

Financial Markets in Continuous Time Translated by Anna Kennedy

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Rose-Anne Dana

Monique Jeanblanc

Université Paris IX (Dauphine) CEREMADE Place de Lattre de Tassigny 75775 Paris Cedex 16, France E-mail: [email protected]