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This book details contemporary advances in a number of key areas of mathematical finance, such as optimal control theory applied to finance, interest rate models, credit risk and credit derivatives and numerical solution of equations of mathematical finance.

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This volume contains a collection of papers dedicated to Professor Eckhard Platen to celebrate his 60th birthday, which occurred in 2009. The contributions have been written by a number of his colleagues and co-authors. All papers have been - viewed and presented as keynote talks at the international conference "Quantitative Methods in Finance" (QMF) in Sydney in December 2009. The QMF Conference Series was initiated by Eckhard Platen in 1993 when he was at the Australian - tional University (ANU) in Canberra. Since joining UTS in 1997 the conference came to be organised on a much larger scale and has grown to become a signi?cant international event in quantitative ?nance. Professor Platen has held the Chair of Quantitative Finance at the University of Technology, Sydney (UTS) jointly in the Faculties of Business and Science since 1997. Prior to this appointment, he was the Founding Head of the Centre for Fin- cial Mathematics at the Institute of Advanced Studies at ANU, a position to which he was appointed in 1994. Eckhard completed a PhD in Mathematics at the Technical University in Dresden in 1975 and in 1985 obtained his Doctor of Science degree (Habilitation degree in the German system) from the Academy of Sciences in Berlin where he headed the Stochastics group at the Weierstrass Institute.

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Probabilistic Aspects of Arbitrage.- Finitely Additive Probabilities and the Fundamental Theorem of Asset Pricing.- M6-On Minimal Market Models and Minimal Martingale Measures.- The Economic Plausibility of Strict Local Martingales in Financial Modelling.- A Remarkable ?-finite Measure Associated with Last Passage Times and Penalisation Problems.- Pricing Without Equivalent Martingale Measures Under Complete and Incomplete Observation.- Existence and Non-uniqueness of Solutions for BSDE.- Comparison Theorems for Finite State Backward Stochastic Differential Equations.- Results on Numerics for FBSDE with Drivers of Quadratic Growth.- Variance Swap Portfolio Theory.- Stochastic Partial Differential Equations and Portfolio Choice.- Issuers´ Commitments Would Add More Value than Any Rating Scheme Could Ever Do.- Pricing and Hedging of CDOs: A Top Down Approach.- Constructing Random Times with Given Survival Processes and Applications to Valuation of Credit Derivatives.- Representation of American Option Prices Under Heston Stochastic Volatility Dynamics Using Integral Transforms.- Buy Low and Sell High.- Continuity Theorems in Boundary Crossing Problems for Diffusion Processes.- Binomial Models for Interest Rates.- Lognormal Forward Market Model (LFM) Volatility Function Approximation.- Maximum Likelihood Estimation for Integrated Diffusion Processes.

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