First European Congress of Mathematics Paris, July 6–10, by Darrell Duffie (auth.), Anthony Joseph, Fulbert Mignot,

By Darrell Duffie (auth.), Anthony Joseph, Fulbert Mignot, François Murat, Bernard Prum, Rudolf Rentschler (eds.)

Desk of Contents: D. Duffie: Martingales, Arbitrage, and Portfolio selection • J. Fröhlich: Mathematical facets of the Quantum corridor influence • M. Giaquinta: Analytic and Geometric points of Variational difficulties for Vector Valued Mappings • U. Hamenstädt: Harmonic Measures for Leafwise Elliptic Operators alongside Foliations • M. Kontsevich: Feynman Diagrams and Low-Dimensional Topology • S.B. Kuksin: KAM-Theory for Partial Differential Equations • M. Laczkovich: Paradoxical Decompositions: A Survey of contemporary effects • J.-F. Le Gall: A Path-Valued Markov strategy and its Connections with Partial Differential Equations • I. Madsen: The Cyclotomic hint in Algebraic K-Theory • A.S. Merkurjev: Algebraic K-Theory and Galois Cohomology • J. Nekovár: Values of L-Functions and p-Adic Cohomology • Y.A. Neretin: Mantles, Trains and Representations of limitless Dimensional teams • M.A. Nowak: The Evolutionary Dynamics of HIV Infections • R. Piene: at the Enumeration of Algebraic Curves - from Circles to Instantons • A. Quarteroni: Mathematical elements of area Decomposition tools • A. Schrijver: Paths in Graphs and Curves on Surfaces • B. Silverman: functionality Estimation and useful facts research • V. Strassen: Algebra and Complexity • P. Tukia: Generalizations of Fuchsian and Kleinian teams • C. Viterbo: houses of Embedded Lagrange Manifolds • D. Voiculescu: substitute Entropies in Operator Algebras • M. Wodzicki : Algebraic K-Theory and sensible research • D. Zagier: Values of Zeta capabilities and Their purposes

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First European Congress of Mathematics Paris, July 6–10, 1992: Vol. II: Invited Lectures (Part 2)

Desk of Contents: D. Duffie: Martingales, Arbitrage, and Portfolio selection • J. Fröhlich: Mathematical features of the Quantum corridor influence • M. Giaquinta: Analytic and Geometric features of Variational difficulties for Vector Valued Mappings • U. Hamenstädt: Harmonic Measures for Leafwise Elliptic Operators alongside Foliations • M.

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Extra info for First European Congress of Mathematics Paris, July 6–10, 1992: Vol. II: Invited Lectures (Part 2)

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Huang, Multiperiod security markets with differential information, Journal of Mathematical Economics 15 (1986),283-303. D. Duffie and R. Kan, A Yield-Factor Model of Interest Rates, Research Paper, Graduate School of Business, Stanford University, 1992. N. EI Karoui and V. Lacoste, Multifactor Models of the Term Structure of Interest Rates, Research Paper, University of Paris, 1992. M. Harrison and D. Kreps, Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory 20 (1979), 381--408.

M. Harrison and S. Pliska, Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and their Applications 11 (1981), 215-260. D. Heath, R. Jarrow, and A. Morton, Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation, Econometrica 60 (1992), 77-105. S. Heston, Testing Continuous-Time Modelll of the Term Structure of Interest Rates, Research Paper, Yale School of Organization and Management, (1991). T. Ho and S.

The solution to (14). Given the properties of h, ).. * is easily computed in practical examples. What we have not done is to indicate a method for solving ()* explicitly. In fact, this can be difficult unless, for example, (8, A) is Markovian, in which case the Hamilton-Jacobi-Bellman equation allows one to compute ()* numerically, or in parametric special cases, explicitly. Extensions of this problem include the effects of transactions costs (Davis and Norman (1990), portfolio constraints (Cvitanic and Karatzas (1991», uncertain income streams (He and Pearson (1991); Karatzas, Lehoczky, Shreve, and Xu (1991); Duffie, Fleming, and Zariphopoulou (1991», and utility expressed over the space of cumulative consumption processes that are not necessarily absolutely continuous (Hindy and Huang (1989», to give but a short list of the many extensions in the literature.

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