TAILIEUCHUNG - Stochastic Finance An Introduction in Discrete Time

In this chapter, we study the mathematical structure of a simple one-period model of a financial market. We consider a finite number of assets. Their initial prices at time t = 0 are known, their future prices at time t = 1 are described as random variables on some probability space. Trading takes place at time t = 0. Already in this simple model, some basic principles of mathematical finance appear very clearly. In Section , we single out those models which satisfy a condition of market efficiency: There are no trading opportunities which yield a profit without any downside risk. The absence of such arbitrage. | deGruyter Studies in Mathematics 27 ị- Hans Follmer Alexander Schied Stochastic Finance An Introduction in Discrete Time 2nd Edition de Gruyter Studies in Mathematics 27 Editors Carlos Kenig Andrew Ranicki Michael Rockner de Gruyter Studies in Mathematics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Riemannian Geometry 2nd rev. ed. Wilhelm P. A. Klingenberg Semimartingales Michel Metivier Holomorphic Functions of Several Variables Ludger Kaup and Burchard Kaup Spaces of Measures Corneliu Constantinescu Knots 2nd rev. and ext. ed. Gerhard Burde and Heiner Zieschang Ergodic Theorems Ulrich Krengel Mathematical Theory of Statistics Helmut Strasser Transformation Groups Tammo tom Dieck Gibbs Measures and Phase Transitions Hans-Otto Georgii Analyticity in Infinite Dimensional Spaces Michel Herve Elementary Geometry in Hyperbolic Space Werner Fenchel Transcendental Numbers Andrei B. Shidlovskii Ordinary Differential Equations Herbert Amann Dirichlet Forms and Analysis on Wiener Space Nicolas Bouleau and Francis Hirsch Nevanlinna Theory and Complex Differential Equations Ilpo Laine Rational Iteration Norbert Steinmetz Korovkin-type Approximation Theory and its Applications Francesco Altomare and Michele Campiti Quantum Invariants of Knots and 3-Manifolds Vladimir G. Turaev Dirichlet Forms and Symmetric Markov Processes Masatoshi Fukushima Yoichi Oshima and Masayoshi Takeda Harmonic Analysis of Probability Measures on Hypergroups Walter R. Bloom and Herbert Heyer Potential Theory on Infinite-Dimensional Abelian Groups Alexander Bendikov Methods of Noncommutative Analysis Vladimir E. Nazaikinskii Victor E. Shatalov and Boris Yu. Sternin Probability Theory Heinz Bauer Variational Methods for Potential Operator Equations Jan Chabrowski The Structure of Compact Groups Karl H. Hofmann and Sidney A. Morris Measure and Integration Theory Heinz Bauer Stochastic Finance 2nd rev. and ext. ed. Hans Follmer and Alexander Schied Painleve .

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