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Stochastic finance : an introduction in discrete time

Author: Hans Föllmer; Alexander Schied
Publisher: Berlin ; New York : Walter de Gruyter, 2004.
Series: De Gruyter studies in mathematics, 27.
Edition/Format:   Print book : English : 2nd rev. and extended ed
Summary:
"This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry."--Jacket.
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Hans Föllmer; Alexander Schied
ISBN: 3110183463 9783110183467
OCLC Number: 56608129
Description: xi, 459 pages ; 25 cm.
Contents: Preface to the second edition --
Introduction --
I Mathematical finance in one period --
1 Arbitrage theory --
1.1 Assets, portfolios, and arbitrage opportunities --
1.2 Absence of arbitrage and martingale measures --
1.3 Derivative securities --
1.4 Complete market models --
1.5 Geometric characterization of arbitrage-free models --
1.6 Contingent initial data --
2 Preferences --
2.1 Preference relations and their numerical representation --
2.2 Von Neumann-Morgenstern representation --
2.3 Expected utility --
2.4 Uniform preferences --
2.5 Robust preferences on asset profiles --
2.6 Probability measures with given marginals --
3 Optimality and equilibrium --
3.1 Portfolio optimization and the absence of arbitrage --
3.2 Exponential utility and relative entropy --
3.3 Optimal contingent claims --
3.4 Microeconomic equilibrium --
4 Monetary measures of risk --
4.1 Risk measures and their acceptance sets --
4.2 Robust representation of convex risk measures. 4.3 Convex risk measures on L8 --
4.4 Value at Risk --
4.5 Law-invariant risk measures --
4.6 Concave distortions --
4.7 Comonotonic risk measures --
4.8 Measures of risk in a financial market --
4.9 Shortfall risk --
x Contents --
II Dynamic hedging --
5 Dynamic arbitrage theory --
5.1 The multi-period market model --
5.2 Arbitrage opportunities and martingale measures --
5.3 European contingent claims --
5.4 Complete markets --
5.5 The binomial model --
5.6 Exotic derivatives --
5.7 Convergence to the Black-Scholes price --
6 American contingent claims --
6.1 Hedging strategies for the seller --
6.2 Stopping strategies for the buyer --
6.3 Arbitrage-free prices --
6.4 Stability under pasting --
6.5 Lower and upper Snell envelopes --
7 Superhedging --
7.1 P-supermartingales --
7.2 Uniform Doob decomposition --
7.3 Superhedging of American and European claims --
7.4 Superhedging with liquid options --
8 Efficient hedging --
8.1 Quantile hedging. 8.2 Hedging with minimal shortfall risk --
9 Hedging under constraints --
9.1 Absence of arbitrage opportunities --
9.2 Uniform Doob decomposition --
9.3 Upper Snell envelopes --
9.4 Superhedging and risk measures --
10 Minimizing the hedging error --
10.1 Local quadratic risk --
10.2 Minimal martingale measures --
10.3 Variance-optimal hedging --
Appendix --
A.1 Convexity --
A.2 Absolutely continuous probability measures --
A.3 Quantile functions --
A.4 The Neyman-Pearson lemma --
A.5 The essential supremum of a family of random variables --
A.6 Spaces of measures --
A.7 Some functional analysis --
Notes --
References --
List of symbols --
Index.
Series Title: De Gruyter studies in mathematics, 27.
Responsibility: Hans Föllmer, Alexander Schied.
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Abstract:

"This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry."--Jacket.

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