Research Catalog

Title

Stochastic finance : an introduction in discrete time / Hans Föllmer, Alexander Schied.

Author

Föllmer, Hans.

Publication

Berlin ; New York : Walter de Gruyter, 2004.

Items in the Library & Off-site

Details

Additional Authors

Schied, Alexander.

Description

xi, 459 pages; 25 cm.

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.

Series Statement

De Gruyter studies in mathematics ; 27

Uniform Title

De Gruyter studies in mathematics ; 27.

Subject

• Finance > Statistical methods
• Stochastic analysis
• Probabilities
• Probability
• probability
• Finance > Statistical methods
• Probabilities
• Stochastic analysis
• Finanzmathematik
• Stochastisches Modell
• Financiën
• Statistische methoden
• Processos estocásticos (aplicações)
• Finanças

Bibliography (note)

• Includes bibliographical references (p. [439]-448) and index.

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.

ISBN

• 3110183463
• 9783110183467

LCCN

• 2004021608
• 9783110183467

OCLC

• ocm56608129
• 56608129
• SCSB-1361463

Owning Institutions

Princeton University Library