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by Alexander Schied, Hans Föllmer
Stochastic Finance, 4th Edition
Cover
Title
Copyright
Preface to the fourth edition
Preface to the third edition
Preface to the second edition
Preface to the first edition
Contents
Part 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 Stochastic dominance
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 Optimal payoff profiles for uniform preferences
3.5 Robust utility maximization
3.6 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 L∞
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 Utility-based shortfall risk and divergence risk measures
Part 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
8.3 Efficient hedging with convex risk measures
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
11 Dynamic risk measures
11.1 Conditional risk measures and their robust representation
11.2 Time consistency
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
Bibliographical notes
References
List of symbols
Index
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Hans Föllmer, Alexander Schied
Stochastic Finance
De Gruyter Graduate
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