Contents

Preface to the fourth edition

Preface to the third edition

Preface to the second edition

Preface to the first edition

Part I: Mathematical finance in one period

1Arbitrage theory

1.1Assets, portfolios, and arbitrage opportunities

1.2Absence of arbitrage and martingale measures

1.3Derivative securities

1.4Complete market models

1.5Geometric characterization of arbitrage-free models

1.6Contingent initial data

2Preferences

2.1Preference relations and their numerical representation

2.2Von Neumann–Morgenstern representation

2.3Expected utility

2.4Stochastic dominance

2.5Robust preferences on asset profiles

2.6Probability measures with given marginals

3Optimality and equilibrium

3.1Portfolio optimization and the absence of arbitrage

3.2Exponential utility and relative entropy

3.3Optimal contingent claims

3.4Optimal payoff profiles for uniform preferences

3.5Robust utility maximization

3.6Microeconomic equilibrium

4Monetary measures of risk

4.1Risk measures and their acceptance sets

4.2Robust representation of convex risk measures

4.3Convex risk measures on L∞

4.4Value at Risk

4.5Law-invariant risk measures

4.6Concave distortions

4.7Comonotonic risk measures

4.8Measures of risk in a financial market

4.9Utility-based shortfall risk and divergence risk measures

Part II: Dynamic hedging

5Dynamic arbitrage theory

5.1The multi-period market model

5.2Arbitrage opportunities and martingale measures

5.3European contingent claims

5.4Complete markets

5.5The binomial model

5.6Exotic derivatives

5.7Convergence to the Black–Scholes price

6American contingent claims

6.1Hedging strategies for the seller

6.2Stopping strategies for the buyer

6.3Arbitrage-free prices

6.4Stability under pasting

6.5Lower and upper Snell envelopes

7Superhedging

7.1P-supermartingales

7.2Uniform Doob decomposition

7.3Superhedging of American and European claims

7.4Superhedging with liquid options

8Efficient hedging

8.1Quantile hedging

8.2Hedging with minimal shortfall risk

8.3Efficient hedging with convex risk measures

9Hedging under constraints

9.1Absence of arbitrage opportunities

9.2Uniform Doob decomposition

9.3Upper Snell envelopes

9.4Superhedging and risk measures

10Minimizing the hedging error

10.1Local quadratic risk

10.2Minimal martingale measures

10.3Variance-optimal hedging

11Dynamic risk measures

11.1Conditional risk measures and their robust representation

11.2Time consistency

Appendix

A.1Convexity

A.2Absolutely continuous probability measures

A.3Quantile functions

A.4The Neyman–Pearson lemma

A.5The essential supremum of a family of random variables

A.6Spaces of measures

A.7Some functional analysis

Bibliographical notes

References

List of symbols

Index

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