Part I: Mathematical finance in one period
1.1Assets, portfolios, and arbitrage opportunities
1.2Absence of arbitrage and martingale measures
1.5Geometric characterization of arbitrage-free models
2.1Preference relations and their numerical representation
2.2Von Neumann–Morgenstern representation
2.5Robust preferences on asset profiles
2.6Probability measures with given marginals
3.1Portfolio optimization and the absence of arbitrage
3.2Exponential utility and relative entropy
3.4Optimal payoff profiles for uniform preferences
3.5Robust utility maximization
4.1Risk measures and their acceptance sets
4.2Robust representation of convex risk measures
4.5Law-invariant risk measures
4.8Measures of risk in a financial market
4.9Utility-based shortfall risk and divergence risk measures
5.1The multi-period market model
5.2Arbitrage opportunities and martingale measures
5.7Convergence to the Black–Scholes price
6.1Hedging strategies for the seller
6.2Stopping strategies for the buyer
6.5Lower and upper Snell envelopes
7.3Superhedging of American and European claims
7.4Superhedging with liquid options
8.2Hedging with minimal shortfall risk
8.3Efficient hedging with convex risk measures
9.1Absence of arbitrage opportunities
9.4Superhedging and risk measures
10Minimizing the hedging error
10.2Minimal martingale measures
11.1Conditional risk measures and their robust representation
A.2Absolutely continuous probability measures
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