Market-Consistent Prices: An Introduction to Arbitrage Theory

Preface
	A Glimpse at the Theory
	The Scope of the Book
	The Distinguishing Features of This Book
	Prerequisites
	Acknowledgement
Contents
1 Random Variables: Linearity and Order
	1.1 Outcomes and Events
	1.2 Random Variables
	1.3 The Linear Structure
	1.4 Linear Functionals
	1.5 Convex Sets and Functionals
	1.6 The Order Structure
	1.7 Monotone Functionals
	1.8 Exercises
2 Probabilities and Expectations
	2.1 Probability Measures
	2.2 Probability Mass Function
	2.3 Independent Events
	2.4 Expected Value
	2.5 Variance and Covariance
	2.6 Change of Probability
	2.7 The Meaning of Probability
	2.8 Exercises
3 Random Variables: Topology and Geometry
	3.1 The Norm Structure
	3.2 The Topological Structure
	3.3 Topology and Order
	3.4 Continuous Functionals
	3.5 The Inner-Product Structure
	3.6 Orthogonality
	3.7 Exercises
4 Extensions of Linear Functionals
	4.1 Separation Theorems
	4.2 Extension Results
	4.3 Representation Results
	4.4 Exercises
5 Single-Period Financial Markets
	5.1 The Elements of the Market
	5.2 Portfolios of Securities
	5.3 Replicable Payoffs
	5.4 Complete Markets
	5.5 Changing the Unit of Account
	5.6 Exercises
6 Market-Consistent Prices for Replicable Payoffs
	6.1 Price and Payoff Arbitrage
	6.2 The Law of One Price
	6.3 Market-Consistent Prices
	6.4 The Pricing Functional
	6.5 Exercises
7 Fundamental Theorem of Asset Pricing
	7.1 Pricing Extensions
	7.2 Pricing Densities
	7.3 Pricing Measures
	7.4 Exercises
8 Market-Consistent Prices for General Payoffs
	8.1 Marketed Bounds
	8.2 Market-Consistent Prices
	8.3 Characterizing Market-Consistent Prices
	8.4 Sub- and Superreplication Prices
	8.5 Exercises
9 Random Variables: Information and Measurability
	9.1 Partitions and Atoms
	9.2 Observable Events
	9.3 Refining Partitions
	9.4 Measurable Random Variables
	9.5 Exercises
10 Conditional Probabilities and Expectations
	10.1 Conditional Probabilities
	10.2 Expectations Conditional on Events
	10.3 Expectations Conditional on Partitions
	10.4 Changing the Probability Measure
	10.5 Exercises
11 Conditional Linear Functionals
	11.1 Conditional Functionals
	11.2 Localizations
	11.3 Linearity, Convexity, Monotonicity
	11.4 Exercises
12 Extensions of Conditional Linear Functionals
	12.1 Scalarizations
	12.2 Extension Results
	12.3 Representation Results
	12.4 Exercises
13 Information and Stochastic Processes
	13.1 Information Structures
	13.2 Stochastic Processes
	13.3 Adapted Processes
	13.4 Martingale Processes
	13.5 Conditional Functionals
	13.6 Exercises
14 Multi-Period Financial Markets
	14.1 The Elements of the Market
	14.2 Trading Strategies
	14.3 Replicable Payoffs
	14.4 Complete Markets
	14.5 Changing the Unit of Account
	14.6 Exercises
15 Market-Consistent Prices for Replicable Payoffs
	15.1 Price and Payoff Arbitrage
	15.2 The Law of One Price
	15.3 Market-Consistent Prices
	15.4 Pricing Functionals
	15.5 Exercises
16 Fundamental Theorem of Asset Pricing
	16.1 Pricing Extensions
	16.2 Pricing Densities
	16.3 Pricing Measures
	16.4 Exercises
17 Market-Consistent Prices for General Payoffs
	17.1 Marketed Bounds
	17.2 Market-Consistent Prices
	17.3 Characterizing Market-Consistent Prices
	17.4 Sub- and Superreplication Prices
	17.5 Exercises
18 Market-Consistent Prices for Payoff Streams
	18.1 Payoff Streams
	18.2 Terminal-Payoff Equivalents
	18.3 Replicable Payoff Streams
	18.4 Market-Consistent Prices
	18.5 Characterizing Market-Consistent Prices
	18.6 Sub- and Superreplication Prices
	18.7 Exercises
19 Market-Consistent Prices for American Options
	19.1 American Options
	19.2 Exercise Strategies
	19.3 Marketed Bounds
	19.4 Market-Consistent Prices
	19.5 Replicable American Options
	19.6 Characterizing Market-Consistent Prices
	19.7 Sub- and Superreplication Prices
	19.8 Market-Consistent Strategies
	19.9 Characterizing Market-Consistent Strategies
	19.10 Exercises
A Sets and Maps
	A.1 Logical Symbols
	A.2 Sets and Maps
	A.3 Basic Combinatorics
B Vector Spaces
	B.1 The Vector Space Axioms
	B.2 Linear Subspaces
	B.3 Bases and Dimensions
	B.4 Linear Maps
C Normed Spaces
	C.1 The Normed Space Axioms
	C.2 Norm and Topology
	C.3 Sequences and Convergence
	C.4 Continuous Maps
D Inner-Product Spaces
	D.1 The Inner-Product Space Axioms
	D.2 Orthogonal Vectors
	D.3 Orthogonal Projections
	D.4 Riesz Representation
Bibliography
Index
Index of Symbols