CONTINUOUS-TIME ASSET PRICING THEORY a martingale-based approach.

Preface
	Philosophy
	The Key Topics
	The Key Insights
	The Martingale Approach
	Discrete Versus Continuous-Time
	Mean-Variance Efficiency and the Static CAPM
	Stochastic Calculus
	Traditional Asset Pricing Theory Versus Market Microstructure
	Themes
	Changes to the Second Edition
Contents
List of Notation
Part I Arbitrage Pricing Theory
	Overview
	1 Stochastic Processes
		1.1 Stochastic Processes
		1.2 Stochastic Integration
		1.3 Quadratic Variation
		1.4 Uniqueness of the Stochastic Integral Representation
		1.5 Integration by Parts
		1.6 Ito\'s Formula
		1.7 Girsanov\'s Theorem
		1.8 Essential Supremum
		1.9 Optional Decomposition
		1.10 Martingale Representation
		1.11 Equivalent Probability Measures
		1.12 Notes
	2 The Fundamental Theorems
		2.1 The Set-Up
			2.1.1 Trading Strategies
			2.1.2 Admissibility and Doubling Strategies
			2.1.3 Suicide Strategies
			2.1.4 The Frictionless Market Assumption
		2.2 Change of Numeraire
		2.3 Cash Flows
			2.3.1 Reinvest in the MMA
			2.3.2 Reinvest in the Risky Asset
			2.3.3 Summary
		2.4 Non-redundant Assets
		2.5 The First Fundamental Theorem
			2.5.1 No Arbitrage (NA)
			2.5.2 No Unbounded Profits with Bounded Risk(NUPBR)
			2.5.3 Properties of Dl
			2.5.4 No Free Lunch with Vanishing Risk (NFLVR)
			2.5.5 The First Fundamental Theorem
			2.5.6 Equivalent Local Martingale Measures
			2.5.7 The State Price Density
		2.6 The Second Fundamental Theorem
			2.6.1 Attainable Securities
			2.6.2 Complete Markets
		2.7 The Third Fundamental Theorem
			2.7.1 Risk Neutral Valuation
			2.7.2 Synthetic Derivative Construction
		2.8 Finite Dimension Brownian Motion Market
			2.8.1 The Set-Up
			2.8.2 NFLVR
			2.8.3 Complete Markets
			2.8.4 ND
		2.9 Notes
		Appendix
	3 Asset Price Bubbles
		3.1 The Set-Up
		3.2 The Market Price and Fundamental Value
		3.3 The Asset Price Bubble
			3.3.1 Complete Markets
			3.3.2 Incomplete Markets
		3.4 Theorems Under NFLVR and ND
		3.5 Notes
	4 Basis Assets, Multiple-Factor Beta Models, and Systematic Risk
		4.1 The Set-Up
		4.2 Basis Assets
		4.3 The Multiple-Factor Beta Model
		4.4 Positive Alphas
		4.5 The State Price Density
		4.6 Arrow Debreu Securities
		4.7 Systematic Risk
		4.8 Diversification
		4.9 Notes
	5 The Black Scholes Merton Model
		5.1 NFLVR, Complete Markets, and ND
		5.2 The BSM Call Option Formula
		5.3 The Synthetic Call Option
		5.4 Original Derivation of the BSM Formula
		5.5 Merton\'s Structural Model
		5.6 Notes
	6 The Heath Jarrow Morton Model
		6.1 The Set-Up
		6.2 Term Structure Evolution
		6.3 Arbitrage-Free Conditions
		6.4 Examples
			6.4.1 Ho and Lee Model
			6.4.2 Lognormally Distributed Forward Rates
			6.4.3 Vasicek Model
			6.4.4 Cox Ingersoll Ross Model
			6.4.5 Affine Model
		6.5 Forward and Futures Contracts
			6.5.1 Forward Contracts
				6.5.1.1 The Forward Price Measure
				6.5.1.2 An Alternative Characterization of QM
				6.5.1.3 Risk Neutral Valuation (Revisited)
			6.5.2 Futures Contracts
		6.6 The Libor Model
		6.7 Notes
	7 Reduced Form Credit Risk Models
		7.1 The Set-Up
		7.2 The Risky Firm
		7.3 Existence of an Equivalent Martingale Measure
		7.4 Risk Neutral Valuation
			7.4.1 Cash Flow 1
			7.4.2 Cash Flow 2
			7.4.3 Cash Flow 3
			7.4.4 Cash Flow 4
		7.5 Examples
			7.5.1 Coupon Bonds
			7.5.2 Credit Default Swaps (CDS)
			7.5.3 First-to-Default Swaps
		7.6 Notes
	8 Incomplete Markets
		8.1 The Set-Up
		8.2 The Super-Replication Cost
		8.3 The Super-Replication Trading Strategy
		8.4 The Sub-replication Cost
		8.5 Notes
Part II Portfolio Optimization
	Overview
	9 Utility Functions
		9.1 Preference Relations
		9.2 State Dependent EU Representation
			9.2.1 Rationality Axioms
			9.2.2 Additional Properties
			9.2.3 Risk Aversion
		9.3 Strict Concavity and Risk Aversion
			9.3.1 Independent Gambles
			9.3.2 Risk Aversion
			9.3.3 Characterization Theorems
		9.4 Measures of Risk Aversion for Independent Gambles
		9.5 State Dependent Utility Functions
		9.6 Conjugate Duality
		9.7 Reasonable Asymptotic Elasticity
		9.8 Differential Beliefs
		9.9 Notes
	10 Complete Markets (Utility Over Terminal Wealth)
		10.1 The Set-Up
		10.2 Problem Statement
		10.3 Existence of a Solution
		10.4 Characterization of the Solution
			10.4.1 The Characterization
			10.4.2 Summary
		10.5 The Shadow Price
		10.6 The Local Martingale Deflator
		10.7 The Optimal Trading Strategy
		10.8 An Example
			10.8.1 The Market
			10.8.2 The Utility Function
			10.8.3 The Optimal Wealth Process
			10.8.4 The Optimal Trading Strategy
			10.8.5 The Value Function
		10.9 Notes
		Appendix
			Proof of Expression (10.7)
			Proof of Expression (10.8)
	11 Incomplete Markets (Utility Over Terminal Wealth)
		11.1 The Set-Up
		11.2 Problem Statement
		11.3 Existence of a Solution
		11.4 Characterization of the Solution
			11.4.1 The Characterization
			11.4.2 Summary
		11.5 The Shadow Price
		11.6 The Supermartingale Deflator
		11.7 The Optimal Trading Strategy
		11.8 An Example
			11.8.1 The Market
			11.8.2 The Utility Function
			11.8.3 The Optimal Supermartingale Deflator
			11.8.4 The Optimal Wealth Process
			11.8.5 The Optimal Trading Strategy
			11.8.6 The Value Function
		11.9 Differential Beliefs
		11.10 Notes
		Appendix
	12 Incomplete Markets (Utility Over Intermediate Consumption and Terminal Wealth)
		12.1 The Set-Up
		12.2 Problem Statement
		12.3 Existence of a Solution
		12.4 Characterization of the Solution
			12.4.1 Utility of Consumption (U20)
				12.4.1.1 The Solution
				12.4.1.2 The Shadow Price
				12.4.1.3 The Supermartingale Deflator Process
				12.4.1.4 The Optimal Trading Strategy
				12.4.1.5 Summary
			12.4.2 Utility of Terminal Wealth (U10)
			12.4.3 Utility of Consumption and Terminal Wealth
		12.5 Notes
		Appendix
Part III Equilibrium
	Overview
	13 Equilibrium
		13.1 The Set-Up
			13.1.1 Supply of Shares
			13.1.2 Traders in the Economy
			13.1.3 Aggregate Market Wealth
			13.1.4 Trading Strategies
			13.1.5 An Economy
		13.2 Equilibrium
		13.3 Theorems
		13.4 Intermediate Consumption
			13.4.1 Supply of the Consumption Good
			13.4.2 Demand for the Consumption Good
			13.4.3 An Economy
		13.5 Notes
	14 A Representative Trader Economy
		14.1 The Aggregate Utility Function
		14.2 The Portfolio Optimization Problem
		14.3 Representative Trader Economy Equilibrium
		14.4 Pareto Optimality
		14.5 Existence of an Equilibrium
		14.6 Uniqueness of the Equilibrium
			14.6.1 Uniqueness of the Equilibrium Price Process
			14.6.2 Uniqueness of the Supermartingale Deflators
		14.7 Examples
			14.7.1 Identical Traders
			14.7.2 Logarithmic Preferences
		14.8 Intermediate Consumption
		14.9 Notes
	15 Characterizing the Equilibrium
		15.1 The Set-Up
		15.2 The Supermartingale Deflator
		15.3 Asset Price Bubbles
			15.3.1 Complete Markets
			15.3.2 Incomplete Markets
		15.4 Systematic Risk
		15.5 Consumption CAPM
		15.6 Intertemporal CAPM
		15.7 Intermediate Consumption
			15.7.1 Systematic Risk
			15.7.2 Consumption CAPM
			15.7.3 Intertemporal CAPM
		15.8 Notes
	16 Market Informational Efficiency
		16.1 The Set-Up
		16.2 The Definition
		16.3 The Theorem
		16.4 Information Sets and Efficiency
		16.5 Testing for Market Efficiency
			16.5.1 Profitable Trading Strategies
			16.5.2 Positive Alphas
			16.5.3 Asset Price Evolutions
		16.6 Random Walks and Efficiency
			16.6.1 The Set-Up
			16.6.2 Random Walk
			16.6.3 Market Efficiency  Random Walk
			16.6.4 Random Walk  Market Efficiency
		16.7 Notes
	17 Epilogue (The Fundamental Theorems and the CAPM)
		17.1 The Fundamental Theorems
			17.1.1 The First Fundamental Theorem
			17.1.2 The Second Fundamental Theorem
			17.1.3 Risk Neutral Valuation
			17.1.4 Finite State Space Market
		17.2 Basis Assets, Multi-Factor Beta Models, and Systematic Risk
		17.3 Utility Functions
		17.4 Portfolio Optimization
			17.4.1 The Dual Problem
			17.4.2 The Primal Problem
			17.4.3 The Optimal Trading Strategy
		17.5 Beta Model (Revisited)
		17.6 The Efficient Frontier
			17.6.1 The Solution (Revisited)
			17.6.2 Summary
			17.6.3 The Risky Asset Frontier and Efficient Frontier
		17.7 Equilibrium
		17.8 Notes
		Appendix
Part IV Trading Constraints
	Overview
	18 The Trading Constrained Market
		18.1 The Set-Up
		18.2 Trading Constraints
		18.3 Support Functions
		18.4 Examples (Trading Constraints and Their Support Functions)
			18.4.1 No Trading Constraints
			18.4.2 Prohibited Short Sales
			18.4.3 No Borrowing
			18.4.4 Margin Requirements
		18.5 Wealth Processes
	19 Arbitrage Pricing Theory
		19.1 No Unbounded Profits with Bounded Risk (NUPBRC)
		19.2 No Free Lunch with Vanishing Risk (NFLVRC)
		19.3 Asset Price Bubbles
		19.4 Systematic Risk
	20 The Auxiliary Markets
		20.1 The Auxiliary Markets
		20.2 The Normalized Auxiliary Markets
	21 Super- and Sub-Replication
		21.1 The Set-Up
			21.1.1 Auxiliary Market (0,0)
			21.1.2 Auxiliary Markets (ν0,ν)
		21.2 Local Martingale Deflators
		21.3 Wealth Processes Revisited
		21.4 Super-Replication
		21.5 Sub-Replication
	22 Portfolio Optimization
		22.1 The Set-Up
		22.2 Wealth Processes (Revisited)
		22.3 The Optimization Problem
		22.4 Existence of a Solution
		22.5 Characterization of the Solution
		22.6 The Shadow Price of the Budget Constraint
		22.7 The Supermartingale Deflator
		22.8 The Shadow Prices of the Trading Constraints
		22.9 Asset Price Bubbles
		22.10  Systematic Risk
	23 Equilibrium
		23.1 The Set-Up
		23.2 Representative Trader
			23.2.1 The Solution
			23.2.2 Buy and Hold Trading Strategies
		23.3 Existence of Equilibrium
		23.4 Characterization of Equilibrium
References
Index