Scalar and Vector Risk in the General Framework of Portfolio Theory: A Convex Analysis Approach (CMS/CAIMS Books in Mathematics, 9)

Preface
Contents
1 Introduction
	1.1 General Motivation
	1.2 Literature Review on Portfolio Theory
	1.3 The Role of Duality
	1.4 Preview of the Forthcoming
2 Efficient Portfolios for Scalar Risk Functions
	2.1 One-Period Financial Markets and Related Risk and Utility Functions
		2.1.1 The Payoff Space
		2.1.2 One-Period Financial Markets
		2.1.3 Portfolios
		2.1.4 Risk Functions
		2.1.5 Utility Functions
	2.2 Multi-period Financial Markets and Related Risk and Utility Functions
		2.2.1 Geometric Multi-period Financial Market Model
		2.2.2 Multi-period Wealth Process for the Fixed Fraction Trading Strategy
		2.2.3 The Log TWR Utility Function
		2.2.4 Further Multi-period Utility Functions
		2.2.5 Multi-period Log Drawdown Risk Functions
	2.3 Efficient Trade-Off Between Risk and Utility: The Efficient Frontier
		2.3.1 The Risk-Utility Space
		2.3.2 The Efficient Frontier
		2.3.3 Connectedness of the Efficient Frontier
	2.4 Efficient Portfolios
		2.4.1 Existence of Efficient Portfolios
		2.4.2 Uniqueness of Efficient Portfolios
		2.4.3 Relationship with the Efficient Frontier
		2.4.4 Examples of Efficient Frontiers for Scalar Risk
3 Efficient Portfolios for Vector Risk Functions
	3.1 Efficient Frontier for the Vector Risk-Utility Trade-Off
		3.1.1 Technical Assumptions
		3.1.2 Representation of the Efficient Frontier
		3.1.3 Partial Continuity of the Representing Functions
	3.2 Connectedness of the Efficient Frontier
		3.2.1 Case Study for Two-Dimensional Risk Vectors
		3.2.2 Connectivity for Higher-Dimensional Risk Vectors
	3.3 Efficient Portfolios in the Vector Risk Case
		3.3.1 Existence and Uniqueness of Efficient Portfolios
		3.3.2 Connections of Scalar Risk and Vector Risk Theory
		3.3.3 Markowitz Portfolios with Tracking Error
4 Application Examples
	4.1 Bank Balance Sheet Management Problems
		4.1.1 Bank Balance Sheet Problems
		4.1.2 Risks and Their Measurements
	4.2 Bank Balance Sheet Problems Involving Linear Interest Rate and Credit Risk
		4.2.1 Linear Programming Model
		4.2.2 The Dual Problem
		4.2.3 Optimal Balance Sheet
		4.2.4 Efficient Frontier
		4.2.5 Financial Meanings
		4.2.6 Linear Bank Balance Sheet Example with Real Data
	4.3 Bank Balance Sheet Problem: Quadratic Interest Rate, Linear Credit Risk
		4.3.1 Balance Sheets Enforcing Sign Constraints
		4.3.2 An Approach to Bank Balance Sheets Using the Tracking Error
		4.3.3 Efficient Frontier for the Tracking Error Approach
		4.3.4 Determining the Radius of the Ball rb to Use in the Tracking Error Problem
		4.3.5 Example Using Real-World Data
	4.4 Comments and Further Developments
		4.4.1 Linear Model Involving More Than Two Kinds of Risks
		4.4.2 Linear-Quadratic Model Involving More Than Two Kinds of Risks
		4.4.3 Diversification by Modifying a Benchmark
		4.4.4 Log Drawdown Risk and Log TWR Utility Application
		4.4.5 Efficient Frontier for Drawdown, Variance, and Log TWR
5 Conclusion
Convex Programming Problems
	A.1 Semi-continuity
	A.2 Convexity
	A.3 Convex Programming Problems
	A.4 Duality
References
Index