Algorithms for Worst-Case Design and Applications to Risk Management Book

	Preface
Ch. 1	Introduction to minimax	1
	Background and Notation	1
	Continuous Minimax	10
	Optimality Conditions and Robustness of Minimax	11
	Saddle Points and Saddle Point Conditions	15
Ch. 2	A survey of continuous minimax algorithms	23
	The Algorithm of Chaney	25
	The Algorithm of Panin	30
	The Algorithm of Kiwiel	31
Ch. 3	Algorithms for computing saddle points	37
	Computation of Saddle Points	37
	The Algorithms	42
	Global Convergence of Newton-type Algorithms	50
	Achievement of Unit Stepsizes and Superlinear Convergence	54
Ch. 4	A quasi-Newton algorithm for continuous minimax	63
	Basic Concepts and Definitions	66
	The quasi-Newton Algorithm	70
	Basic Convergence Results	76
	Global Convergence and Local Convergence Rates	81
Ch. 5	Numerical experiments with continuous minimax algorithms	93
	The Algorithms	94
	Implementation	96
	Test Problems	98
	Summary of the Results	110
Ch. 6	Minimax as a robust strategy for discrete rival scenarios	121
	Introduction to Rival Models and Forecast Scenarios	121
	The Discrete Minimax Problem	123
	The Robust Character of the Discrete Minimax Strategy	125
	Augmented Lagrangians and Convexification of Discrete Minimax	132
Ch. 7	Discrete minimax algorithm for nonlinear equality and inequality constrained models	139
	Basic Concepts	141
	The Discrete Minimax Algorithm	142
	Convergence of the Algorithm	152
	Achievement of Unit Stepsizes	156
	Superlinear Convergence Rates of the Algorithm	162
	The Algorithm for Only Linear Constraints	172
Ch. 8	A continuous minimax strategy for options hedging	179
	Options and the Hedging Problem	181
	The Black and Scholes Option Pricing Model and Delta Hedging	183
	Minimax Hedging Strategy	187
	Simulation	196
	Illustrative Hedging Problem: A Limited Empirical Study	204
	Multiperiod Minimax Hedging Strategies	207
	Simulation Study of the Performance of Different Multiperiod Strategies	213
	CAPM-based Minimax Hedging Strategy	215
	Simulation Study of the Performance of CAPM Minimax	222
	The Beta of the Hedge Portfolio for CAPM Minimax	226
	Hedging Bond Options	226
Ch. 9	Minimax and asset allocation problems	247
	Models for Asset Allocation Based on Minimax	249
	Minimax Bond Portfolio Selection	252
	Dual Benchmarking	261
	Other Minimax Strategies for Asset Allocation	271
	Multistage Minimax Portfolio Selection	277
	Portfolio Management Using Minimax and Options	284
Ch. 10	Asset/liability management under uncertainty	291
	The Immunization Framework	296
	Illustration	300
	The Asset/Liability (A/L) Risk in Immunization	303
	The Continuous Minimax Directional Immunization	308
	Other Immunization Strategies	309
	The Stochastic ALM Model 1	315
	The Stochastic ALM Model 2	325
Ch. 11	Robust currency management	341
	Strategic Currency Management 1: Pure Currency Portfolios	345
	Strategic Currency Management 2: Currency Overlay	351
	A Generic Currency Model for Tactical Management	357
	The Minimax Framework	359
	The Interplay between the Strategic Benchmark and Tactical Management	373
	Currency Management Using Minimax and Options	374
	Index	381