A new approach to optimizing or hedging a portfolio of financial instruments to reduce risk is presented and tested on applications. It focuses on minimizing Conditional Value-at-Risk (CVaR) rather… (More)

I I I I Abstract. For the problem of minimizing a lower semicontinuous proper convex function f on a Hilbert space, the proximal point algorithm in exact form generates a sequence {z"}by taking Zk+1… (More)

Fundamental properties of conditional value-at-risk, as a measure of risk with significant advantages over value-at-risk, are derived for loss distributions in finance that can involve discreetness.… (More)

Errata and Additions: December 2013 p. 10, l. 14 xν → x should be xν → x̄ p. 31, l. 10 argmin f should be argmin f̄ p. 45, Fig.2-7 the x-axis should be just IR not IRn p. 108, l. -6 insert ‘to’ after… (More)

The theory of the proximal point algorithm for maximal monotone operators is applied to three algorithms for solving convex programs, one of which has not previously been formulated.… (More)

General deviation measures are introduced and studied systematically for their potential applications to risk management in areas like portfolio optimization and engineering. Such measures include… (More)

Linear and nonlinear variational inequality problems over a polyhedral convex set are analyzed parametrically. Robinson’s notion of strong regularity, as a criterion for the solution set to be a… (More)

Recently Clarke, Stern and Wolenski characterized, in a Hilbert space, the closed subsets C for which the distance function dC is continuously differentiable everywhere on an open “tube” of uniform… (More)

Decisions often need to be made before all the facts are in. A facility must be built to withstand storms, floods, or earthquakes of magnitudes that can only be guessed from historical records. A… (More)