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

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^k \} $ by taking $z^{k + 1} $… Expand

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.… Expand

Errata and Additions: December 2013 p.2-7 the x-axis should be just IR not IRn p.3-7 argmin f should be argminf̄ p.4-7 S(B) should be S (B) p.5-7 Proposition 4.Expand

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 and is shown to have much the same convergence properties, but with some potential advantages.Expand

This paper develops for the first time a rigorous algorithmic procedure for determining a robust decision policy in response to any weighting of the scenarios.Expand

Fundamental properties of conditional value-at-risk are derived for loss distributions in finance that can involve discreetness and provides optimization shortcuts which, through linear programming techniques, make practical many large-scale calculations that could otherwise be out of reach.Expand

The Role of Convexity and Duality Examples of Convex Optimization Problems Conjugate Convex Functions in Paired Spaces Dual Problems and Lagrangians Examples of Duality Schemes Continuity and… Expand

is called the effective domain of F, and F is said to be locally bounded at a point x e D(T) if there exists a neighborhood U of x such that the set (1.4) T(U) = (J{T(u)\ueU} is a bounded subset of… Expand