Portfolio optimization problems involving value at risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains...

Convex underestimators of a polynomial on a box. Given a non convex polynomial <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${f\in \mathbb{R}[{\rm x}]}$$</EquationSource> </InlineEquation> and a box <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${{\rm B}\subset \mathbb{R}^n}$$</EquationSource> </InlineEquation>, we construct a sequence of convex polynomials <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$${(f_{dk})\subset \mathbb{R}[{\rm x}]}$$</EquationSource> </InlineEquation>, which converges in a strong sense to the...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>