This paper addresses the robust counterparts of optimization problems containing sums of maxima of linear functions and proposes several reformulations. These problems include many practical problems, e.g. problems with sums of absolute values, and arise when taking the robust counterpart of a...

The least squares estimator is probably the most frequently used estimation method in regression analysis. Unfortunately, it is also quite sensitive to data contamination and model misspecification. Although there are several robust estimators designed for parametric regression models that can...

We propose a new way to derive tractable robust counterparts of a linear conic optimization problem by using the theory of Beck and Ben-Tal on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new convex reformulation of the dual...

This paper makes use of perturbation theory to solve analytically a class of robust control problems implied by Anderson, Hansen and Sargent (2000) (AHS (2000)) model of a preference for robustness. For the constant opportunity set model, we provide (i) asymptotic expressions that characterize...

In this paper we consider ambiguous stochastic constraints under partial information consisting of means and dispersion measures of the underlying random parameters. Whereas the past literature used the variance as the dispersion measure, here we use the mean absolute deviation from the mean...

Orthant probabilities applied in a two-dimensional framework are used to derive quadrant-conditional financial asset return correlations which fully capture both linear and non-linear components of co-variability. We investigate the potential for employing quadrant-conditional correlations in...

This paper considers the non-zero-sum stochastic differential game problem between two ambiguity-averse insurers (AAIs) who encounter model uncertainty and seek the optimal investment and reinsurance decision under relative performance concerns. Each AAI invests in a risky asset and a risk-free...