We study risk sharing games with quantile-based risk measures and heterogeneous beliefs, motivated by the use of internal models in finance and insurance. Explicit forms of Pareto-optimal allocations and competitive equilibria are obtained by solving various optimization problems. For Expected...

We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called Range-Value-at-Risk (RVaR), as their preferences. The family of RVaR includes the Value-at-Risk (VaR) and the Expected Shortfall (ES), the two popular and competing...

We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement related optimization problem is robust, which we call "robustness against optimization". The new notion is studied for...

For the classic problem of fair allocation of indivisible goods, we introduce the notion of minimum social inequality allocations and discuss its connection to other fair allocation rules such as minimum envy. We show that a fair allocation problem can always be cast as the problem of finding an...

We study a synchronization problem with multiple instances. First, we show that the problem we consider can be formulated as the problem of finding an intra-column rearrangement for multiple matrices (which reflect problem instances) such that the row sums across the various matrices show...

Abstract In this paper, we survey, extend and improve several bounds for the distribution function and the tail probabilities of portfolios, where the dependence structure within the portfolio is completely unknown or only partially known. We present various methods for obtaining bounds based on...

We give analytical bounds on the Value-at-Risk and on convex risk measures for a portfolio of random variables with fixed marginal distributions under an additional positive dependence structure. We show that assuming positive dependence information in our model leads to reduced dependence...