The convexity-cone approach to comparative risk and downside risk.

We establish a calculus characterization of the core of supermodular games, which reduces the description of the core to the computation of suitable Gateaux derivatives of the Choquet integrals associated with the game. Our result generalizes to infinite games a classic result of Shapley (1971). As a secondary contribution, we provide a fairly complete analysis of the Gateaux and Frechet differentiability of the Choquet integrals of supermodular measure games.

Ultramodular functions.

We study the properties of ultramodular functions, a class of functions that generalizes scalar convexity and that naturally arises in some economic and statistical applications.

To split or not to split: Capital allocation with convex risk measures

Convex risk measures were introduced by Deprez and Gerber (1985). Here the problem of allocating risk capital to subportfolios is addressed, when aggregate capital is calculated by a convex risk measure. The Aumann-Shapley value is proposed as an appropriate allocation mechanism. Distortion-exponential measures are discussed extensively and explicit capital allocation formulas are obtained for the case that the risk measure belongs to this family. Finally the implications of capital allocation with a convex risk measure for the stability of portfolios are discussed

How to cut a pizza fairly: fair division with descreasing marginal evaluations.

Existential and constructive solutions to the classic problems of fair division are known for individuals with constant marginal evaluations. By considering nonatomic concave capacities instead of nonatomic probability measures, we extend some of these results to the case of individuals with decreasing marginal evaluations.

Capital allocation rules and the no-undercut property

This paper makes the point on a well known property of capital allocation rules, namely the one called no-undercut. Its desirability in capital allocation stems from some stability game theoretical features related to the notion of core, both for finite and infinite games. We review these aspects, by relating them to the properties of the risk measures involved in capital allocation problems. We also discuss some problems and possible extensions arising when we deal with non-coherent risk measures

Cores and stable sets of finite dimensional games.

In this paper we study exact TU games having finite dimensional non-atomic cores, a class of games that includes relevant economic games. We first characterize them by showing that they are a particular type of market games. Using this characterization, we then show that in such a class the cores are their unique von Neumann- Morgenstern stable sets.

To split or not to split: capital allocation with convex risk measures

Convex risk measures were introduced by Deprez and Gerber [Deprez, O., Gerber, H.U., 1985. On convex principles of premium calculation. Insurance: Math. Econom. 4 (3), 179–189]. Here the problem of allocating risk capital to subportfolios is addressed, when convex risk measures are used. The Aumann–Shapley value is proposed as an appropriate allocation mechanism. Distortion-exponential measures are discussed extensively and explicit capital allocation formulas are obtained for the case that the risk measure belongs to this family. Finally the implications of capital allocation with a convex risk measure for the stability of portfolios are discussed. It is demonstrated that using a convex risk measure for capital allocation can produce an incentive for infinite fragmentation of portfolios

An Extended Mean Field Game for Storage in Smart Grids

We consider a stylized model for a power network with distributed local power generation and storage. This system is modeled as network connection a large number of nodes, where each node is characterized by a local electricity consumption, has a local electricity production (e.g. photovoltaic panels), and manages a local storage device. Depending on its instantaneous consumption and production rates as well as its storage management decision, each node may either buy or sell electricity, impacting the electricity spot price. The objective at each node is to minimize energy and storage costs by optimally controlling the storage device. In a non-cooperative game setting, we are led to the analysis of a non-zero sum stochastic game with $N$ players where the interaction takes place through the spot price mechanism. For an infinite number of agents, our model corresponds to an Extended Mean-Field Game (EMFG). In a linear quadratic setting, we obtain and explicit solution to the EMFG, we show that it provides an approximate Nash-equilibrium for $N$-player game, and we compare this solution to the optimal strategy of a central planner.Comment: 27 pages, 5 figures. arXiv admin note: text overlap with arXiv:1607.02130 by other author

Portfolio Selection with Monotone Mean-Variance Preferences.

We propose a portfolio selection model based on a class of preferences that coincide with mean-variance preferences on their domain of monotonicity, but differ where mean-variance preferences fail to be monotone.

Portfolio Selection with Monotone Mean-Variance Preferences

We propose a portfolio selection model based on a class of preferences that coincide with mean-variance preferences on their domain of monotonicity, but differ where mean-variance preferences fail to be monotone.Portfolio selection. Mean-variance. Risk measures. Convex risk measures. Ambiguity. Robustness. Asymmetric returns.