In this paper we propose a new rule to allocate risk capital to portfolios or divisions within a firm. Specifically, we determine the capital allocation that minimizes the excesses of sets of portfolios in lexicographical sense. The excess of a set of portfolios is defined as the expected loss...

In this paper we propose a new rule to allocate risk capital to portfolios or divisions within a firm. Specifically, we determine the capital allocation that minimizes the excesses of sets of portfolios in lexicographical sense. The excess of a set of portfolios is defined as the expected loss...

Unlike classic risk sharing problems based on expected utilities or convex risk measures, quantile-based risk sharing games exhibit two special features. First, quantile-based risk measures (such as the Value-at-Risk) are often not convex, and second, they ignore some part of the distribution of...

In coalitional games with uncertain payoffs, a deviating coalition can only form expectations regarding its post-deviation payoff. Classical approaches address the problem from the side of conservatism, expecting the worst, or by explicit assumptions of the emerging state of the world. We borrow...

In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a two stage stochastic programming approach. We show that under relatively mild assumptions the cooperative games associated with...

In this paper we model wholesale electricity markets as infinitely repeated games played under demand uncertainty. We examine the uniform-price auction, showing that symmetric bidding at the price cap constitutes the optimal collusive equilibrium under both perfectly inelastic demand and demand...

We consider a risk sharing problem in which agents pool their random costs together and seek an allocation rule to redistribute the risk back to each agent. The problem is put into a cooperative game framework and we focus on two salient properties of an allocation rule: stability and...

If it reaches 4° or more, global warming may cause severe economic damage with the consequence that a significant portion of the value of a diversified equity investment portfolio will be placed at risk. In the accompanying Part 1 we analysed this risk. We estimated that in a plausible worst...

The measurement and the allocation of risk are fundamental problems of portfolio management. Coherent measures of risk provide an axiomatic approach to the former problem. In an environment given by a coherent measure of risk and the various portfolios' realization vectors, risk allocation games...

Risk allocation games are cooperative games that are used to attribute the risk of a financial entity to its divisions. In this paper, we extend the literature on risk allocation games by incorporating liquidity considerations. A liquidity policy specifies state-dependent liquidity requirements...