Good Deals: a new perspective

We study Good Deals in a scenario whereby a representative agent uses decision-making tools based on a risk measure, and where the market prices are given by a sub-linear pricing rule. We consider a hedging problem where the shortfall risk is minimized subject to a given budget constraint. First, we observe that, given a coherent risk measure, the existence of a Good Deal is equivalent to the incompatibility between the pricing rule and the risk measure. Therefore, from a regulatory point of view, the coherent risk measure is modified to one which rules out Good Deals and stabilizes the market. Second, given that the coherent risk measures are not robust, we set up the hedging problem for robust risk measures. We observe that in this setting Good Deals always exist. To deal with this caveat the minimal law invariant modification of a risk measure is introduced and its robustness properties are studied. At the end, in order for applying this setting to the market real data, further development of the notion of Good Deals are presented.