Ridesharing is a promising approach for reducing congestion and pollution, and many variants have been studied in the literature over the past decades. In this paper, we consider a novel setting where individuals walk to a common pick-up point and ride together to a single drop-off point from where they walk to their final destination. This setting requires finding the optimal composition of riders and pick-up and drop-off meeting points, as well as an equitable distribution of the costs whereby riders are incentivised to participate. Based on game-theoretic principles, we propose a methodology to determine the optimal pick-up and drop-off points, together with a cost allocation method that is equitable in the sense that it ensures proportionality for sharing the costs, i.e., those who walk more should pay less. We present a formal evaluation of our cost allocation method and empirical evaluation against the Shapley value using realworld and simulated data. Our results show that our approach is computationally more tractable than the Shapley value, as it is linear in time while guaranteeing individual rationality under certain conditions.
The use of CVA to cover credit risk is widely spread, but has its limitations. Namely, dealers face the problem of the illiquidity of instruments used for hedging it, hence forced to warehouse credit risk. As a result, dealers tend to offer a limited OTC derivatives market to highly risky counterparties. Consequently, those highly risky entities rarely have access to hedging services precisely when they need them most.In this paper we propose a method to overcome this limitation. We propose to extend the CVA risk-neutral framework to compute an initial margin (IM) specific to each counterparty, which depends on the credit quality of the entity at stake, transforming the effective credit rating of a given netting set to AAA, regardless of the credit rating of the counterparty.The proposed methodology is fully compliant with the risk-neutral pricing framework, enables improved risk management for dealers and, subsequently, a route for troubled institutions to access the derivative markets.By transforming CVA requirement into IM ones, as proposed in this paper, an institution could rely on the existing mechanisms for posting and calling of IM, hence ensuring the operational viability of this new form of managing warehoused risk. The main difference with the currently standard framework is the creation of a Specific Initial Margin, that depends in the credit rating of the counterparty and the characteristics of the netting set in question. In this paper we propose a methodology for such transformation in a sound manner, and hence this method overcomes some of the limitations of the CVA framework. Using a range of Swaps and Swaptions, we present realistic numerical examples of CVA values under margining, IM values as computed nowadays, as well as the new amounts of The authors would like to thank Andrew S.Dickinson, Martin Dahlgren and Wujiang Lou The opinions expressed here are those of the authors, and do not necessarily represent the view of their employers 1 arXiv:1812.09407v1 [q-fin.RM]
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