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No-Arbitrage Pricing with \alpha-DS Mixtures in a Market with Bid-Ask Spreads

This paper introduces \alpha-DS mixtures, which are normalized capacities that can be represented (generally not in a unique way) as the \alpha-mixture of a belief function and its dual plausibility function. Assuming a finite state space, such capacities extend to a Choquet expectation functional that can be given a Hurwicz-like expression. In turn, \alpha-DS mixtures and their Choquet expectations appear to be particularly suitable to model prices in a market with frictions, where bid-ask prices are usually averaged taking \alpha=\frac{1}{2}. For this, we formulate a no-arbitrage one-period pricing problem in the framework of \alpha-DS mixtures and prove the analogues of the first and second fundamental theorems of asset pricing. Finally, we perform a calibration on market data to derive a market consistent no-arbitrage \alpha-DS mixture pricing rule.