Dynamic bid–ask pricing under Dempster-Shafer uncertainty
研究了多期二项式市场模型中存在买卖价差摩擦时的定价问题，提出了动态Choquet定价规则，并证明了其与无套利条件的一致性。
We deal with the problem of pricing in a multi-period binomial market model, allowing for frictions in the form of bid–ask spreads. We introduce and characterize time-homogeneous Markov multiplicative binomial processes under Dempster-Shafer uncertainty together with the induced conditional Choquet expectation operator. Given a market formed by a frictionless risk-free bond and a non-dividend paying stock with frictions, we prove the existence of an equivalent one-step Choquet martingale belief function. We then propose a dynamic Choquet pricing rule with bid–ask spreads showing that the discounted lower price process of a European derivative contract on the stock is a Choquet super-martingale. We finally provide a normative justification in terms of a dynamic generalized no-arbitrage condition relying on the notion of partially resolving uncertainty due to Jaffray.