A dynamic Choquet pricing rule with bid-ask spreads under ambiguity

We introduce a dynamic pricing rule allowing for frictions in the form of bid-ask spreads, by modeling “risk-neutral” uncertainty through belief functions.

The aim is to face pricing in a multi-period binomial market model under ambiguity. To this purpose, we introduce and characterize Dempster-Shafer multiplicative binomial processes together with the induced conditional Choquet expectation operator.

Next, we consider a market formed by a frictionless risk-free bond (whose price is modeled by a deterministic process) and a non-dividend paying stock with frictions (whose lower price is modeled by a Dempster Shafer multiplicative binomial process). In this market we prove an analog of the classical theorem of change of measure relying on the notion of 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 also provide a normative justification in terms of a dynamic generalized no-arbitrage condition.

We finally discuss the connections of the introduced dynamic pricing rule with time-consistency and dynamic risk measures.

The talk is based on papers in collaboration with A.Cinfrignini and D. Petturiti