## Team : mathfi

## Section: Application Domains

**Keywords: ***incomplete markets*.

## Pricing contingent claims in incomplete markets

**Participants:**M.C. Quenez, D. Lamberton.

In incomplete markets, the available information may not be restricted to the underlying assets prices. Perfect hedge may not be possible for some contingent claims and pricing can not be done by arbitrage techniques. Moreover, there exists several probabilities, equivalent to the initial one P, under which the discounted prices are martingales. By duality, these probabilities are associated to various prices (see [82] et [83]). The upper bound of these prices is characterised as the smallest supermartingale which is equal to B at time T. This Q-supermartingale can be written as the difference between a Q-martingale corresponding to the discounted value of a superhedging portfolio and an optional nondecreasing process. This decomposition implies that this upper bound corresponds to the selling price defined as the lowest price for which there exists a superhedging strategy.