Stability of marketable payoffs with re-trading

We consider a stochastic financial exchange economy with a finite date-event tree representing time and uncertainty and a financial structure with possibly long-term assets. We have addressed in Bonnisseau-Chéry [3] the question of the stability of financial structures thanks to a suitable Assumption R which is based only on the return of the assets independently of the price of the assets. However, Assumption R is never satisfied in the structures with re-trading (See [3]), which is a very common feature in many papers (See [5]). The main purpose of this new paper is to deepen the study of the stability of financial structures with long-term assets and especially to address the stability in cases where there is a re-trading of assets after their issuance at different dates. We exhibit a newsufficient condition, which allows to have the equality between the kernel of payoffs matrices, and, thus the stability of the marketable payoffs. This sufficient condition is then used to get the stability result for the re-trading extension of a financial structure. We also show that the situation is more complex when all initial assets are not issued at the initial date and we then provide a stronger condition to cover this case.