Dynamic asset pricing theory with uncertain time-horizon

This paper addresses the problem of pricing and hedging a random cash-flow received at a random date. In a general setup with a random time that is not a stopping time of the filtration generated by asset prices, we first provide an explicit characterization of the set of equivalent martingale measures. We also present price bounds consistent with perfect replication in the absence of arbitrage. As is often the case, such bounds are too wide to be of any practical use and we consider several choices for narrowing down to one the number of equivalent martingale measures.