Dynamic Asset Pricing Theory with Uncertain Time-Horizon

Christophette Blanchet-Scalliet, Nicole El Karoui, Lionel Martellini: This paper addresses the problem of pricing and hedging a random cash-flow received at a random date in a general stochastic environment.

Author(s):

Christophette Blanchet-Scalliet

Université de Nice-Sophia-Antipolis

Nicole El Karoui

Ecole Polytechnique

Lionel Martellini

EDHEC Business School

We first argue that specific timing risk is induced by the presence of an uncertain time-horizon if and only if the random time under consideration is not a stopping time of the filltration generated by prices of traded assets. In that context, we provide an explicit characterisation of the set of equivalent martingale measures, as well as a necessary and sufficient condition for a convenient separation between adjustment for market risk and timing risk. We also present price bounds consistent with perfect replication in the absence of arbitrage for an asset paying off a random amount at a random time. As is often the case, such bounds are actually too wide to be of any practical use and we consider several choices (minimal martingale measure, minimum entropy measure) for narrowing down to one the number of equivalent martingale measures.

Type: Working paper
Date: le 01/07/2004
Research Cluster : Finance

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