In an incomplete market the price of a claim f in general can not be uniquely identified by no arbitrage arguments. However, the "classical" super-replication price is a sensible indicator of the (maximum selling) value of the claim. When f satisfies certain pointwise conditions (e.g. f is bounded from below), the super-replication price is equal to sup_{Q}E_{Q}[f], where Q varies on the whole set of pricing measures. Unfortunately, this price is often too high: a typical situation is here discussed in the examples. We thus define the less expensive weak super-replication price and we relax the requirements on f by asking just for "enough" integrability conditions. By building up a proper duality theory, we show its economic meaning and its relation with the investor's preferences. Indeed, it turns out that the weak super-replication price of f coincides with sup_{Q∈M_{Φ}}E_{Q}[f], where M_{Φ} is the class of pricing measures with finite generalized entropy (i.e. E[Φ(((dQ)/(dP)))]<∞) and where Φ is the convex conjugate of the utility function of the investor.
Titolo: | On the super-replication price of unbounded claims |
Autori: | FRITTELLI, MARCO (Ultimo) |
Parole Chiave: | Super replication price; generalized entropy; reasonable asymptotic elasticity; preferences; incomplete markets; utility maximization; duality |
Settore Scientifico Disciplinare: | Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie |
Data di pubblicazione: | 2004 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | 10.1214/105051604000000459 |
Appare nelle tipologie: | 01 - Articolo su periodico |