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.

On the super-replication price of unbounded claims / S. Biagini, M. Frittelli. - In: THE ANNALS OF APPLIED PROBABILITY. - ISSN 1050-5164. - 14:4(2004), pp. 1970-1991. [10.1214/105051604000000459]

On the super-replication price of unbounded claims

M. Frittelli
Ultimo
2004

Abstract

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.
Super replication price; generalized entropy; reasonable asymptotic elasticity; preferences; incomplete markets; utility maximization; duality
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
2004
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/24985
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 14
social impact