# On the super replication price of unbounded claims

## Author Info

• Sara Biagini
• Marco Frittelli
Registered author(s):

## Abstract

In an incomplete market the price of a claim f in general cannot 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_QE_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\in M_{\Phi}}E_Q[f], where M_{\Phi} is the class of pricing measures with finite generalized entropy (i.e., E[\Phi (\frac{dQ}{dP})]

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File URL: http://arxiv.org/pdf/math/0503550

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number math/0503550.

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 Length: Date of creation: Mar 2005 Date of revision: Publication status: Published in Annals of Applied Probability 2004, Vol. 14, No. 4, 1970-1991 Handle: RePEc:arx:papers:math/0503550 Contact details of provider: Web page: http://arxiv.org/

## References

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1. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B 294, University of Bonn, Germany.
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