Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
| ||

``Probabilités et Modèles Aléatoires''
| ||

**Auteur(s): **

**Code(s) de Classification MSC:**

- 90A09 Finance, portfolios, investment
- 93E20 Optimal stochastic control

**Résumé:** We work in the Uncertain Volatility Model setting of
Avellaneda, Levy, Paras [1] and Lyons [10] , (cf. also [11] ). We first look at European options in a market
with no interest rate and focus on the extreme case where the
volatility has a lower bound but no upper bound. We show that the
smallest riskless selling price of the claim is the Black-Scholes
price (at volatility given by the lower bound) of an option with
payoff the smallest concave function above the initial payoff. We
next extend our results to the case with interest rate.

**Mots Clés:** *European options ; Hamilton-Jacobi-Bellman equation ; Stochastic control ; Superstrategies*

**Date:** 2000-11-15

**Prépublication numéro:** *PMA-620*