A note on Yoshida's optimal stopping model for option pricing

We argue that the optimal stopping model which has been used by Yoshida to discuss option pricing can many times lead to an overoptimistic evaluation of payoffs (put option prices). This effect is due to the method used to compare fuzzy payoffs, using a Sugeno integral. It is shown that each fuzzy payoff can be associated with an indifferent non-fuzzy payoff which is never smaller than the highest value having membership 1. Several examples are given in which this property seems to be inconvenient. We also show that this inconvenience cannot be avoided by replacing Sugeno integrals by any other integral-like functional like a t-seminormed integral or a Choquet integral. Finally we suggest to use the Compos–González ranking criterion instead.