Pricing a contingent claim with random interval or fuzzy random payoff in one-period setting

This article proposes a method for pricing a contingent claim with random interval and fuzzy random payoff. On introduction of the acceptability concept based on classical no-arbitrage argument, a price interval and a fuzzy price are obtained in random interval market and fuzzy random market, respectively. New definitions on replicative strategies, sub-replicative and sup-replicative ones, in two market setting are given. Some interesting results similar to those in the classical random market are presented.