The space of fuzzy set-valued square integrable martingales

In this paper, we shall introduce the concept of a fuzzy set-valued square integrable martingale, define a metric between two fuzzy set-valued square integrable martingales. Then we prove that the family of all right-continuous fuzzy set-valued square integrable martingales with respect to the metric is a complete space and the family of all continuous fuzzy set-valued square integrable martingales is its closed subset. This discussion will be useful in the study of fuzzy set-valued stochastic integrals, stochastic differential equations with applications in finance.