The martingale difference is considered widely in finance and economic because of its application in efficient market, in which the conditional expectation $E[d_t\vert\F_{t-1}]=0$ a.s., $\forall t\ge 2$ for a sequence of asset returns $\{d_t,t\ge 1\}$ and related historical information $\F_{t-1}$. However, the concept of martingale difference in set-valued random variables (i.e. random sets) has not been studied. This paper proves some properties of a set-valued random variable sequence called a weak set-valued martingale difference. By studying its characteristic properties, we propose a method of testing the weak set-valued martingale difference hypothesis and perform some simulations with real data.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 3
Year: 2022

DOI: 10.12732/ijam.v35i3.4

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