WEAK SET-VALUED MARTINGALE DIFFERENCE
AND ITS APPLICATIONS
Luc Tri Tuyen1, Pham Quoc Vuong1,
Vu Xuan Quynh1, Nguyen Gia Dang1 1 Department of Computational Statistics
Institute of Information Technology
Vietnam Academy of Science and Technology
Hanoi - 10000, VIETNAM 2 Department of Expert Systems and Soft Computing
Institute of Information Technology
Vietnam Academy of Science and Technology
Hanoi - 10000, VIETNAM
The martingale difference is considered widely in finance and economic because of its application in efficient market, in which the conditional expectation
a.s.,
for a sequence of asset returns
and related historical information . 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.
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