  In this paper we introduce some new copulas emerging from shock models. It
was shown earlier that reflected maxmin copulas (RMM for short) are not just
some specific singular copulas; they contain many important absolutely
continuous copulas including the negative quadrant dependent part of the
Eyraud-Farlie-Gumbel-Morgenstern class. The main goal of this paper is to
develop the RMM copulas with dependent endogenous shocks and give evidence that
RMM copulas may exhibit some characteristics better than the original maxmin
copulas (MM for short): (1) An important evidence for that is the iteration
procedure of the RMM transformation which we prove to be always convergent and
we give many properties of it that are useful in applications. (2) Using this
result we find also the limit of the iteration procedure of the MM
transformation thus answering a question proposed earlier by Durante,
Omladi\v{c}, Ora\v{z}em, and Ru\v{z}i\'{c}. (3) We give the multivariate
dependent RMM copula that compares to the MM version given by Durante,
Omladi\v{c}, Ora\v{z}em, and Ru\v{z}i\'{c}. In all our copulas the
idiosyncratic and systemic shocks are combined via asymmetric linking functions
as opposed to Marshall copulas where symmetric linking functions are used.
