Asymmetric linkages: maxmin vs. reflected maxmin copulas
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In this paper we introduce some new copulas emerging from shock models, motivated by applications, i.e. the reflected maxmin copulas with dependent endogenous shocks and their extension to multivariate case. Our main goal is to show that reflected maxmin copulas exhibit conceptually better characteristics as the original maxmin copulas. An important evidence for that is the iteration procedure of the reflected maxmin transformation which we prove to be always convergent and we give many properties of it that are useful in applications. Even more, using this result we find also the limit of the iteration procedure of the maxmin transformation thus answering a question proposed earlier by Durante, Omladič, Oražem, and Ružić. The third main result of ours is the multivariate (dependent) reflected maxmin copula which is conceptually simpler than the standard version of it. 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.
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