English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study the problem of maximizing the probability that (i) an electriccomponent or financial institution $X$ does not default before anothercomponent or institution $Y$ and (ii) that $X$ and $Y$ default jointly withinthe class of all random variables $X,Y$ with given univariate continuousdistribution functions $F$ and $G$, respectively, and show that themaximization problems correspond to finding copulas maximizing the mass of theendograph $\Gamma^\leq(T)$ and the graph $\Gamma(T)$ of $T=G \circ F^-$,respectively. After providing simple, copula-based proofs for the existence ofcopulas attaining the two maxima $\overline{m}_T$ and $\overline{w}_T$ wegeneralize the obtained results to the case of general (not necessarilymonotonic) transformations $T:[0,1] \rightarrow [0,1]$ and derive simple andeasily calculable formulas for $\overline{m}_T$ and $\overline{w}_T$ involvingthe distribution function $F_T$ of $T$ (interpreted as random variable on$[0,1]$). The latter are then used to charac\-terize all non-decreasingtransformations $T:[0,1] \rightarrow [0,1]$ for which $\overline{m}_T$ and$\overline{w}_T$ coincide. A strongly consistent estimator for the maximumprobability that $X$ does not default before $Y$ is derived and proven to beasymptotically normal under very mild regularity conditions. Several examplesand graphics illustrate the main results and falsify some seemingly naturalconjectures.

On distributions with fixed marginals maximizing the joint or the prior default probability, estimation, and related results