This paper shows that patients with private health insurance (PHI) are being offered significantly shorter waiting times than patients with statutory health insurance (SHI) in German acute hospital care. This behavior may be driven by the higher expected profitability of PHI relative to SHI holders. Further, we find that hospitals offering private insurees shorter waiting times when compared with SHI holders have a significantly better financial performance than those abstaining from or with less discrimination.

We prove that the componentwise maximum of an i.i.d. triangular array of chi-square random vectors converges in distribution, under appropriate assumptions on the dependence within the vectors and after normalization, to the max-stable Hüsler-Reiss distribution. As a by-product we derive a conditional limit result.

Abstract. In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are different and mainly probabilistic relying on coupling methods adapted to the special situation under investigation. Moreover we answer a question raised by Ben-Ari and Pinsky concerning the dependence of the spectral gap on the jump distribution in a multi-dimensional setting.

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In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case of a large drift and prove that there is a threshold drift above which the bottom of the spectrum no longer depends on the drift. As a corollary to our result we are able to answer two questions concerning elliptic eigenvalue problems with non-local boundary conditions formulated previously by Iddo Ben-Ari and Ross Pinsky.