A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes

This article provides an importance sampling algorithm for computing the probability of ruin with recuperation of a spectrally negative Lévy risk process with light-tailed downwards jumps. Ruin with recuperation corresponds to the following double passage event: for some t∈(0,∞)t∈(0,∞), the risk process starting at level x∈[0,∞)x∈[0,∞) falls below the null level during the period [0,t][0,t] and returns above the null level at the end of the period tt. The proposed Monte Carlo estimator is logarithmic efficient, as t,x→∞t,x→∞, when y=t/xy=t/x is constant and below a certain bound.

Metrics of the normal anterior sclera: imaging with optical coherence tomography

BACKGROUND To investigate anterior scleral thickness in a cohort of healthy subjects using enhanced depth imaging anterior segment optical coherence tomography. METHODS Observational case series. The mean scleral thickness in the inferonasal, inferotemporal, superotemporal, and superonasal quadrant was measured 2 mm from the scleral spur on optical coherence tomography in healthy volunteers. RESULTS Fifty-three eyes of 53 Caucasian patients (25 male and 28 female) with an average age of 48.6 years (range: 18 to 92 years) were analysed. The mean scleral thickness was 571 μm (SD 84 μm) in the inferonasal quadrant, 511 μm (SD 80 μm) in the inferotemporal quadrant, 475 (SD 81 μm) in the superotemporal, and 463 (SD 64 μm) in the superonasal quadrant. The mean scleral thickness was significantly different between quadrants (p < 0.0001, repeated measures one-way ANOVA). The association between average scleral thickness and age was statistically significant (p < 0.0001, Pearson r = 0.704). CONCLUSIONS Enhanced depth imaging optical coherence tomography revealed the detailed anatomy of the anterior sclera and enabled non-invasive measurements of scleral thickness in a non-contact approach. The anterior scleral thickness varies significantly between quadrants, resembling the spiral of Tillaux. An association of increasing scleral thickness with age was found.

Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.

RRREG: Stata module to estimate linear probability model for randomized response data

rrreg fits a linear probability model for randomized response data