Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by creeping (i.e. induced by the diffusion term) and by jumping (i.e. by a claim amount) are provided. It is shown that these algorithms have either bounded relative error or logarithmic efficiency, as t,x→∞t,x→∞, where t>0t>0 is the time horizon and x>0x>0 is the starting point of the risk process, with y=t/xy=t/x held constant and assumed either below or above a certain constant.

Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

This article proposes computing sensitivities of upper tail probabilities of random sums by the saddlepoint approximation. The considered sensitivity is the derivative of the upper tail probability with respect to the parameter of the summation index distribution. Random sums with Poisson or Geometric distributed summation indices and Gamma or Weibull distributed summands are considered. The score method with importance sampling is considered as an alternative approximation. Numerical studies show that the saddlepoint approximation and the method of score with importance sampling are very accurate. But the saddlepoint approximation is substantially faster than the score method with importance sampling. Thus, the suggested saddlepoint approximation can be conveniently used in various scientific problems.

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.

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.

Stochastic simulation of rare events

Stochastic simulation is an important and practical technique for computing probabilities of rare events, like the payoff probability of a financial option, the probability that a queue exceeds a certain level or the probability of ruin of the insurer's risk process. Rare events occur so infrequently, that they cannot be reasonably recorded during a standard simulation procedure: specifc simulation algorithms which thwart the rarity of the event to simulate are required. An important algorithm in this context is based on changing the sampling distribution and it is called importance sampling. Optimal Monte Carlo algorithms for computing rare event probabilities are either logarithmic eficient or possess bounded relative error.

Gradient-Domain Bidirectional Path Tracing

Gradient-domain path tracing has recently been introduced as an efficient realistic image synthesis algorithm. This paper introduces a bidirectional gradient-domain sampler that outperforms traditional bidirectional path tracing often by a factor of two to five in terms of squared error at equal render time. It also improves over unidirectional gradient-domain path tracing in challenging visibility conditions, similarly as conventional bidirectional path tracing improves over its unidirectional counterpart. Our algorithm leverages a novel multiple importance sampling technique and an efficient implementation of a high-quality shift mapping suitable for bidirectional path tracing. We demonstrate the versatility of our approach in several challenging light transport scenarios.

Efficiency of risk-based vs . random sampling for the monitoring of tetracycline residues in slaughtered calves in Switzerland

In all European Union countries, chemical residues are required to be routinely monitored in meat. Good farming and veterinary practice can prevent the contamination of meat with pharmaceutical substances, resulting in a low detection of drug residues through random sampling. An alternative approach is to target-monitor farms suspected of treating their animals with antimicrobials. The objective of this project was to assess, using a stochastic model, the efficiency of these two sampling strategies. The model integrated data on Swiss livestock as well as expert opinion and results from studies conducted in Switzerland. Risk-based sampling showed an increase in detection efficiency of up to 100% depending on the prevalence of contaminated herds. Sensitivity analysis of this model showed the importance of the accuracy of prior assumptions for conducting risk-based sampling. The resources gained by changing from random to risk-based sampling should be transferred to improving the quality of prior information.

Atmospheric CO₂, δ(O₂/N₂) and δ13CO2 measurements at Jungfraujoch, Switzerland: results from a flask sampling intercomparison program

We present results from an intercomparison program of CO2, δ(O2/N2) and δ13CO2 measurements from atmospheric flask samples. Flask samples are collected on a bi-weekly basis at the High Altitude Research Station Jungfraujoch in Switzerland for three European laboratories: the University of Bern, Switzerland, the University of Groningen, the Netherlands and the Max Planck Institute for Biogeochemistry in Jena, Germany. Almost 4 years of measurements of CO2, δ(O2/N2) and δ13CO2 are compared in this paper to assess the measurement compatibility of the three laboratories. While the average difference for the CO2 measurements between the laboratories in Bern and Jena meets the required compatibility goal as defined by the World Meteorological Organization, the standard deviation of the average differences between all laboratories is not within the required goal. However, the obtained annual trend and seasonalities are the same within their estimated uncertainties. For δ(O2/N2) significant differences are observed between the three laboratories. The comparison for δ13CO2 yields the least compatible results and the required goals are not met between the three laboratories. Our study shows the importance of regular intercomparison exercises to identify potential biases between laboratories and the need to improve the quality of atmospheric measurements.

Screening for Rheumatic Heart Disease among Peruvian Children: A Two-Stage Sampling Observational Study.

BACKGROUND The objective of the study was to evaluate the implications of different classifications of rheumatic heart disease on estimated prevalence, and to systematically assess the importance of incidental findings from echocardiographic screening among schoolchildren in Peru. METHODS We performed a cluster randomized observational survey using portable echocardiography among schoolchildren aged 5 to 16 years from randomly selected public and private schools in Arequipa, Peru. Rheumatic heart disease was defined according to the modified World Health Organization (WHO) criteria and the World Heart Federation (WHF) criteria. FINDINGS Among 1395 eligible students from 40 classes and 20 schools, 1023 (73%) participated in the present survey. The median age of the children was 11 years (interquartile range [IQR] 8-13 years) and 50% were girls. Prevalence of possible, probable and definite rheumatic heart disease according to the modified WHO criteria amounted to 19.7/1000 children and ranged from 10.2/1000 among children 5 to 8 years of age to 39.8/1000 among children 13 to 16 years of age; the prevalence of borderline/definite rheumatic heart disease according to the WHF criteria was 3.9/1000 children. 21 children (2.1%) were found to have congenital heart disease, 8 of which were referred for percutaneous or surgical intervention. CONCLUSIONS Prevalence of RHD in Peru was considerably lower compared to endemic regions in sub-Saharan Africa, southeast Asia, and Oceania; and paralleled by a comparable number of undetected congenital heart disease. Strategies to address collateral findings from echocardiographic screening are necessary in the setup of active surveillance programs for RHD. TRIAL REGISTRATION ClinicalTrials.gov identifier: NCT02353663.