This paper studies the approximation of extreme quantiles of random sums of heavy-tailed random variables, or more specifically, subexponential random variables. A key application of this approximation is the calculation of operational VaR (value at risk) for financial institutions, to determine...

1 Introduction and summary -- 2 Basic concepts of reliability analysis -- 2.1 Mission profile, reliability block diagram -- 2.2 Failure rate -- 2.3 Reliability function, MTTF, MTBF -- 2.4 More general considerations on the concept of redundancy -- 2.5 Failure mode analysis and other reliability...

We discuss efficiency of the quadratic bridge volatility estimator in comparison with Parkinson, Garman-Klass and Roger-Satchell estimators. It is shown in particular that point and interval estimations of volatility, resting on bridge estimator, are considerably more efficient than analogous...

In this paper we apply the idea of the WKB method to derive an effective single lognormal approximation for the probability distribution of the sum of two correlated lognormal variables. An approximate probability distribution of the sum is determined in closed form, and illustrative numerical...