In this paper, we present a procedure for consistent estimation of the severity and frequency distributions based on incomplete insurance data and demonstrate that ignoring the thresholds leads to a serious underestimation of the ruin probabilities. The event frequency is modelled with a...

Property Claim Services (PCS) provides indices for losses resulting from catastrophic events in the US. In this paper we study these indices and take a closer look at distributions underlying insurance claims. Surprisingly, the lognormal distribution seems to give a better fit than the Paretian...

A typical model for insurance risk, the so-called collective risk model, has two main components: one characterizing the frequency (or incidence) of events and another describing the severity (or size or amount) of gain or loss resulting from the occurrence of an event. Here we focus on...

This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another...

Electromagnetic field (EMF) measurements have limited accuracy, which is additionally impaired by meter self-noise influence. In this paper a novel noise cancellation method is proposed, based on the Hidden Markov Model (HMM) methodology. It allows to calculate the overall field intensity with a...

This chapter develops on risk processes which, perhaps, are most suitable for computer visualization of all insurance objects. At the same time, risk processes are basic instruments for any non-life actuary – they are vital for calculating the amount of loss that an insurance company may incur.

In this paper we establish a spectral representation of any symmetric stable self-similar process in terms of multiplicative flows and cocycles. Applying the Lamperti transformation we obtain a unique decomposition of a symmetric stable self-similar process into three independent parts: mixed...

In this paper we introduce a generalization of the De Vylder approximation. Our idea is to approximate the ruin probability with the one for a different process with gamma claims, matching first four moments. We compare the two approximations studying mixture of exponentials and lognormal...

It is common practice in most insurance lines for the coverage to be restricted by a deductible. In the paper we investigate the influence of deductibles on pure risk premiums. We derive simple but practical formulae for premiums under franchise, fix amount, proportional, limited proportional...

In the article we consider accumulated values of annuities-certain with yearly payments with independent random interest rates. We focus on general annuities with payments varying in arithmetic and geometric progression which are important basic varying annuities (see Kellison, 1991). They are...