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...

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...

This paper is intended as a guide to statistical inference for loss distributions. There are three basic approaches to deriving the loss distribution in an insurance risk model: empirical, analytical, and moment based. The empirical method is based on a sufficiently smooth and accurate estimate...

This paper is intended as a guide to simulation of risk processes. 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 describing the...

An important issue in fitting stochastic models to electricity spot prices is the estimation of a component to deal with trends and seasonality in the data. Unfortunately, estimation routines for the long-term and short-term seasonal pattern are usually quite sensitive to extreme observations,...

We calibrate Markov regime-switching (MRS) models to mean daily spot prices from the EEX market. Our empirical study shows that (i) models with shifted spike regime distributions lead to more realistic models of electricity spot prices and that (ii) introducing heteroskedasticity in the base...

In this paper we propose a new goodness-of-fit testing scheme for the marginal distribution of regime-switching models. We consider models with an observable (like threshold autoregressions), as well as, a latent state process (like Markov regime-switching). The test is based on the...

We calibrate Markov regime-switching (MRS) models to spot (log-)prices from two major power markets. We show that while the price-capped (or truncated) spike distributions do not give any advantage over the standard specification in case of moderately spiky markets (such as NEPOOL), they improve...

One of the most profound features of electricity spot prices are the price spikes. Markov regime-switching (MRS) models seem to be a natural candidate for modeling this spiky behavior. However, in the studies published so far, the goodness-of-fit of the proposed models has not been a major...

In this paper we propose a novel goodness-of-fit testing scheme for regime-switching models. We consider models with an observable, as well as, a latent state process. The test is based on the Kolmogorov-Smirnov supremum-distance statistic and the concept of the weighted empirical distribution...