Risks2014, 2(1), 49-73; doi:10.3390/risks2010049 - published online 11 March 2014 Show/Hide Abstract
Abstract: In a bonus-malus system in car insurance, the bonus class of a customer is updated from one year to the next as a function of the current class and the number of claims in the year (assumed Poisson). Thus the sequence of classes of a customer in consecutive years forms a Markov chain, and most of the literature measures performance of the system in terms of the stationary characteristics of this Markov chain. However, the rate of convergence to stationarity may be slow in comparison to the typical sojourn time of a customer in the portfolio. We suggest an age-correction to the stationary distribution and present an extensive numerical study of its effects. An important feature of the modeling is a Bayesian view, where the Poisson rate according to which claims are generated for a customer is the outcome of a random variable specific to the customer.
Risks2014, 2(1), 25-48; doi:10.3390/risks2010025 - published online 27 February 2014 Show/Hide Abstract
Abstract: Recent crises in the financial industry have shown weaknesses in the modeling of Risk-Weighted Assets (RWAs). Relatively minor model changes may lead to substantial changes in the RWA numbers. Similar problems are encountered in the Value-at-Risk (VaR)-aggregation of risks. In this article, we highlight some of the underlying issues, both methodologically, as well as through examples. In particular, we frame this discussion in the context of two recent regulatory documents we refer to as Basel 3.5.
Risks2014, 2(1), 3-24; doi:10.3390/risks2010003 - published online 21 February 2014 Show/Hide Abstract
Abstract: Shot-noise processes generalize compound Poisson processes in the following way: a jump (the shot) is followed by a decline (noise). This constitutes a useful model for insurance claims in many circumstances; claims due to natural disasters or self-exciting processes exhibit similar features. We give a general account of shot-noise processes with time-inhomogeneous drivers inspired by recent results in credit risk. Moreover, we derive a number of useful results for modeling and pricing with shot-noise processes. Besides this, we obtain some highly tractable examples and constitute a useful modeling tool for dynamic claims processes. The results can in particular be used for pricing Catastrophe Bonds (CAT bonds), a traded risk-linked security. Additionally, current results regarding the estimation of shot-noise processes are reviewed.
Risks2014, 2(1), 1-2; doi:10.3390/risks2010001 - published online 21 February 2014 Show/Hide Abstract
Abstract: “What is complicated is not necessarily insightful and what is insightful is not necessarily complicated: Risks welcomes simple manuscripts that contribute with insight, outlook, understanding and overview”—a quote from the first editorial of this journal . Good articles are not characterized by their level of complication but by their level of imagination, innovation, and power of penetration. Creativity sessions and innovative tasks are most elegant and powerful when they are delicately simple. This is why the articles you most remember are not the complicated ones that you struggled to digest, but the simpler ones you enjoyed swallowing.
Risks2013, 1(3), 192-212; doi:10.3390/risks1030192 - published online 13 December 2013 Show/Hide Abstract
Abstract: This paper is concerned with an insurance risk model whose claim process is described by a Lévy subordinator process. Lévy-type risk models have been the object of much research in recent years. Our purpose is to present, in the case of a subordinator, a simple and direct method for determining the finite time (and ultimate) ruin probabilities, the distribution of the ruin severity, the reserves prior to ruin, and the Laplace transform of the ruin time. Interestingly, the usual net profit condition will be essentially relaxed. Most results generalize those known for the compound Poisson claim process.
Risks2013, 1(3), 176-191; doi:10.3390/risks1030176 - published online 12 December 2013 Show/Hide Abstract
Abstract: We study a new risk measure inspired from risk theory with a heat wave risk analysis motivation. We show that this risk measure and its sensitivities can be computed in practice for relevant temperature stochastic processes. This is in particular useful for measuring the potential impact of climate change on heat wave risk. Numerical illustrations are given.