Further developments in the Erlang(n) risk process

For actuarial aplications, we consider the Sparre–Andersen risk model when the interclaim times are Erlang(n) distributed. We first address the problem of solving an integro-differential equation that is satisfied by the survival probability and other probabilities, and show an alternative and improved method to solve such equations to that presented by Li (2008). This is done by considering the roots with positive real parts of the generalized Lundberg’s equation, and establishing a one–one relation between them and the solutions of the integro-differential equation mentioned before. Afterwards, we apply our findings above in the computation of the distribution of the maximum severity of ruin. This computation depends on the non-ruin probability and on the roots of the fundamental Lundberg’s equation. We illustrate and give explicit formulae for Erlang(3) interclaim arrivals with exponentially distributed single claim amounts and Erlang(2) interclaim times with Erlang(2) claim amounts. Finally, considering an interest force, we consider the problem of calculating the expected discounted dividends prior to ruin, finding an integro-differential equation that they satisfy and solving it. Numerical examples are also provided for illustrationinfo:eu-repo/semantics/publishedVersio

Ruin problems in the generalized Erlang (n) risk model

For actuarial applications we consider the Sparre–Andersen risk model when the interclaim times are Generalized Erlang(n) distributed. Unlike the standard Erlang(n) case, the roots of the generalized Lundberg’s equation with positive real parts can be multiple. This has a significant impact in the formulae for ruin probabilities that have to be found. We start by addressing the problem of solving an integro–differential equation that is satisfied by the survival probability, as well as other probabilities related, and present a method to solve such equation. This is done by considering the roots with positive real parts of the generalized Lundberg’s equation, and then establishing a one-one relation between them and the solutions of the integro–differential equation mentioned above. We first study the cases when all the roots are single and when there are roots with higher multiplicity. Secondly, we show that it is possible to have double roots but no higher multiplicity. Also, we show that the number of double roots depend on the choice of the parameters of the generalized Erlang(n) distribution, with a maximum number depending on n being even or odd. Afterwards, we extend our findings above for the computation of the distribution of the maximum severity of ruin as well as, considering an interest force, to the study the expected discounted future dividends, prior to ruin. Our findings show an alternative and more general method to the one provided by Albrecher et al. (2005), by considering a general claim amount distributioninfo:eu-repo/semantics/publishedVersio

Further developments in the Erlang(n) risk process

For actuarial aplications, we consider the Sparre–Andersen risk model when the interclaim times are Erlang(n) distributed. We first address the problem of solving an integro-differential equation that is satisfied by the survival probability and other probabilities, and show an alternative and improved method to solve such equations to that presented by Li (2008). This is done by considering the roots with positive real parts of the generalized Lundberg’s equation, and establishing a one–one relation between them and the solutions of the integro-differential equation mentioned before. Afterwards, we apply our findings above in the computation of the distribution of the maximum severity of ruin. This computation depends on the non-ruin probability and on the roots of the fundamental Lundberg’s equation. We illustrate and give explicit formulae for Erlang(3) interclaim arrivals with exponentially distributed single claim amounts and Erlang(2) interclaim times with Erlang(2) claim amounts. Finally, considering an interest force, we consider the problem of calculating the expected discounted dividends prior to ruin, finding an integro-differential equation that they satisfy and solving it. Numerical examples are also provided for illustration

Cyber risk : an analysis of self-protection and the prediction of claims

For a set of Brazilian companies, we study the occurrence of cyber risk claims by analyzing the impact of self protection and the prediction of their occurrence. We bring a new perspective to the study of cyber risk analyzing the probabilities of acquiring protection against this type of risk by using propensity scores. We consider the problem of whether acquiring cyber protection improves network security using a matching method that allows a fair comparison among companies with similar characteristics. Our analysis, assisted with Brazilian data, shows that despite informal arguments that favor self-protection against cyber risks as a tool to improve network security, we observed that in the presence of self-protection against cyber risks, the incidence of claims is higher than if there were no protection. Regarding the prediction of the occurrence of a claim, a system considering a feedforward multilayer perceptron neural network was created, and its performance was measured. Our results show that, when applied to the relevant information of the companies under study, it presents a very good performance, reaching an eciency in general classication above 85%. The fact is that the use of neural networks can be quite opportune to help in solving the problem presented.info:eu-repo/semantics/publishedVersio

On dividends in the phase–type dual risk model

The dual risk model assumes that the surplus of a company decreases at a constant rate over time, and grows by means of upward jumps which occur at random times with random sizes. In the present work, we study the dual risk renewal model when the waiting times are phasetype distributed. Using the roots of the fundamental and the generalized Lundberg’s equations, we get expressions for the ruin probability and the Laplace transform of the time of ruin for an arbitrary single gain distribution. Then, we address the calculation of expected discounted future dividends particularly when the individual common gains follow a phase-type distribution. We further show that the optimal dividend barrier does not depend on the initial reserve. As far as the roots of the Lundberg equations and the time of ruin are concerned, we address the existing formulae in the corresponding Sparre-Andersen insurance risk model for the first hitting time, and we generalize them to cover also the situations where we have multiple roots. We do that working a new approach and technique, approach we also use for working the dividends, unlike others, it can be also applied for every situationinfo:eu-repo/semantics/publishedVersio

The Cramér-Lundberg and the dual risk models : ruin dividend problems and duality features

In the present paper we study some existing duality features between two very known models in Risk Theory. The classical Cramér–Lundberg risk model with application to insurance, and the dual risk model with (some) financial application. For simplicity the former will be referred as the primal model. The former has been of extensive treatment in the literature, it assumes that a given surplus process has constant deterministic gains (premiums) and random loses (claims) that come at random times. On the other hand, the latter, called as dual model, works in opposite direction, losses (costs) are constant and deterministic, and the gains (earnings) are random and come at random times. Sometimes this one is called the negative model. Similar quantities, with similar mathematical properties, work in opposite direction and have different meanings. There is however an important feature that makes the two models quite distinct, either in their application or in their nature: the loading condition, positive or negative, respectively. The primal model has been worked extensively and focuses essentially in ruin problems (in many different aspects) whereas the dual model has developed more recently and focuses on dividend payments. I most cases, they have been worked apart, however they have connection points that allow us to use methods and results from one to another. basically form the first to the second. Identifying the right connection, or duality, is crucial so that we transport methods and results. In the work by Afonso et al. (2013) this connection is first addressed in the case when the times between claims/gains follow an exponential distribution. We can easily understand that the ruin time in the primal has a correspondence to the dividend time in the latter. On the opposite side the time to hit an upper barrier in the primal model has a correspondence to the time to ruin in the dual model. Another interesting feature is the severity of ruin in the former and the size of the dividend payment in the latter.info:eu-repo/semantics/publishedVersio

Application of the penalty coupling method for the analysis of blood vessels

Due to the significant health and economic impact of blood vessel diseases on modern society, its analysis is becoming of increasing importance for the medical sciences. The complexity of the vascular system, its dynamics and material characteristics all make it an ideal candidate for analysis through fluid structure interaction (FSI) simulations. FSI is a relatively new approach in numerical analysis and enables the multi-physical analysis of problems, yielding a higher accuracy of results than could be possible when using a single physics code to analyse the same category of problems. This paper introduces the concepts behind the Arbitrary Lagrangian Eulerian (ALE) formulation using the penalty coupling method. It moves on to present a validation case and compares it to available simulation results from the literature using a different FSI method. Results were found to correspond well to the comparison case as well as basic theory

Electroactive biofilms: new means for electrochemistry

This work demonstrates that electrochemical reactions can be catalysed by the natural biofilms that form on electrode surfaces dipping into drinking water or compost. In drinking water, oxygen reduction was monitored with stainless steel ultra-microelectrodes under constant potential electrolysis at )0.30 V/SCE for 13 days. 16 independent experiments were conducted in drinking water, either pure or with the addition of acetate or dextrose. In most cases, the current increased and reached 1.5–9.5 times the initial current. The current increase was attributed to biofilm forming on the electrode in a similar way to that has been observed in seawater. Epifluorescence microscopy showed that the bacteria size and the biofilm morphology depended on the nutrients added, but no quantitative correlation between biofilm morphology and current was established. In compost, the oxidation process was investigated using a titanium based electrode under constant polarisation in the range 0.10–0.70 V/SCE. It was demonstrated that the indigenous micro-organisms were responsible for the current increase observed after a few days, up to 60 mA m)2. Adding 10 mM acetate to the compost amplified the current density to 145 mA m)2 at 0.50 V/SCE. The study suggests that many natural environments, other than marine sediments, waste waters and seawaters that have been predominantly investigated until now, may be able to produce electrochemically active biofilm

Ruin and dividend measures in the renewal dual risk model

In this manuscript we consider the dual risk model with financial application, where the random gains occur under a renewal process. We particularly work the Erlang(n) case for common distribution of the inter-arrival times, from there it is easy to understand that our method or procedures can be generalised to other cases under the matrix-exponential family case. We work several and different problems involving future dividends and ruin. We also show that our results are valid even if the usual income condition is not satisfied. In most known works under the dual model, the main target under study have been the calculation of expected discounted future dividends and optimal strategies, where the dividend calculation have been done on aggregate. We can find works, at first using the classical compound Poisson model, then some examples of other renewal Erlang models. Knowing that ruin is ultimately achieved, we find important that dividends should be evaluated on an individual basis, where the early dividend contribution for the aggregate are of utmost importance. From our calculations we can really see how much important is the contribution of the first dividend. Afonso et al. (Insur Math Econ, 53(3), 906–918, 2013) had worked similar problems for the classical compound Poisson dual model. Besides that we find explicit formulae for both the probability of getting a dividend and the distribution of the amount of a single dividend. We still work the probability distribution of the number of gains to reach a given upper target (like a constant dividend barrier) as well as for the number of gains down to ruin. We complete the study working some illustrative numerical examples that show final numbers for the several problems under study.info:eu-repo/semantics/publishedVersio

ADN forense: problemas éticos y jurídicos

Coordinació: María Casado y Margarita GuillénLos análisis genéticos afectan a derechos fundamentales, por lo que el uso de esta información debe estar supeditado a vías de control democrático. En la actualidad, la lucha contra grandes delitos, como por ejemplo el terrorismo, aparentemente legitima a invadir derechos antes considerados intangibles. La presente obra, fruto del trabajo multidisciplinar llevado a cabo por juristas, filósofos, biólogos, técnicos y médicos, tiene por objetivo poner de manifiesto cuáles son los problemas ético-jurídicos derivados de la obtención, el análisis y el almacenamiento del ADN, así como sus usos judiciales y extrajudiciales. Ante el difícil equilibrio entre libertad individual y seguridad colectiva, este libro ayuda a comprender los conflictos que subyacen en el manejo de una herramienta informativa tan poderosa como son las muestras y los perfiles del ADN