On the Optimal Stochastic Control of Dividend and Penalty Payments in an Insurance Company

In this thesis we consider the surplus of a non-life insurance company and assume that it follows either the classical Cramér-Lundberg model or its diffusion approximation. That is, we consider a continuous time model, where premiums are cashed at a constant rate and claims occur randomly with random sizes modelled by a compound Poisson process. In actuarial mathematics the risk of an insurance company is traditionally measured by the probability of ruin, where the time of ruin is defined as the first time when the surplus becomes negative. Using the ruin probability as a risk measure has been criticised because it is unrealistic to assume that an insurance company is ruined as soon as the surplus becomes negative. In this thesis, we assume that the insurer is not ruined although the surplus becomes negative. In order to avoid ruin, penalty payments occur, depending on the level of the surplus. For example, penalty payments occur if the insurance company needs to borrow money. In the first part of this thesis we consider the diffusion approximation to the Cramér-Lundberg model and we aim to determine a dividend strategy that maximises the difference between the expected discounted dividend and penalty payments, where penalty payments are either modelled by an exponential, linear or quadratic function. We show that the optimal strategy is a so-called barrier strategy and calculate the optimal barrier. The second part studies the analogous problem where the surplus process of an insurance company is given by a Cramér-Lundberg model. Here, similar results are obtained. In conclusion, we consider the problem where we have to determine an optimal investment and reinsurance strategy and the surplus follows the diffusion approximation. The insurance company can invest in several risky assets and reduce the insurance risk either by excess of loss or proportional reinsurance. The aim is to find a strategy which minimises the penalty payments that are necessary to avoid ruin. Various penalty functions are considered and closed form solutions are derived

Cross-sectional associations between air pollution and chronic bronchitis: an ESCAPE meta-analysis across five cohorts

BACKGROUND: This study aimed to assess associations of outdoor air pollution on prevalence of chronic bronchitis symptoms in adults in five cohort studies (Asthma-E3N, ECRHS, NSHD, SALIA, SAPALDIA) participating in the European Study of Cohorts for Air Pollution Effects (ESCAPE) project. METHODS: Annual average particulate matter (PM10, PM2.5, PMabsorbance, PMcoarse), NO2, nitrogen oxides (NOx) and road traffic measures modelled from ESCAPE measurement campaigns 2008-2011 were assigned to home address at most recent assessments (1998-2011). Symptoms examined were chronic bronchitis (cough and phlegm for ≥3 months of the year for ≥2 years), chronic cough (with/without phlegm) and chronic phlegm (with/without cough). Cohort-specific cross-sectional multivariable logistic regression analyses were conducted using common confounder sets (age, sex, smoking, interview season, education), followed by meta-analysis. RESULTS: 15 279 and 10 537 participants respectively were included in the main NO2 and PM analyses at assessments in 1998-2011. Overall, there were no statistically significant associations with any air pollutant or traffic exposure. Sensitivity analyses including in asthmatics only, females only or using back-extrapolated NO2 and PM10 for assessments in 1985-2002 (ECRHS, NSHD, SALIA, SAPALDIA) did not alter conclusions. In never-smokers, all associations were positive, but reached statistical significance only for chronic phlegm with PMcoarse OR 1.31 (1.05 to 1.64) per 5 µg/m(3) increase and PM10 with similar effect size. Sensitivity analyses of older cohorts showed increased risk of chronic cough with PM2.5abs (black carbon) exposures. CONCLUSIONS: Results do not show consistent associations between chronic bronchitis symptoms and current traffic-related air pollution in adult European populations

The Skin Ivory Spot. A Possible Indicator for Skinfield Photo-Carcinogenesis in Recreational Sunbed Addicts

Introduction: For a decade or so, artificial sources of restricted light wavelengths, particularly sunbeds, have progressively gained popularity among adolescents and young adults. Warnings were raised focusing on the risk of accelerated photoaging and photocarcinogenesis. The ULEV (ultraviolet light-enhanced visualization) method is a convenient noninvasive way identifying subtle pigmentary changes presenting as a mottled subclinical melanoderma (MSM). Of note, rare spotty amelanotic macules presenting as skin ivory spots (SIS) was reported on any part of the body. Subjects and method: This work is the first attempt at evaluating the changes in the MSM and SIS spots developed on the skin of 33 phototype III young women designated as avid users involved in frequent exposures to sunshine and sunbeds for lifestyle purposes for a duration of at least 120 months. Results: MSM was markedly heterogeneous and was distinctly obvious in the majority of adepts of frequent natural and artificial photoexposures. SIS was particularly developed in subjects presenting with severe MSM patterns. Discussion: MSM and SIS are more severe in subjects frequently exposed to sunbeds and sun exposures. These signs possibly represent a risk marker for field photocarcinogenesis

Constitutive modelling of skin ageing

The objective of this chapter is to review the main biomechanical and structural aspects associated with both intrinsic and extrinsic skin ageing, and to present potential research avenues to account for these effects in mathematical and computational models of the skin. This will be illustrated through recent work of the authors which provides a basis to those interested in developing mechanistic constitutive models capturing the mechanobiology of skin across the life course