Generalised Fractional Evolution Equations of Caputo Type

This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the solutions. These results encompass known linear and non-linear equations from classical fractional partial differential equations such as the time-space-fractional diffusion equation, as well as their far reaching extensions. \\ Meaning is given to a probabilistic generalisation of Mittag-Leffler functions.Comment: To be published in 'Chaos, Solitons & Fractals

Testing for Adverse Selection into Private Medical Insurance

We develop a test for adverse selection and use it to examine privatehealth insurance markets. In contrast to earlier papers that consider apurely private system or a system in which private insurance supplementsa public system, we focus our attention on a system where privately fundedhealth care is substitutive of the publicly funded one. Using a model ofcompetition among insurers, we generate predictions about the correlationbetween risk and the probability of taking private insurance under bothsymmetric information and adverse selection. These predictions constitutethe basis for our adverse selection test. The theoretical model is also usefulto conclude that the setting that we focus on is especially attractive to testfor adverse selection. Using the British Household Panel Survey, we findevidence that adverse selection is present in this market. We develop a test for adverse selection and use it to examine privatehealth insurance markets. In contrast to earlier papers that consider apurely private system or a system in which private insurance supplementsa public system, we focus our attention on a system where privately fundedhealth care is substitutive of the publicly funded one. Using a model ofcompetition among insurers, we generate predictions about the correlationbetween risk and the probability of taking private insurance under bothsymmetric information and adverse selection. These predictions constitutethe basis for our adverse selection test. The theoretical model is also usefulto conclude that the setting that we focus on is especially attractive to testfor adverse selection. Using the British Household Panel Survey, we find evidence that adverse selection is present in this market