Forecasting the levels of disability in the older population of England: Application of neural nets

Deep neural networks are powerful tools for modelling non-linear patterns and are very effective when the input data is homogeneous such as images and texts. In recent years, there have been attempts to apply neural nets to heterogeneous data, such as tabular and multimodal data with mixed categories. Transformation methods, specialised architectures such as hybrid models, and regularisation models are three approaches to applying neural nets to this type of data. In this study, first, we apply K-modes clustering algorithm to define different levels of disability based on responses related to mobility impairments, difficulty in performing Activities of Daily Livings (ADLs), and Instrumental Activities of Daily Livings (IADLs). We consider three cases, namely binary, 3-level, and 4-level disability. We then try Wide & Deep, TabTransformer, and TabNet models to predict these levels using socio-demographic, health, and lifestyle factors. We show that all models predict different levels of disability reasonably well with TabNet outperforming other models in the case of binary disability and in terms of 4 metrics. We also find that factors such as urinary incontinence, ever smoking, exercise, and education are important features selected by TabNet that affect disability

Risk models with capital injections

© 2016 Dr. Marjan QazviniOne of the main issues in ruin theory is that existing formulae for continuous time models can only be applied to some special claim size distributions and the analytical expressions for other claim size distributions do not exist. This thesis addresses this issue by considering discrete time models as approximations to continuous time models, including the classical risk model, the Markov-modulated risk model and the classical risk model with dividends. It also shows that how these models are affected by the introduction of capital injections. In Chapters 3 and 4 we construct a Gerber-Shiu function and use this to analyse the classical risk model with capital injections both analytically and probabilistically. Quantities such as the ultimate ruin probability and the joint density of the time of ruin and the number of claims until ruin are obtained by the inversion of the Laplace transform of our Gerber-Shiu function. In Chapter 5 we develop a discrete time model to approximate the probability of ruin in infinite and finite time under the classical risk model with capital injections, and show that capital injections can lead to a reduction in the probability of ruin even when claim amounts follow a heavy-tailed distribution. In Chapter 6 we extend our numerical algorithm from Chapter 5 to approximate the ultimate probability of ruin under a two-state Markov-modulated risk model with and without capital injections, and the density of the time of ruin under the same model with more than two states. The final chapter investigates dividend strategies with capital injections. We examine the effect of capital injections on the barrier and threshold strategies and consider a reinsurance arrangement that covers any fall below a positive pre-determined surplus level, so that the insurance company may operate indefinitely

On the validation of claims with excess zeros in liability insurance:a comparative study

In this study, we consider the problem of zero claims in a liability insurance portfolio and compare the predictability of three models. We use French motor third party liability (MTPL) insurance data, which has been used for a pricing game, and show that how the type of coverage and policyholders’ willingness to subscribe to insurance pricing, based on telematics data, affects their driving behaviour and hence their claims. Using our validation set, we then predict the number of zero claims. Our results show that although a zero-inflated Poisson (ZIP) model performs better than a Poisson regression, it can even be outperformed by logistic regression

Ruin problems in Markov-modulated risk models

Chen et al. (2014), studied a discrete semi-Markov risk model that covers existing risk models such as the compound binomial model and the compound Markov binomial model. We consider their model and build numerical algorithms that provide approximations to the probability of ultimate ruin and the probability and severity of ruin in a continuous time two-state Markov-modulated risk model. We then study the finite time ruin probability for a discrete m-state model and show how we can approximate the density of the time of ruin in a continuous time Markov-modulated model with more than two states