Epidemic models in Life insurance

Specialeforsvar: Amalie Riff Brems

Titel:  Epidemic models in Life insurance
Comparison of individual based and population based models of both SIS and SIR structure.

Abstract: The standard way of modelling reserve requirements for life insurances assumes independence among individuals. This assumption does not hold for epidemics, as the infection is transmitted from one individual to another. The epidemic is assumed to have either the SIS or SIR-structure. In this paper, the individual based as well as the population based Markov models are introduced. The in-state probabilities in the individual based models are derived and compared to the amount of individuals in each state in the population based models. These results for the population based models are derived in this paper. For the population based SIS model, it is shown that an underlying deterministic compartment model in the limit
is necessary for the population based SIS model and individual based SIS model to have equivalent shares. For the population based SIR model, the assumptions of asymptotic independence or an underlying deterministic structure for the compartment model are necessary, for the population based SIR model and individual based SIR model to be equivalent. Through numerical examples, these assumptions are shown to be sufficient for the population based models and individual based models to be the same. Furthermore, the numerical examples are used to illustrate the di↵erent reserve requirements in the individual based and
population based models. The reserve in the population based model depends on the population size. Through the numerical example, it is shown that for a population of N = 500, the premium in the individual based model is up to 30% lower than the premium in the population based model. Furthermore, the standard deviation of future payments in the individual based model, is approximately equal to the reserves, indicating great uncertainty. The standard way of calculating reserves and premiums in life insurance is then not enough to cover epidemics.

Vejleder: Mogens Steffensen
Censor:    Jingyu She