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In the context of the Sars-CoV-2 virus pandemic, this paper deals with the analytical framework that involves a stochastic model to describe the probability of contagion and, therefore, of its outcome for a subject; subsequently, an actuarial model for an insurance policy against the risk of contracting the virus is proposed and the quantification of the related premium. It is assumed that the insurance coverage lasts for one year and that during the coverage it could happen the infection. The theoretical distribution of the contagion probability is of geometric type, in which every coverage day is a Bernoulli distribution of infection event. Four outcomes of the infection are considered below: hospitalization in home isolation, in hospital Medic Area, in intensive care and, finally, death. The Gamma distribution is taken into account as the theoretical distribution of number of days for each trajectory of recovery regarding the outcome of the infection, whereas for the outcome of death a lump-sum payment is defined to be paid as a single solution. A payment variable will be obtained whose mathematical expectation is the expected value of the expected benefits, assuming that in the event of death it remains the capital value. For each day of coverage, the expected payment is calculated and then weighted by the probability of infection on that given day; then, the expected payment is discounted to the effective date of coverage and, finally, it is calculated the fair premium of the policy. For this paper it is used the software R for statistical evaluation |
