RESUMEN
This article provides an overview of all papers published on the special issue, Advances in Actuarial Science and Quantitative Finance. The special issue is intended to collect articles that reflect the latest development and emerging topics in these closely related two areas. Topics included in this special issue range from actuarial and risk theory, to optimal control for finance and insurance, to statistical inferences of financial and insurance models, to pricing, valuation and reserving.
RESUMEN
The paper deals with the problem of possible ruin when providing insurance coverage for an epidemic. The model studied is an SIS type epidemic which generalizes the well-known logistic model. Contractually, the premiums are paid by susceptible people while the care costs are reimbursed to infected people via an annuity or a lump-sum benefit. Our goal is to determine the distribution of the main statistics of the ruin when it occurs during the epidemic. The case where the reserve alternates between normal and epidemic episodes is also discussed using a Brownian modeling of the reserve. Finally, some of the results are illustrated for two particular SIS epidemic models.
RESUMEN
Motivated by modelling epidemics like COVID-19, this paper proposes a generalized chain binomial process which integrates two types of infectives, those with symptoms and those without. Testing of infectives and vaccination of susceptibles are then incorporated as preventive protective measures. Our interest relates to the distribution of the state of the population at the end of infection and to the reproduction number [Formula: see text] with the associated extinction condition. The method uses the construction of a family of martingales and a branching approximation for large populations, respectively. A more general branching process for epidemics is also constructed and studied. Finally, some results obtained are illustrated by numerical examples.