Stochastic Modelling of Life Insurance Reserving Process: Assessing Ruin Probability and Adjustment Factors

The paper introduces a comprehensive stochastic model for the reserving process and the corresponding probability of ruin for a life insurance policy or, equivalently, for a portfolio of life policies. Within this framework, a discounted surplus process is established using a general probability space equipped with the natural filtration of past events and a suitable probability measure. Subsequently, it is demonstrated that the surplus process behaves as a submartingale and explores its impact on the probability of ruin, along with the inherent trade-off between the initial expense level and the adjustment factor applied to the net reserves of the life policy. Finally, a thorough numerical analysis is conducted focusing on a whole life insurance policy. In this specific case, a comprehensive range of values for the adjustment factor necessary to uphold the desired probability of ruin is ascertained, considering the corresponding values of the initial expense level.