Description: This paper introduces a rich stochastic modeling framework for understanding risks in multiple-decrement contracts. The example in the paper is a 20-year Term insurance contract. Not only are mortality and lapsation considered stochastic, but the parameters governing them are. For example, mortality risk is composed of four risk elements, including error generated in the underwriting process, volatility around the best estimate, catastrophic events that impact mortality, and the trend in mortality improvement or deterioration. When stochastically modeled, the relative contribution and risk profile of each risk element can be evaluated. Generating stochastic mortality results provides a distribution of results that an organization faces and the severity and incidence of the tail events.

Description: The article explores impact of resetting cap vs static cap choice for the GLWB rider for a Fixed Index Annuity for a Point to Point. Moreover, analysis of a Monthly Sum Cap is provided showing impacts of particular choices of market models (e.g. Black, Heston, Bates) used to price this deal.

Description: The series expansion of a probability density function, known to actuaries by Esscher's name and to statisticians as the saddlepoint approximation, typically gets integrated to approximate probability values under the density, with a location parameter in the expansion chosen to optimize convergence of the integrated series. We review the general form, the accuracy and the derivation of the Esscher approximation. Then we propose using related series expansions for the derivative of a probability density function to approximate the value of the point of maximum likelihood for the density. The key is to make the value of the location parameter an unknown and assume it to be the point of maximum likelihood, which leads to a tractable optimization problem to find its value.