The present work complements the recent paper by Barz and Müller (2012). Specically, upper and lower bounds are derived for the force of mortality when one-year death probabilities are given, assuming a monotonic or convex shape. Based on these bounds, worst-case scenarios are derived depending on the mix of benets in case of survival and of death comprised in a specic insurance policy.
Christiansen, M., & Denuit, M. (2012). Worst-case actuarial calculations consistent with single- and multiple-decrement life tables (ISBA Discussion Paper 2012/27). https://hdl.handle.net/2078.5/204757