It's Actuarial Science

A pension scheme only allows retirement at exact age 65 An investigation of the mortality of the retired members of the scheme was carried out over the period 1 January 2005 to 31 December 2010 The following data were obtained - : | | | Member Date of retirement Date of death (if occurred during the investigation period) 1 01/04/2002 30/04/2009 2 01/08/2004 3 01/02/2005 4 01/06/2006 31/08/2008 5 01/08/2006 31/12/2010 6 01/03/2008 7 01/05/2008 30/11/2010 8 01/01/2009 All months should be assumed to be of equal length. (i) (ii) (iii ) Explain the form or forms of censoring that are present in these data and in this observational plan. (2 marks) Calculate the Kaplan-Meier (product-limit) estimate of the survival function S65(t) from these data, stating clearly any additional assumptions that you make. (10 marks) Estimate the force of transition from alive to dead for a two-state Markov model for age 67 last birthday, using the data given. The exposed to risk should be calculated exactly. State all assumptions required, and state the age to which the estimate would be assumed to apply. (7 marks)