ST301 TIMED COURSEWORK 2022
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ST301 TIMED COURSEWORK 2022
For calculations you will need a standard force of mortality
uⅩ = 0 .0005 + 0 .00007585775 * exp(0 .08749823Ⅹ) ﹒
a force of sickness
σⅩ = 0 .1 + 
and a force of recovery
pⅩ = 
An R script with these functions will be provided .
1. Consider a health-sickness Markov model . The sickness rate is σⅩ , the recovery rate is pⅩ , the mortality rate for a healthy life is 0 .95uⅩ and the mortality rate for a sick life is 2uⅩ . An office is issuing a policy under which a continuous sickness benefit at a rate of 20000 per annum payable while the life is sick is provided . The life is now 30 years old . The policy is financed by a continuous premium at a rate T per annum payable while the life is healthy but has been sick before and 0 .5T per annum while the life is healthy and has not been before (50% no claims discount) . The policy duration is 30 years and initially the life is healthy and has not been sick before . The force of interest to be used for calculations is 0.04.
(a) Calculate the expected present value of the benefit . [10]
(b) Calculate T using a force of interest. [15]
(c) Suppose now that the premium is not payable continuously but annually in advance . Calculate the revised premium [15]
(d) Suppose now that the continuous income benefit is replaced bu a lump sum . An amount b is payable to the policyholder the first time she falls sick and an amount 2b at all subsequent times . Calculate b so that all your previous answers are the same . [20]
2. A with profits pension policy purchased by a 30 year old provides a con- tinuous income of 30000 per annum commencing at age 65 . The policy is financed by a continuous premium till that time . The office that is- sued the policy calculates the premium and reserves using a first order basis consisting of a force of interest of 0 .01 per annum and a force of mortality 0 .9uⅩ .
(a) Calculate he premium . [10]
(b) All surplus emerging during the first 35 year will be rolled over and
paid as a bonus lump sum when the policyholder retires at the age of 65 . Using a second order basis consisting of a force of interest of 0 .02 per annum and a force of mortality of uⅩ , provide a prediction for the bonus lumps sum . [15]
(c) After retirement any surplus that emerges is paid to the policy holder as continuous extra income . Using the same send order basis as in part (b) provide predictions for the rate this income is paid at the start of each of the first 10 year of retirement . [15]
2023-01-05