Macroeconomics questions 1

Express in the form of symbols, and also explain in words, the expressions "death

strain at risk", "expected death strain" and "actual death strain".

(ii) On 1 January 2001 an office issued a number of annual premium policies to a

group of lives, each of whom was then aged exactly 45. All policies were for a

term of 20 years and were of the following types:

? endowment assurances under which the sum assured was payable on

survival to the end of the term or at the end of the year of earlier death

? temporary assurances under which the sum assured was payable only at

the end of the year of death within the policy term

? pure endowments under which the only benefit payable is the sum

assured on survival to the end of the policy term

Assuming that there is no source of decrement other than death, calculate the

profit or loss from mortality for the calendar year 2010 in respect of the policies

issued to this group of lives, given the following information:

Type of policy Sums assured in force Sums assured

on 1 January 2010 by death during 2010 discontinued

Endowment assurance 600,000 4,000

Temporary assurance 200,000 2,000

Pure endowment 80,000 500

Reserving basis: AM92 Ultimate mortality, 4% pa interest. Ignore expenses

An insurance company prices its sickness contracts using the three-state model and transition intensities shown below: 0.05 A = Able S = Sick 0.03 0.02 0.04 D = Dead Level premiums of 2,500 pa are payable continuously while the policyholder is in the able state. An able life aged 50 takes out a 15-year sickness contract that provides a 'no claim' benefit equal to 50% of the total premiums paid (without interest) if the life remains able for the full duration of the contract. Calculate the expected present value of this 'no claim' benefit at outset, assuming that the force of interest is 6% pa. [3] (i) Explain what is meant by a dependent probability of decrement and by an independent probability of decrement. (ii) The following is an extract from a multiple decrement table subject to 3 modes of decrement, a, B and y : Age, X (al)x (ad) (ad ) (ad)x 50 5,000 86 52 14 51 4,848 80 56 20 (a) Calculate the probability that a 50-year-old leaves the population through decrement y between the ages of 51 and 52. (b) Assuming that forces of decrement are constant between integer ages, calculate the independent probabilities q50 and 1950 - A multiple decrement model involves three decrements a, b and c . Decrements a and b occur continuously over the year of age (x, x+1) , but decrement c occurs only at age x + 14 . Also: the forces of decrement due to causes a and b are constant over the year of age (x, x +1) and are equal to 0.03 and 0.01 per annum respectively the probability of decrement by cause c at exact age x +14 is 0.06. Calculate the value of (aq)x . [6]