BUS3024 Tutorial 4 2019 Solutions.pdf (1,6 MB)

Hi guys

How was the column for the Expected Death cost calculated.

Thank you.

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BUS3024 Tutorial 4 2019 Solutions.pdf (1,6 MB)

Hi guys

How was the column for the Expected Death cost calculated.

Thank you.

0 votes

Hi, I haven't seen the memo for this question but I assume the expected death cost for this question would be in the projection of the cashflows of the non-unit fund.

The sum at risk to the insurer is the difference between the fund value and the guaranteed minimum benefit. If, for example, the fund value is 4000 at time 1, then there is 1000 at risk to the insurer (Since the guaranteed minimum benefit is 5000 so 5000-4000). This is because if the policyholder dies with a unit value of 4000 then the insurer has to reach into their own pocket (the non-unit fund) to make up the shortfall of 1000 rand. Hence the expected death cost would be \(1000q_{60}\). In general, the expected death cost for year \(t\) for this question would be \(q_{60+t-1}\times max(0,5000-F_t)\) where \(F_t\) is the fund value which must be projected separately.

The sum at risk to the insurer is the difference between the fund value and the guaranteed minimum benefit. If, for example, the fund value is 4000 at time 1, then there is 1000 at risk to the insurer (Since the guaranteed minimum benefit is 5000 so 5000-4000). This is because if the policyholder dies with a unit value of 4000 then the insurer has to reach into their own pocket (the non-unit fund) to make up the shortfall of 1000 rand. Hence the expected death cost would be \(1000q_{60}\). In general, the expected death cost for year \(t\) for this question would be \(q_{60+t-1}\times max(0,5000-F_t)\) where \(F_t\) is the fund value which must be projected separately.