Question

A portfolio of car insurance claims has claim amounts following the distribution 7 x 3307 f(x)(330+x The number of claims from this portfolio has a Poisson distribution with a mean of 500 per year. The premium income from this portfolio is a total of £30 000 per year. The insurer has an initial surplus of £2000. (a) Find the security loading factor for this example. (b) By assuming that the aggregate claims distribution is approximately nomal what is the probability of ruin at the end of the year? (c) Explain how each of the following would affect the probability of ruin: (i) decreasing the surplus to £1000; (ii) increasing the premium income to £35 000 a year (iii) if the Poisson parameter was 550 rather than 500. [Note there is no need to recalculate the probability of ruin for each case. Just state whether the probabilit will increase / decrease/ stay the same]

Answer 1

Let n denote te Claim amourt and N denote tue foist e catculate Some the Valnes ECX num ot claims Tx330 0(330 330) x1x330 dn 336 330 330 33 0 330 04 A 86 (2A33330 C330)8 330 0

2- -330 os 260 CSS) %-42.35 Since daim numooPoontenlio ECN) S00 clains ,',即Recto, atye gate claims €(N) ECX ) 2 nsoD seity oadin 30,000 22 SDD .. nload 9,09 % 呂6300 00.20 (1105-25)2

p CLO00大Зо,000 -Total Claim10) t 105b25 i-e- Probability ruin ơ.qiy% Lappen a oon the daima 33000