Question $2(16$ marks$)$

a$.$ For the current underwriting year, RSE Insurance Group has a maximum gross retention of $$30,000,000$ and a $50\%$ quota share treaty. Apart from that, RSE Insurance has a $7-$ line first surplus treaty on gross retention.

Upon renewal of its reinsurance programme, RSE Insurance has decided to increase its net retention by $60\%$ and decrease the quota share cession to $30\%.$ Further, RSE Insurance will increase the surplus treaty capacity to $10$ lines.

Suppose the renewal terms for all the reinsurance arrangements are confirmed, determine the maximum amount that RSE Insurance can accept in the next underwriting year after renewal. Show all your calculations.

$8$ marks

b$.$ Sun Insurance Group, in California, US$,$ decided to issue some US dollardenominated catastrophe bonds as a risk financing device on top of the reinsurance arrangement.

The newly issued catastrophe bonds, with a face value of US $$300,000$ will provide a coupon rate of $12$ percent and have a $10$ years to maturity.

The bond contract specifies that if an earthquake registering between $6\mathrm{.}5$ and $8$ on the Richter scale occurs in in any one vear, only $60$ percent of the annual coupon interest will be paid; If an earthquake exceeding $8$ on the Richter scale occurs, no coupon interest is payable.

Assume the scientists estimate that the probability of a $6\mathrm{.}5$ to $8$ earthquake happening in California in any one year is $35$ percent and the probability of an earthquake exceeding $8$ is $5$ percent in any one given year. It is further assumed that the annual probabilities are independent.

What is the most an investor would be willing to pay for one of these newly issued catastrophe bonds if the required rate of return is $18\%?$

$8$ marks