Economics;

A general insurance company writes professional indemnity insurance for solicitors on a losses-occurring basis. The company insures a large law firm whose policy is due for renewal soon. The following data has been provided: Policy Notified Policy Excess Limit per Claim Year Claims (EQQ0) (EOOO) 2008 764 50 150 2009 638 50 150 2010 318 25 100 2011 402 25 100 2012 140 25 100 2013 See below 50 100 Calendar Average Number of Year Solicitors in Year 2008 210 2009 208 2010 215 2011 214 2012 210 2013 213 The following information has been supplied for the data above: All policy years run from 1 July to 30 June. There is no aggregate limit on the total amount of claims in a policy year. Notified claims are as at 31 March 2013. The following assumptions apply: Claims severity inflation is +5% per year. Claims frequency inflation is +2% per year. Claims development factors are as in the following table: Claims Notified as % of Policy Ultimate Year (as at 31 March 2013) 2008 90% 2009 80% 2010 65% 2011 45% 2012 15%The following increased limit factors are applicable to all policy years without the need for adjustments for severity trends: Limit (EOOO) ILF 25 0.50 50 0.70 100 1.00 125 1.15 150 1.25 200 1.40 Estimate the loss cost for the 2013 policy, showing all workings and justifying any further assumptions that you make. [13]A general insurance company uses exposure curves to estimate losses on commercial property risks. Suppose Y is a random variable representing the size of loss as a proportion of the total sum insured (A). The exposure curve is defined as: ((x) = LEV(x) / BY], for x > 0, where LEV(x) is the limited expected value function: where F(y) is the cumulative density function of F. The following table gives values from an exposure curve that is used to price a commercial property risk with a total value of $1m. Giv 2.5% 7.0% 5.0% 14.0%% 7.5% 20.0% 10.0% 27.0% 25.0% 56.0% 50.0% 84.0 75.0% 97.0% Using this curve, the expected loss to a policy covering the layer $475k in excess of $25k has already been calculated as $10,000. Calculate the expected loss to the layer $700k in excess of $50k. (3] A general insurance company is considering the introduction of an "early bird" offer for renewals on its existing book of personal lines policies. Renewal is not automatic and the policy will lapse if no instruction to renew is given. Customers who give instruction to renew at least a month before the renewal date would receive a discount from the standard renewal price. The company has no experience of running such an offer. The company wishes to determine the level of discount to be offered in order to increase the profitability of the book by a target amount over the period of the offer. Outline the process that the company should follow. [7]