This question is very complete. Please anser each and every question. complete......Grossi and Kunreuther define two types of uncertainty, aleatory and epistemic. The definitions are: "Aleatory uncertainty is the inherent randomness associated with natural hazard events ..." "... epistemic uncertainty is the uncertainty due to lack of information or knowledge of the hazard." (a) (2 points) Provide an example of each type of uncertainty with regard to earthquake models and explain why each example reflects that type of uncertainty. (b) (1 point) Describe which of these types of uncertainty can be reduced by collecting more data, and illustrate your response using your example from part (a). (c) (1 point) Explain how logic trees can be used to reflect epistemic uncertainty in the construction of exceedance probability curves.

You are given the following claims information about an insurer that has been operating for three years: Accident Year Paid Claims at Maturity Ages Case Estimates as of Dec. 31, 2012 Ultimate 12 24 36 Claims 2010 7,000 9,000 10,000 10,000 0 2011 5,000 8,000 10,000 1,000 2012 4,000 10,000 4,000 Paid ULAE is equal to 500, 800, and 1,000 in calendar years 2010-2012, respectively. For each accident year, 50% of claims are expected to be paid during the first 12 months, 30% from 12 to 24 months, and 20% from 24 to 36 months. (a) (0.5 points) Describe two of the key assumptions of the classical paid-to-paid method. (b) (1.5 points) Estimate unpaid ULAE as of December 31, 2012 using the classical paid-to-paid method and a multiplier of 50%. Justify any selections. (c) (0.5 points) Describe the Kittel refinement to the classical paid-to-paid method and the weakness it is designed to address. (d) (1 point) Explain the weakness of the classical paid-to-paid method that the Mango-Allen smoothing adjustment is designed to address and identify a situation in which it would be useful. (e) (1 point) Estimate unpaid ULAE as of December 31, 2012 using the classical paid-to-paid method, a multiplier of 50%, and the Mango-Allen smoothing adjustment. (f) (0.5 points) Compare the significance of ULAE for reinsurers to that of primary insurers and explain the reason for any difference.

You are revising your company's automobile insurance rates to include the new risk characteristic color of car, without introducing any change to the overall average rate level. The information in the following table was provided for the classification analysis: Car Color Trended Earned Premium at Current Rate Level Trended Ultimate Claims Ultimate Counts White 568,000 449,000 775 Black 780,000 606,000 935 Other 1,150,000 837,000 1,635 Total 2,498,000 1,892,000 3,345 The full credibility standard is 1,537 ultimate counts. The square root rule is used for partial credibility. The complement of credibility is equal to 1. (a) (2 points) Calculate the indicated class relativities for the risk characteristic color of car. (b) (0.5 points) Explain what is implied by a complement of credibility of 1. (c) (1.5 points) Determine the color of car classification relativities and the revised base rate assuming a base class of other, given that the current base rate is 475. (d) (1 point) Describe how you could check the risk characteristic color of car for distributional bias relative to another risk characteristic such as territory.

You are calculating premium liabilities for Acme Insurance Company, which writes only property and liability business. The claims ratios include ALAE, but not ULAE. The 2012 claims ratios on property reflect the impact of a 1-in-100 year hurricane. ULAE is 10% of claims (including ALAE), which is not covered by reinsurance. There are no reinsurance costs beyond what is reflected in the net unearned premiums. Maintenance expenses are 5% of gross unearned premiums. Commission of 15% of premiums has already been paid. There is no incentive commission. (a) (1.5 points) Select expected claim ratios for each line of business, gross and net of reinsurance, that will be used in the determination of premium liabilities. Justify each selection. (b) (2 points) Calculate the net premium liabilities for Acme as of December 31, 2013 given the selected expected claim ratios in (a) and the information provided. (c) (0.5 points) Explain the purpose of a premium deficiency reserve. (d) (0.5 points) Determine, based on your calculations in (b), Acme's premium deficiency reserve as of December 31, 2013. (e) (0.5 points) Explain how premium liabilities for Acme would change if some of the liability policies are written using sales as an exposure base that are subject to audit following the end of the policy period. Line of Business Unearned Premiums as of Dec. 31, 2013 2011 Ultimate Accident Year Claims Ratio 2012 Ultimate Accident Year Claims Ratio 2013 Ultimate Accident Year Claims Ratio Gross of Reinsurance Property 120,000 60% 500% 50% Liability 120,000 90% 85% 95% Net of Reinsurance Property 100,000 55% 100% 55% Liability 100,000 90% 95% 100%

) You have been given the following information for a projection of ultimate claims: Accident Year Actual Reported Claims A Priori Expected Claims Reported CDF 2008 57,800 62,000 1.00 2009 53,100 59,500 1.05 2010 25,200 51,000 1.10 2011 20,600 49,000 1.50 2012 19,300 52,100 2.00 (a) (2 points) Develop an estimate of ultimate claims for 2008 and 2012 using the following methods: (i) Development method (ii) Expected method (iii) Bornhuetter Ferguson method (iv) Benktander method, one iteration (b) (1 point) Evaluate the reasonableness of the inputs for the Bornhuetter Ferguson method. (c) (1 point) Select estimates of ultimate claims for 2008 and 2012 and justify your selections.

Claim sizes in a particular year are uniformly distributed on (0, 100). Over a number of years, inflation doubles all claim sizes. (a) (1 point) Illustrate this inflationary trend effect on the layer from 0 to 50 and the layer from 50 to 100 using a graph with cumulative claim frequency along the x-axis and claim size along the y-axis. (b) (3 points) Determine the inflationary trend factors that apply to each of the following layers using the graph from (a): (i) 0 to 50 (ii) 50 to 100 (iii) 0 to 100