Consider the following two 4-year investments, with same initial investment given in the spread- sheet: Investment A: In each year, the annual effective rate of return (or rate, for short) is a discrete random variable. The rates in each year are independent and identically distributed, and their probability distribution given in the spreadsheet. Investment B: In year 1, the annual effective rate of return (or rate, for short) is a discrete random variable. The probability distribution of the rate is given in the spreadsheet. Once the rate is chosen for the first year, it stays fixed for the next years. Calculate the expected accumulated value and variance after 4 years under each investment. In your report you should include the following: State the expected accumulated value and variance for each investment. Consider the Bornhuetter-Ferguson method and the chain ladder method in the context of 'devel- opment claims in insurance'. Apply the two methods to the dataset given on the spreadsheet in order to find the reserve required in 2019. You should assume that 2014 claims have completely run off in 2019. Investment A Rate Probability Expected accumulated value for investment A: Expected accumulated value for investment B: (independent identicaly distributed rate) 0.04 0.3 -0.02 0.5 B-F Method Reserves: Accident Year Year of origin 0 1 2 3 4 5 *** 2014 2015 2016 2017 2018 Incremental claim payments 2019 0 3313 3324 3347 3479 3500 3572 0.06 0.2 DATA 1 427 347 603 DISPLAY YOUR ANSWERS HERE 501 403 Investment B Display your final answers here Rate Probability 2 132 138 193 198 Chain Ladder method Given Data (same rate each year determined at time t=0) Development year 3 88 116 170 0.015 0.25 Reserves: 4 61 108 Variance of investment A: Variance of investment B: 5 64 0.02 0.6 0.035 0.15 Initial Investment Earned Premium (EP) Accident Year 2014 2015 2016 2017 2018 2019 EP 4,750.00 4,981.71 5,170.89 5,375.00 5,673.61 5,920.29 10

Consider the following two 4-year investments, with same initial imvestment given in the spreadsheet: Investment A: In each year, the annual effective rate of return (or rate, for short) is a discrete random variable. The rates in each year are independent and identically distributed, and their probability distribution given in the spreadsheet. Investment B: In year 1, the annual effective rate of return (or rate, for short) is a discrete random variable. The probability distribution of the rate is given in the spreadsheet. Once the rate is chosen for the first year, it stays fixed for the next years. Calculate the expected accumulated value and variance after 4 years under each investment. In your report you should include the following: - State the expected accumulated value and variance for each investment. Consider the Bornhuetter-Ferguson method and the chain ladder method in the context of 'development claims in insurance'. Apply the two methods to the dataset given on the spreadsheet in order to find the reserve required in 2019. You should assume that 2014 claims have completely run off in 2019. DISPLAY YOUR ANSWERS HERE Expected accumulated value for investment A : Expected actumulated value for imvesment B: Warlance of imvestment A: Variance of imvetrtint B: DATA Initial Imy Display your final anwers here De Method Reserver: Chain Ladder method Cluen Dute Incremental claim payments farned Premium (fP)