excans:Cbd0c86fe3

Solution: C

Step 1: Calculate the cumulative development factors for AY1 and AY2

The cumulative factor for AY1 equals [math]F_2[/math] and the cumulative development factor for AY2 equals [math]F_1 = F_2 * f_2 [/math] with [math]f_2 = 1.05 [/math]. To calculate [math]F_2[/math], we use the equation:

[[math]] \begin{aligned} R_{BF} = R_{LR}(1-1/F_2) + 1/F_2 * R_{CL} &\implies 400000 = 250000 * (1-1/F_2) + 1/F_2 * 437500 \\ & \implies F_2 = 1.25, F_1 = 1.05 * 1.25 = 1.3125 \end{aligned} [[/math]]

where [math]R_{BF}[/math] is the reserve estimate for AY1 using the Bornhuetter-Ferguson method.

Step 2: Calculate the reserve for AY2 using the chain ladder method

We use the same formula as above but for AY2:

[[math]] \begin{aligned} R_{BF} = R_{LR}(1-1/F_1) + 1/F_1 * R_{CL} &\implies 1120000 = 1200000 * (1-1/1.3125) + 1/1.3125 * R_{CL} \\ & \implies R_{CL} = 1095000 \end{aligned} [[/math]]