CAS Exam 7Estimation of Policy Liabilities, Insurance Company Valuation & ERM

Using Brosius's least-squares method, the fitted relationship between ultimate losses $y$ and reported losses $x$ at 12 months is $y=100+0.8x$. Reported losses for the current accident year are 500. Calculate the least-squares estimate of ultimate losses.

Clark's model uses a Weibull growth curve with $\theta=24$ and $\omega=1.5$ (months). Calculate the expected percentage of ultimate reported at 12 months.

An ODP bootstrap is fitted to a 10×10 incremental triangle (55 cells). Calculate the degrees of freedom used in the scale parameter.

Required capital supporting a run-off is 100 at time 0, 75 at time 1, 50 at time 2 and 25 at time 3, released at the end of each year. Cost of capital is 6% and the risk-free rate is 3%. Calculate the cost-of-capital risk margin.

Which of the following would most directly violate Mack's independence assumption across accident years?

Compare the Mack model and the ODP bootstrap as methods for estimating reserve variability. Address (a) the underlying model of the data, (b) how each captures process and parameter uncertainty, (c) one practical advantage and one limitation of each.

For a development period, two accident years have $C_{i,k}=1{,}000$ and $1{,}500$, developing to $C_{i,k+1}=1{,}950$ and $2{,}850$. Calculate Mack's estimated $\hat f_k$ and $\hat\sigma_k^2$.

An insurer's book value is 50 million and its shares trade at a market value of 70 million. Analysts project the company will earn a 12% return on book equity indefinitely, with a cost of capital of 10%. Using the Miccolis/DCF-style intuition that a P/B multiple above 1.0 reflects returns above the cost of capital, which statement is most consistent with these facts?

Expected held capital supporting a runoff is 80, 60, 40, and 20 at the start of years 1–4 respectively (released at each year-end). Using a cost-of-capital rate of 8% and a discount rate of 3%, calculate the risk margin.

Which of the following is the best example of operational risk, as distinguished from insurance (underwriting) risk or market risk?

Clark's LDF method fits a Weibull growth curve $G(x)=1-\exp[-(x/\theta)^\omega]$ with $\theta=30$ months and $\omega=1.2$. (a) Calculate the expected percentage of ultimate losses reported by 18 months and by 36 months. (b) Calculate the expected incremental percentage of ultimate reported between 18 and 36 months. (c) State one diagnostic Clark's method provides that the simple chain ladder does not.