IAI Actuarial Core Principles · Economic Modelling · Ruin theory
A simulation of annual surplus uses U_n = U_{n-1} + 5 − X_n (Rs crore), with X_n lognormal i.i.d. Which change would most clearly reduce the Monte Carlo standard error of the estimated ruin probability without altering the true value?
Increasing the number of simulated paths reduces the Monte Carlo standard error, since it scales as one over the square root of the number of paths. The other changes alter the true ruin probability or break independence.
- AReducing the premium loading
- BLengthening the projection horizon
- CIncreasing the number of simulated pathsCorrect
- DUsing the same random seed for each claim
- Raising the initial surplus
Explanation
Standard error is sqrt(p(1−p)/n), so more paths reduce it. Changing premium, horizon or initial surplus alters the true ruin probability itself. Reusing one seed for every claim would destroy independence and bias the results.
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