Improving Goovaerts' and De Vylder's Stable Recursive Algorithm

GOOVAERTS and DE VYLDER (1983) provided a stable recursive algorithm for calculating the probability of ultimate rum. Their algorithm yielded bounds for this probability It is shown that in practice their method may be inherently unstable because it is based on the subtraction of nearly equal numbers. An alternative to this type of subtraction IS provided. It is proved that their algorithm converges only at a linear rate to the true value. It is suggested that this slow rate of convergence be improved via an application of the Richardson extrapolation technique. KEYWORDS Ruin probability; rounding errors; truncation errors; order of convergence, Richardson extrapolation