On Stochastic Approximation and Credibility

Stochastic approximation is a powerful tool for sequential estimation of zero points of a function. This methodology is defined and is shown to be related to a broad class of credibility formulae derived for the Exponential Dispersion Family (EDF). We further consider a Location Dispersion Family (LDF) which is rich enough and for which no simple credibility formula exists. For this case, a Generalized Sequential Credibility Formula is suggested and an optimal stepwise gain sequence is derived.