Estimating the adjustment coefficient in an ARMA(p, q) risk model

Estimation of the adjustment coefficient in an ARMA(p, q), risk model introduced by Gerber (1982) is considered here. We propose an empirical-moment generating function type estimator. However, since the original white noise of the time series is not observable, we have to replace the empirical-moment generating function by a suitable estimate based on the time series itself. Strong consistency is proved, and convergence rates are studied, too. Some simulation results are presented as well to illustrate the finite sample behaviour of the proposed estimator.