Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 1, 75--108

A Bayesian Nonparametric Approach to the Estimation of the Adjustment Coefficient, with Applications to Insurance and Telecommunications

By

Antonella Capitanio, Universit\`{a} di Bologna & Pier Luigi Conti, Universit\`{a} di Roma ``La Sapienza

SUMMARY. In this paper, a nonparametric Bayesian approach to the estimation of the adjustment coefficient for the distribution of the maximum of a random walk is performed. Approximations of the posterior distribution of the adjustment coefficient are studied. The consistency and asymptotic normality of its posterior law are also proved under mild conditions. Finally, an application to real data is provided.

AMS (1991) subject classification}. Primary 62G99, 62F15, 62G09, 62E20; secondary 62P30, 62P05.

Key words and phrases. Bootstrap, asymptotics, consistency, Bernstein-von Mises theorem, adjustment coefficient, queues, risk theory.

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