## JMI2009A-2 Generalisation of Mack's formula for claims reserving with arbitrary exponents for the variance assumption (pp.7-15)

Author(s)： Shingo Saito

J. Math-for-Ind. 1A (2009) 7-15.

Abstract
Mack estimated the mean squared errors of the outstanding claims reserve of each accident year and of the overall claims reserve in order to obtain their confidence intervals within his distribution-free model. We generalise his formulae by allowing for arbitrary exponents in the variance assumption. Our formula is also capable of giving a confidence interval of the amount that the insurer is liable to pay each year.

Keyword(s).　 Mack's formula, claims reserving, chain-ladder method, mean squared error