Saddlepoint Approximations to the Distribution of the Total Claim Amount in some Recent Risk Models

The saddlepoint approximation or Esscher approximation for the total claim distribution is extended from the classical risk model to a number of models considered recently in the literature. Theorems are derived for the validity of the approximation. Key words: compound sum, conjugate distribution, log-concave density, tail probability. Reinsurance Research - Loss Distributions, Size of