This paper presents an asymptotic expansion of the ultimate ruin probability under Levy insurance risks as the loading factor tends to zero. The expansion formula is obtained via the Edgeworth type expansion for the compound geometric sum. We give higher-order expansion of the ruin probability,...

We show that classical insurance models based on some compound distributions can well predict information leakage by cyber incidents with reducing the computational cost thanks to the model’s simplicity. We use the negative binomial distribution, a renewal process and a Hawkes process as the...

The paper deals with parametric inference for discretely observed diffusion processes which may neither be ergodic nor even recurrent. We propose a class of contrast functions, which includes least squares, or local-Gauss type contrast functions. We present a family of conditions for consistency...