## Abstract

Suppose the claims arrive according to a Poisson process {
For initial capital reserve

*N*(*t*)} with rate λ and interarrival intervals {*X*_{1}, ⋯,*X*_{ n }, ⋯ }. The consecutive claim amounts {*Y*_{1}, ⋯,*Y*_{ n }, ⋯ } are identically and independently distributed with continuous distribution*F*(*y*) with mean μ > 0, and independent of the arrival times. The premier rate*c*satisfies*c*∕ λ > μ, and \(c = \lambda \mu (1 + \theta )\). This guarantees the profitability in the long run. The risk process*R*_{ t }is defined as$${R}_{t} = ct -{\sum }_{i=1}^{N(t)}{Y }_{ i}.$$

*U*_{0}=*u*, we define the surplus process as \(U_t = u + R_t\) and the time of ruin as$$T = \inf \{t > 0: U_t = u + R_t < 0\}.$$

## Keywords

Moment Generate Function Risk Process Claim Size Claim Amount Renewal Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Copyright information

© Springer Science+Business Media, LLC 2010