Approximation of the fixed-probability level for a compound renewal process

Dealing with compound renewal process with generally distributed jump sizes and inter-renewal intervals, we focus on the approximation for the fixed-probability level, which is the core of inverse level crossing problem. We are developing an analytical technique presented in [15]-[17] and based on Kendall’s identity; this yields (see [18]) inverse Gaussian approximation in the direct level crossing problem. These issues are of great importance in risk theory.