Explicit analytic ruin probabilities for bounded claims

We demonstrate how explicit analytic ruin probabilities can be obtained for claimsize distributions concentrated on a compact interval and constructed arbitrarily from polynomials, exponential functions eax (a ϵ R) and trigonometric functions sin(bx) (x ϵ R), cos(cx) (x ϵ R), by a finite number of additions and multiplications. The method applies also in case of unbounded claims, and then its execution is much simpler than for bounded claims.