  Importance sampling is a well developed method in statistics. Given a random
variable $X$, the problem of estimating its expected value $\mu$ is addressed.
The standard approach is to use the sample mean as an estimator $\bar x$. In
importance sampling, a suitable variable $L$ is introduced such that the random
variable $X/L$ has an estimator with a smaller variance than that of $\bar x$.
As a result, a smaller sample size can lead to the same estimation accuracy.
  In the simulation of reinsurance financial terms for catastrophe loss,
choosing a general variable $L$ is difficult: Even before the application of
financial terms, the loss distribution is often not modelled by a closed-form
distribution. After that, a wide range of financial terms can be applied that
makes the final distribution unpredictable. However, it is evident that the
heavy tail of the resulting net loss distribution makes the use of importance
sampling desirable. We propose an importance sampling technique using a power
function transformation on the cumulative distribution function. The benefit of
this technique is that no prior knowledge of the loss distribution is required.
It is a new technique that has not been documented in the literature. The
transformation depends on the choice of the exponent $k$. For a specific
example we investigate desirable values of $k$.
