  The net-premium principle is considered to be the most genuine and fair
premium principle in actuarial applications. However, an insurance company,
applying the net-premium principle, goes bankrupt with probability one in the
long run, even if the company covers its entire costs by collecting the
respective fees from its customers. It is therefore an intrinsic necessity for
the insurance industry to apply premium principles, which guarantee at least
further existence of the company itself; otherwise, the company naturally could
not insure its clients to cover their potential, future claims. Beside this
intriguing fact the underlying loss distribution typically is not known
precisely. Hence alternative premium principles have been developed. A simple
principle, ensuring risk-adjusted credibility premiums, is the distorted
premium principle. This principle is convenient in insurance companies, as the
actuary does not have to change his or her tools to compute the premiums or
reserves. This paper addresses the distorted premium principle from various
angles. First, dual characterizations are developed. Next, distorted premiums
are typically computed by under-weighting or ignoring low, but over-weighting
high losses. It is demonstrated here that there is an alternative, opposite
point of view, which consists in leaving the probability measure unchanged, but
increasing the outcomes instead. It turns out that this new point of view is
natural in actuarial practice, as it can be used for premium calculations, as
well as to determine the reserves of subsequent years in a time consistent way.
