2013/04/01 by Alois Pichler, Pichler, Alois · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #q-fin.RM
paper · pdf · doi:10.48550/arxiv.1304.0490
arXiv admin note: substantial text overlap with arXiv:1209.3570
arxiv created 2013/04/01 · openalex publication_date 2013/04/01 · arxiv updated 2013/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.