Approximations by Orthogonal Functions in Casualty Insurance.
Abstract
The premium calculation in insurance is of great importance. Knowing past claims (xi sub 1), ..., (xi sub n) one wishes to forecast the next claim (xi sub (n + 1)), or in a more general fashion, forecast a function of (xi sub (n + 1)), f(xi sub (n + 1)). Since one is interested in a least square forecast of f(xi sub (n + 1)), the problem readily reduces to calculating E(f(xi sub (n + 1))/(xi sub 1, ..., xi sub n)). This can formally be done by use of Bayes rule. As Bayes rule is difficult to apply the theory of approximation with an orthonormal set of functions is exploited in the paper, to reveal the nature of the problem. The credibility premium and credible distribution follow as partial results after a generalization of Ericson's Theorem. (Modified author abstract)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1973
- Accession Number
- AD0771974
Entities
People
- Pantelis M. Pechlivanides
Organizations
- University of California, Berkeley