ON SEMI-VALUATIONS. II.

5 Theory of valuations on manifolds , II

This article is the second part in the series of articles where we are developing theory of valuations on manifolds. Roughly speaking valuations could be thought as finitely additive measures on a class of nice subsets of a manifold which satisfy some additional assumptions. The goal of this article is to introduce a notion of a smooth valuation on an arbitrary smooth manifold and establish som...

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

Realization of a certain class of semi-groups as value semi-groups of valuations

Given a well-ordered semi-group Γ with a minimal system of generators of ordinal type at most ωn 1 and of rational rank r, which satisfies a positivity and increasing condition, we construct a zero-dimensional valuation centered on the ring of polynomials with r variables such that the semigroup of the values of the polynomial ring is equal to Γ. The construction uses a generalization of Favre ...

realization of a certain class of semi-groups as value semi-groups of valuations

Analytics on pension valuations

EY Actuaries performs pension calculations for several companies where both the the assets and liabilities are valuated. The provision1 of a company contains the benefits a participant2 is entitled to. Besides that, there could be benefits when a participant dies or become disables. This research consists of two main topics. The purpose of the first topic is to gain insights in the unexplained ...