Most insurance companies publish few data on the occurrence and detection of insurance fraud. This stands in contrast to the previous literature on costly state verification, which has shown that it is optimal to commit to an auditing strategy, as the credible announcement of thoroughly auditing claim reports might act as a powerful deterrent. We show that uncertainty about fraud detection can ...

Abstract. The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are investigated. Several examples are treated in the case of quantum electrodynamics: the complete fermion and photon propagators, the two-body Green function,...

Recently, a max-plus dual space fundamental solution for a class of difference Riccati equations (DREs) has been developed. This fundamental solution is represented in terms of the kernel of a specific max-plus linear operator that plays the role of the dynamic programming evolution operator in a max-plus dual space. In order to fully understand connections between this dual space fundamental s...

The purpose of this paper is to construct the solution of self-adjoint boundary value problems on finite networks. To this end, we obtain explicit expressions of the Green functions for all different boundary value problems. The method consists in reducing each boundary value problem either to a Dirichlet problem or to a Poisson equation on a new network closely related with the former boundary...

The importance of constructing the appropriate Green function to solve a wide range of problems inelectromagnetics and partial differential equations is well-recognized by those dealing with classical electrodynamics and related fields. Although the subject of obtaining the Green function for certain geometries has been extensively studied and addressed in numerous sources, in this paper a syst...

Two-point boundary-value problems for conservative systems are studied in the context of the stationary action principle. In particular, we consider the case where the initial boundary condition is the system position, and the terminal boundary condition may be a combination of position and velocity data. The emphasis is on the N -body problem under gravitation. When the duration is sufficientl...

In 1989, B. Greene, a postdoc of Yau at the time, and R. Plesser constructed an important example of mirror manifolds. Using physics argument, they proved the first case of mirror symmetry for Calabi-Yau threefolds. Their result is considered fundamental, though its proof lacks the precision of a mathematical proof, hence the result does not constitute a mathematical theorem. Two years later, C...

Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two independent variables, by virtue of a conformal symmetry at each order in perturbation theory. The Green function for the perturbative field equations is here analyz...