Sensitivity analysis of the moments of the profit on an Income Protection Policy

The main purpose of this paper is to perform a sensitivity analysis where we quantify and analyse the effects on the mean of the profit on an Income Protection policy and two risk measures of changing the values of the transition intensities. All the calculations carried out are based on a multiple state model for Income Protection proposed in Continuous Mortality Investigation Committee (Continuous Mortality Investigation Reports 1991; 12 ). Within this model, we derive a formula for the mean of the profit, which enables to evaluate it more efficiently. In order to calculate the two risk measures we use the numerical algorithms for the calculation of the moments of the profit proposed by Waters (Insurance: Mathematics and Economics 1990; 9 :101–113). We carry out the sensitivity analysis considering two different situations: in the first situation, we update the premium rates used to calculate the moments of the profit, according to the changes in the values of the transition intensities; in the second one, we do not update the premium rates. Both analyses are of practical interest to insurance companies selling Income Protection policies. Copyright © 2009 John Wiley & Sons, Ltd.     

On discrete Fourier transform,ambiguity, and Hamming-autocorrelation of pseudorandom sequences

We estimate discrete Fourier transform, ambiguity, and Hamming-auto-correlation of \(m\) -ary sequences in terms of their (periodic) correlation measure of order 4. Roughly speaking, we show that every pseudorandom sequence, that is, any sequence with small correlation measure up to a sufficiently large order, cannot have a large discrete Fourier transform, ambiguity, or Hamming-autocorrelation. Conversely, there are sequences, for example the two-prime generator, with large correlation measure of order 4 but small discrete Fourier transform, ambiguity, autocorrelation, and Hamming-autocorrelation.     

Online stochastic UAV mission planning with time windows and time-sensitive targets

In this paper we simultaneously consider three extensions to the standard Orienteering Problem (OP) to model characteristics that are of practical relevance in planning reconnaissance missions of Unmanned Aerial Vehicles (UAVs). First, travel and recording times are uncertain. Secondly, the information about each target can only be obtained within a predefined time window. Due to the travel and recording time uncertainty, it is also uncertain whether a target can be reached before the end of its time window. Finally, we consider the appearance of new targets during the flight, so-called time-sensitive targets, which need to be visited immediately if possible. We tackle this online stochastic UAV mission planning problem with time windows and time-sensitive targets using a re-planning approach. To this end, we introduce the Maximum Coverage Stochastic Orienteering Problem with Time Windows (MCS-OPTW). It aims at constructing a tour with maximum expected profit of targets that were already known before the flight. Secondly, it directs the planned tour to predefined areas where time-sensitive targets are expected to appear. We have developed a fast heuristic that can be used to re-plan the tour, each time before leaving a target. In our computational experiments we illustrate the benefits of the MCS-OPTW planning approach with respect to balancing the two objectives: the expected profits of foreseen targets, and expected percentage of time-sensitive targets reached on time. We compare it to a deterministic planning approach and show how it deals with uncertainty in travel and recording times and the appearance of time-sensitive targets.     

Willmore submanifolds of the Möbius space and a Bernstein-type theorem

We study Willmore immersed submanifoldsf: M ^m →S ⁿ into then-Möbius space, withm≥2, as critical points of a conformally invariant functionalW. We compute the Euler-Lagrange equation and relate this functional with another one applied to the conformal Gauss map of immersions intoS ⁿ . We solve a Bernestein-type problem for compact Willmore hypersurfaces ofS ⁿ , namely, if ?a ∈? ⁿ⁺² such that <γf, a > ≠ 0 onM, whereγ _f is the hyperbolic conformal Gauss map and <, > is the Lorentz inner product of? ⁿ⁺², and iff satisfies an additional condition, thenf(M) is an (n?1)-sphere.     

On the role of arbitrary order Bessel functions in higher dimensional Dirac type equations

This paper exhibits an interesting relationship between arbitrary order Bessel functions and Dirac type equations. Let be the Euclidean Dirac operator in the n-dimensional flat space the radial symmetric Euler operator and α and λ be arbitrary non-zero complex parameters. The goal of this paper is to describe explicitly the structure of the solutions to the PDE system in terms of arbitrary complex order Bessel functions and homogeneous monogenic polynomials. Received: 27 October 2005     

A branch-and-price approach for harvest scheduling subject to maximum area restrictions

Recently, research on exact methods has been undertaken to solve forest management problems subject to constraints on the maximum clearcut area by using the area restriction model approach. Three main basic integer programming models for these problems have been discussed in the literature: the so-called cluster, path and bucket formulations. Solving these models via branch-and-bound, where all variables and constraints are used a priori, is adequately suited for real problems of a small to medium size, but is not appropriate for larger problems. In this paper, we describe a branch-and-price approach for the cluster model, and we show that this formulation dominates the bucket model, by completing the results of the dominance relationships between the bounds of the three models. Branch-and-price was tested on real and hypothetical forests ranging from 45 to 2945 stands and temporal horizons ranging from three to twelve periods were employed. Results show that the solutions obtained by the proposed approach stood within 1% of the optimal solution and were achieved in a short computation time. It was found that branch-and-bound was unable to produce solutions for most forests from 850 stands with either eleven or an average number of stands per clearcut greater or equal than eight.     

On minimal disjoint degenerations of modules over tame path algebras

For representations of tame quivers the degenerations are controlled by the dimensions of various homomorphism spaces. Furthermore, there is no proper degeneration to an indecomposable. Therefore, up to common direct summands, any minimal degeneration from M to N is induced by a short exact sequence 0→U→M→V→0 with indecomposable ends that add up to N. We study these ‘building blocs’ of degenerations and we prove that the codimensions are bounded by two. Therefore, a quiver is Dynkin resp. Euclidean resp. wild iff the codimension of the building blocs is one resp. bounded by two resp. unbounded. We explain also that for tame quivers the complete classification of all the building blocs is a finite problem that can be solved with the help of a computer.     

A spectral Bernstein theorem

We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface M in \({\mathbb{R}^{n+1}}\). (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that M has only essential spectrum consisting of the half line [0, +∞). This is the case when \({{\rm lim}_{\tilde{r}\to +\infty}\,\tilde{r}\kappa_i=0}\), where \({\tilde{r}}\) is the extrinsic distance to a point of M and κ _i are the principal curvatures. (2) If the κ _i satisfy the decay conditions \({|\kappa_i|\leq 1/\tilde{r}}\) and strict inequality is achieved at some point \({y\in M}\), then there are no eigenvalues. We apply these results to minimal graphic and multigraphic hypersurfaces.