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1.
Consider a portfolio containing heterogeneous risks. The premiums of the policyholders might not cover the amount of the payments which an insurance company pays the policyholders. When setting the premium, this risk has to be taken into consideration. On the other hand the premium that the insured pays has to be fair. This fairness is measured by a function of the difference between the risk and the premium paid—we call this function a distance function. For a given small probability of insolvency, we find the premium for each class, such that the distance function is minimized. Next we formulate and solve the dual problem, which is minimizing the insolvency probability under the constraint that the distance function does not exceed a given level. This paper generalizes a previous paper [Zaks, Y., Frostig, E., Levikson, B., 2006. Optimal pricing of a heterogeneous portfolio for a given risk level. Astin Bull. 36 (1), 161–185] where only a square distance function was considered. 相似文献
2.
The purpose of this paper is to establish a conjecture of B. Grünbaum, which states that in every n-polygon P in the plane, n 5, some diagonals intersect in a pattern that defines a new n-polygon (P), such that the product of the cross-rations on the diagonals of P is equal to the product of the corresponding cross-ratios on the diagonals of (P). 相似文献
3.
Shmuel Zaks 《BIT Numerical Mathematics》1984,24(2):196-204
A new algorithm for generating permutations is presented, that generates the next permutation by reversing a certain suffix of its predecessor. The average size of this suffix is less thane 2.8. It is shown how to find the position of a given permutation and how to construct the permutation of a given position, where the position refers to the order in which the permutations are generated, and is also new.On leave from the Department of Computer Science, Technion, Haifa, Israel. This work was supported by NSF grant MCS-8302391. 相似文献
4.
Joseph Zaks 《Geometriae Dedicata》1997,67(2):223-232
Extending earlier results in the plane, we prove that every n-polygon in sufficiently general position in d-dimensional projective space, n d + 2, gives rise to a derived n-polygon, which preserves a few functions; these functions are the cyclial product of (actually affine) ratios of various points, obtained by proper projections on suitable lines. 相似文献
5.
Jurek Czyzowicz Bruno Gaujal Eduardo Rivera-Campo Jorge Urrutia Joseph Zaks 《Geometriae Dedicata》1995,56(2):115-120
A setL of points in thed-spaceE
d
is said toilluminate a familyF={S
1, ...,S
n
} ofn disjoint compact sets inE
d
if for every setS
i
inF and every pointx in the boundary ofS
i
there is a pointv inL such thatv illuminatesx, i.e. the line segment joiningv tox intersects the union of the elements ofF in exactly {x}.The problem we treat is the size of a setS needed to illuminate a familyF={S
1, ...,S
n
} ofn disjoint compact sets inE
d
. We also treat the problem of putting these convex sets in mutually disjoint convex polytopes, each one having at most a certain number of facets. 相似文献
6.
Abraham Zaks 《Israel Journal of Mathematics》1971,9(3):285-289
The purpose of this note is to prove that a Dedekind domain R which contains a field k, and which is a subring ofk[x
1,…,x
n
] is a ring of polynomials. This generalizes similar results of A. Evyatar and A. Zaks on principal ideal domains, and of
P. M. Cohn for the casen=1. Our methods and proofs differ from those introduced previously.
This research was partially supported by the National Science Foundation, Grant GP-23861. 相似文献
7.
The structure of an acyclic directed graph with n vertices and m edges, maximizing the number of distinct paths between two given vertices, is studied. In previous work it was shown that there exists such a graph containing a Hamiltonian path joining the two given vertices, thus uniquely ordering the vertices. It was further shown that such a graph contains k ? 1 full levels (an edge (i, j) belongs to level t = j ?i) and some edges of level k—a deficient k-generalized Fibonacci graph. We investigate the distribution of the edges in level 3 in a deficient 3-generalized Fibonacci graph, and develop tools that might be useful in extending the results to higher levels. 相似文献
8.
S. G. Mairanovskii A. M. Moiseenkov I. V. Proskurovskaya E. V. Polunin V. P. Gul'tyai I. M. Zaks A. V. Semenovskii 《Russian Chemical Bulletin》1978,27(11):2342-2343
Conclusions The electroreduction of sultones in DMF results in the predominant cleavage of the C-O bond with the formation of the salt of the unsaturated sulfonic acid; catalytic hydrogenation also proceeds by the same scheme.Deceased.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2618–2620, November, 1978. 相似文献
9.
10.
Abraham Zaks 《Israel Journal of Mathematics》1971,10(4):442-450
LetR be a bounded Noetherian Prime ring. The Asano-Michler theorem shows thatR is a bounded Dedekind ring if every prime ideal ofR is invertible. We provide a simple proof of the Asano-Michler theorem, and we suggest some possible generalizations. We also
prove that if the proper residue rings ofR areQF-rings thenR is a bounded Dedekind ring, and generalize this result toLD-rings. 相似文献