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Toehold purchase problem: a comparative analysis of two strategies

Banakh I., Banakh T., Vovk M., Trisch P.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

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2015

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Vol. 4, No 1

3--10

EN

Toehold purchase, defined here as purchase of one share in a firm by an investor preparing a tender offer to acquire majority of shares in it, reduces by one the number of shares this investor needs for majority. In the paper we construct mathematical models for the toehold and no-toehold strategies and compare the expected profits of the investor and the probabilities of takeover the firm in both strategies. It turns out that the expected profits of the investor in both strategies coincide. On the other hand, the probability of takeover the firm using the toehold strategy is considerably higher comparing to the no-toehold strategy. In the analysis of the models we apply the apparatus of incomplete Beta functions and some refined bounds for central binomial coefficients.

2

Construction of the approximate stability equations of motion for an elastic cylindrical body under axial compressive load

Banakh I., Kolinko M.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

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2014

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Vol. 3, No 4

69--73

EN

A method of constructing nonlinear motion stability equations for isotropic elastic bodies is developed for cylindrical bodies of standard material of the 2nd order subjected to the action of “dead” axial compressive forces. The perturbation of the displacement vector is given by its approximate decomposition with respect to the base of tensor functions of the 1st, 2nd and 3d valences. The time-dependent tensor coefficients of the decomposition satisfy the system of ordinary differential equations. Based on the obtained equations one can investigate the balance stability of cylindrical bodies under various fixing conditions.

3

Topological Structure of Non-separable Sigma-locally Compact Convex Sets

Banakh I., Banakh T., Koshino K.

Bulletin of the Polish Academy of Sciences. Mathematics

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2013

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Vol. 61, no 2

149--153

EN

For an infinite cardinal K let l2 (K) be the linear hull of the standard othonormal base of the Hilbert space l2(K) of density K. We prove that a non-separable convex subset X of density K = dens(X) in a locally convex linear metric space is homeomorphic to the space.[...]