Marc Levy

Quantum distribution of Gaussian keys using squeezed states

A continuous key-distribution scheme is proposed that relies on a pair of conjugate quantum variables. It allows two remote parties to share a secret Gaussian key by encoding it into one of the two quadrature components of a single-mode electromagnetic field. The resulting quantum cryptographic information versus disturbance trade-off is investigated for an individual attack based on the optimal continuous cloning machine. It is shown that the information gained by the eavesdropper then simply equals the information lost by the receiver.

Control in Pyramidal Structures

Today, the shareholding structure of companies is sometimes so complex that it can be difficult to find back their actual owners and controllers. In particular, in continental Europe and in Asia, control tunnelling appears frequently through pyramidal structure. After describing the ownership structure through a graph association, this paper analyses the voting game at stake in the race for control. It compares existing methods and algorithms to identify the owners and controllers of a firm in a pyramidal structure without cross-ownership. As a real life example, the case of the Belgian retail company, Colruyt, is used to apply these different methods and compare their results. Furthermore, it shows how the ownership structure allows to the Colruyt family to keep the control of Colruyt even if there are discordances inside the family.

The Banzhaf Index in Complete and Incomplete Shareholding Structures: A New Algorithm

In this global world many firms present a complex shareholding structure with indirect participation, such that it may become difficult to assess a firm’s controllers. Furthermore, if there are numerous dominant shareholders, the control can be shared between them. Determining who has the most influence often is a difficult task. To measure this influence, game theory allows modeling voting game and computing the Banzhaf index. This paper first offers a new algorithm to compute this index in all structures and suggests some modelisations of the floating shareholder. Then, our model is applied to a real case study: The French Group Lafarge. This exemplary case demonstrates how the float’s structure and hidden coalition can impact the power relationship between dominant shareholders.

Corporate Control with Cross-Ownership

Cross-ownership breaks the traditional rule of one-sided corporate control. Using a novel approach based on stochastic voting processes, this paper proposes a general method to determine control stakes in the presence of cross-ownership. It offers a generalization of the Banzhaf index, which allows coping with cross-ownership-inclusive ownership graphs. The original feature of this approach is its absolute sequentiality. We also operationalize this new approach by building an algorithm, which determines the shareholders’ respective control powers in any corporate structure. From a governance viewpoint, we emphasize that cross-ownership may act as a powerful device for shareholders’ expropriation. To make this point, we revisit the leading example of the German Allianz Group.