An Intrisic Topology for Orthomodular Lattices

We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of a boolean algebra, the obtained topology is the discrete one. Thus, our construction provides a general tool for studying orthomodular lattices but also a way to distinguish classical and quantum logics.Comment: Under submission to the International Journal of Theoretical Physic

The price of rapid exit in venture capital-backed IPOs

This paper proposes an explanation for two empirical puzzles surrounding initial public offerings (IPOs). Firstly, it is well documented that IPO underpricing increases during “hot issue” periods. Secondly, venture capital (VC) backed IPOs are less underpriced than non-venture capital backed IPOs during normal periods of activity, but the reverse is true during hot issue periods: VC backed IPOs are more underpriced than non-VC backed ones. This paper shows that when IPOs are driven by the initial investor’s desire to exit from an existing investment in order to finance a new venture, both the value of the new venture and the value of the existing firm to be sold in the IPO drive the investor’s choice of price and fraction of shares sold in the IPO. When this is the case, the availability of attractive new ventures increases equilibrium underpricing, which is what we observe during hot issue periods. Moreover, I show that underpricing is affected by the severity of the moral hazard problem between an investor and the firm’s manager. In the presence of a moral hazard problem the degree of equilibrium underpricing is more sensitive to changes in the value of the new venture. This can explain why venture capitalists, who often finance firms with more severe moral hazard problems, underprice IPOs less in normal periods, but underprice more strongly during hot issue periods. Further empirical implications relating the fraction of shares sold and the degree of underpricing are presented

Topological geometric lattices

SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman