No abstract

Research summary: Venture debt lending is a form of start-up financing that lies at the intersection of venture capital and traditional debt. We analyze the lending decision criteria of 55 senior U.S. venture debt lenders (VDLs) using a discrete choice experiment in order to understand how VDLs overcome barriers that traditionally hamper start-ups' access to debt. We find, first, that the provision of patents as collateral is as important as the provision of tangible assets to lenders. Second, VDLs showed a marked preference for start-ups that offered warrants. Third, venture capitalists' backing substitutes for a startup's positive cash flows.Managerial summary: This article provides insights into the business model of venture debt lenders. Venture debt is an equity efficient way to raise money: it limits equity dilution by prolonging runways and allowing entrepreneurs and investors to raise equity at the next funding round at a higher valuation. The research suggests that venture debt plays an important role in new venture financing, with about one venture debt dollar provided for every seven venture capital dollar invested. It further suggests that backing by venture capitalists (VCs) and the provision of patents as collateral significantly increase the chance of obtaining venture debt. Therefore, it provides additional rationales for having VCs onboard and for applying for patents. More generally, the research illustrates that debt, in the form of venture debt, is available to start-ups with negative cash flows and no tangible assets.

No abstract

No abstract

We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The resulting Wigner function displays the axioms of a quasiprobability distribution, and any Weyl-ordered operator gets associated with the corresponding phase-space function, even in the absence of continuous symmetries. The corresponding quantum Liouville equation reduces to the classical curved space Liouville equation in the semiclassical limit. We demonstrate the formalism for a point particle moving on two-dimensional manifolds, such as a paraboloid or the surface of a sphere. The latter clarifies the treatment of compact coordinate spaces as well as the relation of the presented phase-space representation to symmetry groups of the configuration space.Comment: 14 pages. Corresponds to published versio