Financial contracts and strategic customer exclusion

The paper studies an incentive contract in a monopolistic and duopolistic credit market where borrowers are different in risk. One lender is in an advantaged position with respect to the other due to past relations with the borrowers. The features of the equilibrium contract are investigated. It is shown that the equilibrium contract drastically changes between the monopolistic and the duopolistic situations and are sensitive to other parameters. In some cases, the superior lender strategically yields borrowers, especially the better ones to the opponent lender

The revelation principle and regularity conditions

The revelation principle asserts that every outcome brought by a mechanism is realized by a truthful direct mechanism. The present paper investigates the regularity conditions of these two mechanisms in the continuous space of the agent’s type. It questions what regularity condition a general mechanism confers upon a direct mechanism through the revelation principle. By so doing, we elucidate the limit of the revelation principle

The IPO spread and conflicts of interests

The level of the IPO spread taken by the underwriter is a controversial issue. Some claim that the level is too high and attributes it to collusion between investment banks while others contend to the contrary. The paper examines the spread in the framework of conflicts of interests between the issuer, the underwriter and the informed investor. The argument is developed, based upon incentives for the underwriter. It is shown that the issuer should have the spread large enough for the underwriter to stay faithful to the issuer

The pricing mechanism to the buyer with a budget constraint and an indirect mechanism

The present article considers the situation in which the buyer’s taste and budget are his private information. In this multi-dimensional setting, we study the optimal mechanism through a canonical mechanism in the traditional one-dimensional context: a function of one variable, the buyer’s taste. In our multi-dimensional context, however, this is an indirect mechanism. We investigate the effectiveness and limit of this indirect mechanism in the framework of the revelation principle

The 19-Vertex Model at critical regime ∣q∣=1|q|=1

We study the 19-vertex model associated with the quantum group $U_q(\hat{sl_2})$ at critical regime $|q|=1$. We give the realizations of the type-I vertex operators in terms of free bosons and free fermions. Using these free field realizations, we give the integral representations for the correlation functions.Comment: LaTEX2e, 19page

Determinant representation for dynamical correlation functions of the Quantum nonlinear Schr\"odinger equation

The foundation for the theory of correlation functions of exactly solvable models is determinant representation. Determinant representation permit to describe correlation functions by classical completely integrable differential equations [Barough, McCoy, Wu]. In this paper we show that determinant represents works not only for free fermionic models. We obtained determinant representation for the correlation function $$ of the quantum nonlinear Schr\"odinger equation, out of free fermionic point. In the forthcoming publications we shall derive completely integrable equation and asymptotic for the quantum correlation function of this model of interacting fermions.Comment: LaTEX file, 35 pages, to appear in C.M.P. (1997

Supergravity in 2+ϵ2+\epsilon Dimensions

Supergravity theory in $2+\epsilon$ dimensions is studied. It is invariant under supertransformations in 2 and 3 dimensions. One-loop divergence is explicitly computed in the background field method and a nontrivial fixed point is found. In quantizing the supergravity, a gauge fixing condition is devised which explicitly isolates conformal and superconformal modes. The renormalization of the gravitationally dressed operators is studied and their anomalous dimensions are computed. Problems to use the dimensional reduction are also examined.Comment: 36 pages, TIT/HEP-238, Imperial/TP/93-94/

Completely Integrable Equation for the Quantum Correlation Function of Nonlinear Schr\"odinger Eqaution

Correlation functions of exactly solvable models can be described by differential equation [Barough, McCoy, Wu]. In this paper we show that for non free fermionic case differential equations should be replaced by integro-differential equations. We derive an integro-differential equation, which describes time and temperature dependent correlation function $_T$ of penetrable Bose gas. The integro-differential equation turns out be the continuum generalization of classical nonlinear Schr\"odinger equation.Comment: LaTEX file, 23 page

The Riemann-Hilbert problem associated with the quantum Nonlinear Schrodinger equation

We consider the dynamical correlation functions of the quantum Nonlinear Schrodinger equation. In a previous paper we found that the dynamical correlation functions can be described by the vacuum expectation value of an operator-valued Fredholm determinant. In this paper we show that a Riemann-Hilbert problem can be associated with this Fredholm determinant. This Riemann-Hilbert problem formulation permits us to write down completely integrable equations for the Fredholm determinant and to perform an asymptotic analysis for the correlation function.Comment: 21 pages, Latex, no figure

Multi-Higgs Mass Spectrum in Gauge-Higgs Unification

We study an SU(2) supersymmetric gauge model in a framework of gauge-Higgs unification. Multi-Higgs spectrum appears in the model at low energy. We develop a useful perturbative approximation scheme for evaluating effective potential to study the multi-Higgs mass spectrum. We find that both tree-massless and massive Higgs scalars obtain mass corrections of similar size from finite parts of the loop effects. The corrections modify multi-Higgs mass spectrum, and hence, the loop effects are significant in view of future verifications of the gauge-Higgs unification scenario in high-energy experiments.Comment: 32 pages; typos corrected and a few comments added, published versio