123137491
A finiteness theorem for a dynamical class of entire functions
121662994
Uniformization of attracting basins for exponential maps
Soit la famille exponentielle complexe Eλ(Z)=λ exp(Z). Il y a un ensemble ouvert de valeurs de λ dans le plan complexe pour lesquelles Eλ a un point fixe attractif unique; Ωλ est le bassin d'attraction pour ces valeurs. On considere l'uniformisation Φλ de Ωλ et on etudie la dynamique induite par Φλ sur le disque unite
122711858
On the multiplier of a repelling fixed point
We estimate the multiplier λ of a repelling fixed point with rational rotation number for a polynomial in one complex variable. We show that a canonical branch of the logarithm of λ lies in a small disk tangent to the imaginary axis. The radius of the disk is determined by the degree of the polynomial, the rotation number of the fixed point and the escape rates and external arguments of the critical values.
122379004
Catalan numbers and branched coverings by the Riemann sphere
Abstract We prove that the number of PGL(2, C) equivalence classes of degree d rational maps with a fixed branch set is generically equal to the “Catalan number” ϱ(d) = ( 1 d )( 2d−2 d−1 ) . Several (previously known) applications of Catalan numbers to combinatorics and algebraic geometry are discussed throughout the course of the article.
123686855
On the shape of the unit sphere in Q(Δ)
We show that the unit sphere in the Banach space of L 1 holomorphic quadratic differentials on the disk is weakly uniformly convex with exponent 1/2 at certain points
533051
Volatility of the short rate in the rational lognormal model
Abstract. A recent article of Flesaker and Hughston introduces a one factor interest rate model called the rational lognormal model. This model has a lot to recommend it including guaranteed finite positive interest rates and analytic tractability. Consequently, it has received a lot of attention among practioners and academics alike. However, it turns out to have the undesirable feature of predicting that the asymptotic value of the short rate volatility is zero. This theoretical result is proved rigorously in this article. The outcome of an empirical study complementing the theoretical result is discussed at the end of the article. European call options are valued with the rational lognormal model and a comparably calibrated mean reverting Gaussian model. unsurprisingly, rational lognormal option values are considerably lower than the analogous mean reverting Gaussian option values. In other words, the volatility in the rational lognormal model declines so quickly that options are severely undervalued.
