How Fast Is the Bandit?

Abstract

In this article we investigate the rate of convergence of the so-called two-armed bandit algorithm. The behavior of the algorithm turns out to be highly non standard: no central limit theorem, possible occurrence of two different rates of convergence with positive probability.     

Optimal stopping with irregular reward functions

We consider optimal stopping problems with finite horizon for one-dimensional diffusions. We assume that the reward function is bounded and Borel-measurable, and we prove that the value function is continuous and can be characterized as the unique solution of a variational inequality in the sense of distributions.     

Mearsine,a unique isoquinuclidine alkaloid: x-ray crystal structure of mearsine picrate

X-ray crystallography shows that mearsine, a minor alkaloid of the north Queensland plant $\text{Peripentadenia mearsii}$, has the novel isoquinuclidine structure 1, which permits charge transfer to take place between carbonyl and an azomethine group.     

Brownian Optimal Stopping and Random Walks

One way to compute the value function of an optimal stopping problem along Brownian paths consists of approximating Brownian motion by a random walk. We derive error estimates for this type of approximation under various assumptions on the distribution of the approximating random walk.     

Crystal and molecular structure of powerine: Methyl 10,17-dihydroxy-(16β,17β,20α)-yohimban-16-carboxylate

The methanol adduct of powerine [methyl 10,17-dihydroxy-(16,17,20)-yohimban-16-carboxylate], C₂₁H₂₆N₂O₄. CH₃ OH, crystallizes in the orthorhombic space groupP2₁2₁2₁ (no. 19) with cell dimensionsa = 8.558(3),b = 14.162(7),c = 16.993(7) Å. The crystal and molecular structure has been determined by X-ray diffraction analysis and refined using full-matrix least squares methods to a reliability index,R, of 0.090 with 1139 observed (F 2.5 _F ) intensities. With the configuration at C15 arbitrarily assigned those at the chiral centers C3-H, C16-CO₂Me, C17-OH and C20-H are respectively ,,,: theC-D ring junction istrans and that ofD-E iscis. All bond lengths and bond angles are normal.     

Brownian Optimal Stopping and Random Walks

One way to compute the value function of an optimal stopping problem along Brownian paths consists of approximating Brownian motion by a random walk. We derive error estimates for this type of approximation under various assumptions on the distribution of the approximating random walk.     

Variational inequalities and the pricing of American options

This paper is devoted to the derivation of some regularity properties of pricing functions for American options and to the discussion of numerical methods, based on the Bensoussan-Lions methods of variational inequalities. In particular, we provide a complete justification of the so-called Brennan-Schwartz algorithm for the valuation of American put options.Research supported in part by a contract from Banque INDOSUEZ.     

Laser induced medium perturbation in a pulsed CO2 laser

Laser induced medium perturbation (LIMP) has been identified by time-resolved interferometry observations of the lasing/non-lasing boundaries in a pulsed, kilojoule CO₂ electron beam laser, working at atmospheric pressure. This fundamental effect destroys the quality of the laser output beam and therefore has serious implications in laser design.