If BB and f(B)f(B) are Brownian motions, then ff is affine

It is shown that if the processes $B$ and $f(B)$ are both Brownian motions (without a random time change) then $f$ must be an affine function. As a by-product of the proof, it is shown that the only functions which are solutions to both the Laplace equation and the eikonal equation are affine.Comment: 4 page

Inequalities for the Gaussian measure of convex sets

This note presents families of inequalities for the Gaussian measure of convex sets which extend the recently proven Gaussian correlation inequality in various directions

Uniform bounds for Black--Scholes implied volatility

In this note, Black--Scholes implied volatility is expressed in terms of various optimization problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries of the Black--Scholes formula are exploited to derive new bounds from old. These bounds are used to reprove asymptotic formulas for implied volatility at extreme strikes and/or maturities

Determination of void content in filament wound composites

The use of image analysis for the determination of fibre volume fraction void content and void distribution in translucent composite parts was developed in order to reduce time and cost of quality assurance while maintaining reliability. The apparatus and methods are described, advantages and disadvantages are discussed, and typical results are presented. The validity of results was checked using resin bum off and composite density techniques. On the basis of this it is suggested that the techniques described are more than adequate for the assessment of material quality for both development and production purposes

A Black–Scholes inequality: applications and generalisations

Abstract: The space of call price curves has a natural noncommutative semigroup structure with an involution. A basic example is the Black–Scholes call price surface, from which an interesting inequality for Black–Scholes implied volatility is derived. The binary operation is compatible with the convex order, and therefore a one-parameter sub-semigroup gives rise to an arbitrage-free market model. It is shown that each such one-parameter semigroup corresponds to a unique log-concave probability density, providing a family of tractable call price surface parametrisations in the spirit of the Gatheral–Jacquier SVI surface. An explicit example is given to illustrate the idea. The key observation is an isomorphism linking an initial call price curve to the lift zonoid of the terminal price of the underlying asset