Understanding duration and convexity of fixed income. A second order taylor series expansion will capture the curvature in addition to the trend and will often well. Preface the following notes were written before and during the course on convex geometry which was held at the university of karlsruhe in the winter term 20022003. Hence, convexity of the curve increases the increase in price, and reduces the loss in price, compared to what is given by a linear measure of duration. The study of the concavity and convexity is done using the inflection points. In fact, this function is most often a convex decreasing function. Notes on online convex optimization karl stratos online convex optimization oco is a principled framework for online learning. Pdf stochastic convexity and concavity of markov processes. Concavity, convexity and points of inflexion submitted by. Inflection points an inflection point is defined as the point in which the function changes from being convex to concave or vice versa.
R is concave convex if and only if its restriction to every line segment of rn is concave convex function of one variable. Roughly speaking concavity of a function means that the graph is above chord. Notes on online convex optimization columbia university. A course on convex geometry university of ljubljana. Just like dollar duration and duration, dollar convexities add, convexities average. Concavity and convexity, inflection points of a function. The convexity of a portfolio is the average convexity of its securities, weighted by present value. Convexity is fundamental to the whole area of optimization, and it is also of great importance in mathematical statistics, economics, functional analysis, approximation theory etc. Preface this book serves as an introduction to the expanding theory of online convex optimization.