Optimal Execution of Portfolio Transactions with Geometric Price Process
Abstract
In this talk we derive the optimal execution trajectory for a trader who wishes to buy or sell a large position of shares which evolve as a geometric Brownian process in contrast to the arithmetic model which prevails in the existing literature (see for instance Almgren and Chriss 2000), and with a general temporary impact h. We will provide a couple of examples which illustrate the results. We would like to stress the fact that in this paper we use understandable user-friendly techniques, which might lead to an approach to solving the problem of optimal execution of derivatives.
Description:
Can Strain Stimulus Create Spatial Ordering in Large Cell Populations?
Brian Cox
Teledyne Scientific Co LLC, Thousand Oaks, California
Friday October 16th, 3:00PM
MEC 341, Mechanical Engineering Building
Refreshments at 2:30PM in MAE Faculty Lounge, MEC 305
The popular view in biological science is that the spatial arrangement of cells in organs results from the response of the cells to chemical signals, whose presence can be traced back to the genetic code. For many aspects of morphogenesis, this paradigm may ultimately yield a continuous account of the development of many aspects of organ morphology from the embryonic stage all the way through to maturity. However, in numerous cases, triggering features of organ morphology in a large population of cells that is spatially uniform at some epoch in development requires the breaking of symmetry, for which no obvious mechanism based purely on chemical signaling exists. Morphogenesis may be correlated with chemical gradients, but why do the chemical gradients arise in the first place? We propose here that the primitive signal that breaks symmetry and triggers morphological development in at least several cases is strain stimulus. Furthermore, the patterning of morphology by strain stimulus can only be understood by considering the interactions a large population (thousands or millions) of cells, whereas the considerable literature on strain stimulus predominantly addresses the chemical and mechanical behavior of individual cells.
Three examples will be discussed. The first two demonstrate for the first time the existence of a strain-induced ordering transition in cell populations, i.e., a strain-induced transition in the spatial patterns they form. One is based on a theoretical analysis of the microstructure of dental enamel, where the ordering transition occurs over the cusp of the tooth during the migration of ameloblasts during amelogenesis. The second is an experimental result recently obtained for a large population of smooth muscle cells subjected to strain cycling in vitro, where the cells are seen to spontaneously re-organize into rows under strain, whereas they lie randomly in space without strain stimulus. The last example is a theory of the formation of network structures in organs, e.g., nervous networks in the gut or vascular capillary networks.