PPT-Stochastic Calculus for Finance II

Steven E Shreve Chap 11 Introduction to Jump Process 財研二 范育誠 AGENDA 115 Stochastic Calculus for Jump Process 1151 ItoDoeblin Formula for One Jump Process 1152 ItoDoeblin Formula for Multiple Jump Process. N is the process noise or disturbance at time are IID with 0 is independent of with 0 Linear Quadratic Stochastic Control 52 brPage 3br Control policies statefeedback control 0 N called the control policy at time roughly speaking we choo adding it all up. Integral Calculus. 1. Goal. Compute the . signed. area . under some portion of an arbitrary curve. Integral Calculus. 2. Divide and Conquer. Integral Calculus. 3. Animatedly. Integral Calculus. Gradient Descent Methods. Jakub . Kone. čný. . (joint work with Peter . Richt. árik. ). University of Edinburgh. Introduction. Large scale problem setting. Problems are often structured. Frequently arising in machine learning. Part I: Multistage problems. Anupam. Gupta. Carnegie Mellon University. stochastic optimization. Question: . How to model uncertainty in the inputs?. data may not yet be available. obtaining exact data is difficult/expensive/time-consuming. Anupam. Gupta. Carnegie Mellon University. stochastic optimization. Question: . How to model uncertainty in the inputs?. data may not yet be available. obtaining exact data is difficult/expensive/time-consuming. How . do you know . how fast. You are going? . “well . how do you know. How fast you’re going. Right now,. At this very second?” . Push your friend so . that his/her . speed . changes. Try . AC 2311 C ** Calculus I ( 4 ) AC 2312 ** Calculus II ( 4 ) AC 2313 ** ( 4 ) HY 2048 C ** Physics for Engineers I ( 4 ) HY 2049 C ** Physics for Engineers II ( 4 ) AP 2302 ** Differential Newton & Leibniz. Summary. Calculus seems to demand some concept of the infinitesimal. Magnitude. New number. Or both?. But infinitesimals lack . clarity . Concepts that are not mathematical being used to interpret mathematics?.  . What is . λ-calculus ?. . “Lambda . calculus.  . is . a formal . system.  in . mathematical logic.  and computer science for expressing computation based on function abstraction and application using variable . The Return of the Infinitesimal?. So far on this course we’ve stayed close to mainstream mathematics.. In this final session we look at some more “fancy” material, much of it very recent.. These aren’t just techniques for doing complicated calculations – they represent new ways to think about geometry and continuity, and so they promise to raise some old philosophical questions. . Galerkin. Methods and Software. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.. How . do you know . how fast. You are going? . “well . how do you know. How fast you’re going. Right now,. At this very second?” . Push your friend so . that his/her . speed . changes. Try . "QFT methods in stochastic nonlinear dynamics". ZIF, 18-19 March, 2015. D. Volchenkov. The analysis of stochastic problems sometimes might be easier than that of nonlinear dynamics – at least, we could sometimes guess upon the asymptotic solutions.. Section 1.1. Functions and Change. Calculus, 7th edition, Hughes-Hallett et.al., Copyright 2017 by John Wiley & Sons, All Rights Reserved. Definition of a Function. A . function . is a rule that takes certain numbers as inputs and assigns to each a definite output number. The set of all input numbers is called the .