Optimal-Transportation Meshfree. for Fluid and Plastic Flows
|
|
|
- Howard Hines
- 5 years ago
- Views:
Transcription
1 Optimal-Transportation Meshfree Approximation Schemes for Fluid and Plastic Flows M. Ortiz Bo Li, Feras Habbal California Institute of Technology Barcelona, September 3, 2009
2 Objective: Hypervelocity impact Hypervelocity impact is of interest to a broad scientific community: Micrometeorite shields, geological l impact cratering Hypervelocity impact test of multi-layer micrometeorite shield (Ernst-Mach Institut, Germany) The International Space Station uses 200 different types of shield to protect it from impacts
3 Simulation requirements Hypervelocity impact: Grand challenge in scientific computing Main simulation requirements: Hypersonic dynamics, high-energy density (HED) Multiphase flows (solid, fluid, gas, plasma) Free boundaries + contact Fracture, fragmentation, perforation Complex material phenomena: HED/extreme conditions Ionization, excited states, plasma Multiphase equation of state, transport Viscoplasticity, thermomechanical coupling Brittle/ductile fracture, fragmentation...
4 Optimal-Transportation Meshfree (OTM) Time integration (OT): Optimal transportation methods: Geometrically exact, discrete Lagrangians Discrete mechanics, variational time integrators: Symplecticity, exact conservation properties Variational material updates, inelasticity: Incremental variational a a structure u Spatial discretization (M): Max-ent meshfree nodal interpolation: Kronecker-delta property at boundary Material-point sampling: Numerical quadrature, material history Dynamic reconnection, on-the-fly adaptivity
5 Optimal transportation theory Gaspard Monge Beaune (1746), Paris (1818) "Sur la théorie des déblais et des remblais" (Mém. de l acad. de Paris, 1781) Leonid V. Kantorovich Saint Petersbourg (1912) Moscow (1986) Nobel Prize in Economics (1975)
6 Mass flows Optimal transportation Flow of non-interacting particles in Initial and final conditions:
7 Mass flows Optimal transportation Benamou & Brenier minimum principle: Reformulation as optimal transportation problem: McCann s interpolation:
8 Euler flows Optimal transportation Semidiscrete action: inertia internal energy Discrete Euler-Lagrange equations: geometrically exact mass conservation!
9 Optimal-Transportation Meshfree (OTM) Optimal transportation theory is a useful tool for generating geometrically-exact exact discrete Lagrangians for flow problems Inertial part of discrete Lagrangian measures distance between consecutive mass densities (in sense of Wasserstein) Discrete Hamilton principle i of stationary ti action: Variational time integration scheme: Symplectic, time reversible Exact conservation properties (linear and angular momenta, energy) Strong variational i convergence (in sense of Γ- convergence, non-linear phase error analysis)
10 nodal points: material points OTM Spatial discretization Question: How can we reconstruct from nodal coordinates?
11 OTM Max-ent interpolation Problem: Reconstruct function from nodal sample so that: Reconstruction is least biased Reconstruction is most local Optimal shape functions (Arroyo & MO, IJNME, 2006): shape function width information entropy
12 OTM Max-ent interpolation
13 OTM Max-ent interpolation Max-ent interpolation is smooth, meshfree Finite-element interpolation is recovered in the limit of β Rapid decay, short range Monotonicity, maximum principle Good mass lumping properties Kronecker-delta property at the boundary: Displacement boundary conditions Compatibility with finite elements
14 nodal points: material points OTM Spatial discretization
15 nodal points: material points OTM Spatial discretization
16 OTM Spatial discretization Np = local neighborhood of material point COMPLAS p X
17 nodal points: material points OTM Spatial discretization Max-ent interpolation at node p determined by nodes in its local environment Np Local environments determined on-the-fly by range searches Local environments evolve continuously during flow (dynamic reconnection) Dynamic reconnection requires no remapping of history variables!
18 OTM Flow chart (i) Explicit nodal coordinate update: (ii) Material point update: position: deformation: volume: density: (iii) Constitutive update at material points (iv) Reconnect nodal and material points (range searches), recompute max-ext shape functions
19 OTM Riemann problem (Kg/m 3 ) density 1 error no orm density L convergence rate ~ 1 position (m) computed vs. exact wave structure mesh size (h) density convergence (L 1 norm)
20 OTM Shock tube problem Shock tube problem velocity snapshots
21 OTM Shock tube problem vel ocity L 2 error nor m convergence rate ~ 1 den nsity L 1 error norm convergence rate ~ 1 mesh size (h) mesh size (h) velocity convergence (L 2 norm) density convergence (L 1 norm) Shock tube problem convergence plots
22 OTM Taylor anvil test t=0 t=7.5 µs copper 750 m/s t=15 µs t=28 µs
23 OTM Taylor anvil test t=0 t=7.5 µs copper 750 m/s t=15 µs t=28 µs
24 OTM Bouncing balloons FE membrane (rubber, Kapton) OTM fluid (water, air)
25 OTM Bouncing balloons FE membrane (rubber, Kapton) OTM fluid (water, air)
26 OTM Bouncing balloons FE membrane (rubber, Kapton) OTM fluid (water, air)
27 OTM Bouncing balloons FE membrane (rubber, Kapton) OTM fluid (water, air)
28 OTM Terminal ballistics steel projectile 1500 m/s aluminum plate
29 OTM Terminal ballistics steel projectile 1500 m/s aluminum plate
30 OTM Summary and outlook Optimum-Transportation-Meshfree method: OT is a useful tool for generating geometrically- exact discrete Lagrangians for flow problems Max-ent approach supplies an efficient meshfree, continuously adaptive, remapping-free, FEcompatible, interpolation scheme Material-point sampling effectively addresses the issues of numerical quadrature, history variables Extensions include: Contact (seizing contact for free!) Fracture and fragmentation (provably convergent) Outlook: Parallel implementation, UQ
Optimal-Transportation Meshfree Approximation Schemes for Fluid and Plastic Flows
Optimal-Transportation Meshfree Approximation Schemes for Fluid and Plastic Flows M. Ortiz California Institute of Technology In collaboration with: Bo Li, Feras Habbal (Caltech), B. Schmidt (TUM), A.
Optimal-Transportation Meshfree Approximation Schemes
Optimal-Transportation Meshfree Approximation Schemes M. Ortiz California Institute of Technology In collaboration with: Bo Li (Caltech), B. Schmidt (Augsburg), Mini-Workshop on Variational Methods for
HIGH ORDER DISCONTINUOUS GALERKIN METHODS FOR 1D PARABOLIC EQUATIONS. Ahmet İzmirlioğlu. BS, University of Pittsburgh, 2004
HIGH ORDER DISCONTINUOUS GALERKIN METHODS FOR D PARABOLIC EQUATIONS by Ahmet İzmirlioğlu BS, University of Pittsburgh, 24 Submitted to the Graduate Faculty of Art and Sciences in partial fulfillment of
Project 1: Double Pendulum
Final Projects Introduction to Numerical Analysis II http://www.math.ucsb.edu/ atzberg/winter2009numericalanalysis/index.html Professor: Paul J. Atzberger Due: Friday, March 20th Turn in to TA s Mailbox:
University of Illinois at Urbana-Champaign College of Engineering
University of Illinois at Urbana-Champaign College of Engineering CEE 570 Finite Element Methods (in Solid and Structural Mechanics) Spring Semester 2014 Quiz #1 March 3, 2014 Name: SOLUTION ID#: PS.:
Partial Differential Equations of Fluid Dynamics
Partial Differential Equations of Fluid Dynamics Ville Vuorinen,D.Sc.(Tech.) 1 1 Department of Energy Technology, Internal Combustion Engine Research Group Department of Energy Technology Outline Introduction
AUTODYN. Explicit Software for Nonlinear Dynamics. Jetting Tutorial. Revision
AUTODYN Explicit Software for Nonlinear Dynamics Jetting Tutorial Revision 4.3 www.century-dynamics.com AUTODYN is a trademark of Century Dynamics, Inc. Copyright 2005 Century Dynamics Inc. All Rights
As an example, we consider the following PDE with one variable; Finite difference method is one of numerical method for the PDE.
7. Introduction to the numerical integration of PDE. As an example, we consider the following PDE with one variable; Finite difference method is one of numerical method for the PDE. Accuracy requirements
Provisional Application for United States Patent
Provisional Application for United States Patent TITLE: Unified Differential Economics INVENTORS: Xiaoling Zhao, Amy Abbasi, Meng Wang, John Wang USPTO Application Number: 6235 2718 8395 BACKGROUND Capital
Monte Carlo Methods in Finance
Monte Carlo Methods in Finance Peter Jackel JOHN WILEY & SONS, LTD Preface Acknowledgements Mathematical Notation xi xiii xv 1 Introduction 1 2 The Mathematics Behind Monte Carlo Methods 5 2.1 A Few Basic
Unblinded Sample Size Re-Estimation in Bioequivalence Trials with Small Samples. Sam Hsiao, Cytel Lingyun Liu, Cytel Romeo Maciuca, Genentech
Unblinded Sample Size Re-Estimation in Bioequivalence Trials with Small Samples Sam Hsiao, Cytel Lingyun Liu, Cytel Romeo Maciuca, Genentech Goal Describe simple adjustment to CHW method (Cui, Hung, Wang
A local RBF method based on a finite collocation approach
Boundary Elements and Other Mesh Reduction Methods XXXVIII 73 A local RBF method based on a finite collocation approach D. Stevens & H. Power Department of Mechanical Materials and Manufacturing Engineering,
Statistical and Computational Inverse Problems with Applications Part 5B: Electrical impedance tomography
Statistical and Computational Inverse Problems with Applications Part 5B: Electrical impedance tomography Aku Seppänen Inverse Problems Group Department of Applied Physics University of Eastern Finland
EC316a: Advanced Scientific Computation, Fall Discrete time, continuous state dynamic models: solution methods
EC316a: Advanced Scientific Computation, Fall 2003 Notes Section 4 Discrete time, continuous state dynamic models: solution methods We consider now solution methods for discrete time models in which decisions
Markov Decision Process
Markov Decision Process Human-aware Robotics 2018/02/13 Chapter 17.3 in R&N 3rd Ø Announcement: q Slides for this lecture are here: http://www.public.asu.edu/~yzhan442/teaching/cse471/lectures/mdp-ii.pdf
CS 188: Artificial Intelligence
CS 188: Artificial Intelligence Markov Decision Processes Dan Klein, Pieter Abbeel University of California, Berkeley Non-Deterministic Search 1 Example: Grid World A maze-like problem The agent lives
Investigation of Interaction between Guidewire and Native Vessel Using Finite Element Analysis
Visit the SIMULIA Resource Center for more customer examples. Investigation of Interaction between Guidewire and Native Vessel Using Finite Element Analysis Atul Gupta 1, Subham Sett 2, Srinivasan Varahoor
Monte Carlo Methods (Estimators, On-policy/Off-policy Learning)
1 / 24 Monte Carlo Methods (Estimators, On-policy/Off-policy Learning) Julie Nutini MLRG - Winter Term 2 January 24 th, 2017 2 / 24 Monte Carlo Methods Monte Carlo (MC) methods are learning methods, used
Scenario reduction and scenario tree construction for power management problems
Scenario reduction and scenario tree construction for power management problems N. Gröwe-Kuska, H. Heitsch and W. Römisch Humboldt-University Berlin Institute of Mathematics Page 1 of 20 IEEE Bologna POWER
A Study on Numerical Solution of Black-Scholes Model
Journal of Mathematical Finance, 8, 8, 37-38 http://www.scirp.org/journal/jmf ISSN Online: 6-44 ISSN Print: 6-434 A Study on Numerical Solution of Black-Scholes Model Md. Nurul Anwar,*, Laek Sazzad Andallah
astro-ph/ Oct 1998
The Density s of Supersonic Random Flows By A K E N O R D L U N D ;2 AND P A O L O P A D O A N 3 Theoretical Astrophysics Center, Juliane Maries Vej 30, 200 Copenhagen, Denmark 2 Astronomical Observatory
Strong Stability Preserving Time Discretizations
Strong Stability Preserving Time Discretizations Sigal Gottlieb University of Massachusetts Dartmouth AFOSR Computational Math Program Review August 2015 SSP time stepping August2015 1 / 33 Past and Current
Schémas implicites ou explicites sur mailles décalées pour Euler et Navier-Stokes compressible
Schémas implicites ou explicites sur mailles décalées pour Euler et Navier-Stokes compressible R. Herbin, with T. Gallouët, L. Gastaldo, W. Kheriji, J.-C. Latché, T.T. Nguyen Université de Provence Institut
Chapter 5 Finite Difference Methods. Math6911 W07, HM Zhu
Chapter 5 Finite Difference Methods Math69 W07, HM Zhu References. Chapters 5 and 9, Brandimarte. Section 7.8, Hull 3. Chapter 7, Numerical analysis, Burden and Faires Outline Finite difference (FD) approximation
Using Fiber Reinforced Polymer to Restore Deteriorated Structural Members
International Journal of Material and Mechanical Engineering, 01, 1: 1-7 - 1 - Published Online April 01 http://www.ijm-me.org Using Fiber Reinforced Polymer to Restore Deteriorated Structural Members
Monte Carlo Methods in Financial Engineering
Paul Glassennan Monte Carlo Methods in Financial Engineering With 99 Figures
Boundary conditions for options
Boundary conditions for options Boundary conditions for options can refer to the non-arbitrage conditions that option prices has to satisfy. If these conditions are broken, arbitrage can exist. to the
Chapter 4: Commonly Used Distributions. Statistics for Engineers and Scientists Fourth Edition William Navidi
Chapter 4: Commonly Used Distributions Statistics for Engineers and Scientists Fourth Edition William Navidi 2014 by Education. This is proprietary material solely for authorized instructor use. Not authorized
(Refer Slide Time: 01:17)
Computational Electromagnetics and Applications Professor Krish Sankaran Indian Institute of Technology Bombay Lecture 06/Exercise 03 Finite Difference Methods 1 The Example which we are going to look
Monte Carlo Methods in Structuring and Derivatives Pricing
Monte Carlo Methods in Structuring and Derivatives Pricing Prof. Manuela Pedio (guest) 20263 Advanced Tools for Risk Management and Pricing Spring 2017 Outline and objectives The basic Monte Carlo algorithm
Finite Element Method
In Finite Difference Methods: the solution domain is divided into a grid of discrete points or nodes the PDE is then written for each node and its derivatives replaced by finite-divided differences In
Overnight Index Rate: Model, calibration and simulation
Research Article Overnight Index Rate: Model, calibration and simulation Olga Yashkir and Yuri Yashkir Cogent Economics & Finance (2014), 2: 936955 Page 1 of 11 Research Article Overnight Index Rate: Model,
Applied Stochastic Processes and Control for Jump-Diffusions
Applied Stochastic Processes and Control for Jump-Diffusions Modeling, Analysis, and Computation Floyd B. Hanson University of Illinois at Chicago Chicago, Illinois siam.. Society for Industrial and Applied
Hedging Derivative Securities with VIX Derivatives: A Discrete-Time -Arbitrage Approach
Hedging Derivative Securities with VIX Derivatives: A Discrete-Time -Arbitrage Approach Nelson Kian Leong Yap a, Kian Guan Lim b, Yibao Zhao c,* a Department of Mathematics, National University of Singapore
Dynamic Response of Jackup Units Re-evaluation of SNAME 5-5A Four Methods
ISOPE 2010 Conference Beijing, China 24 June 2010 Dynamic Response of Jackup Units Re-evaluation of SNAME 5-5A Four Methods Xi Ying Zhang, Zhi Ping Cheng, Jer-Fang Wu and Chee Chow Kei ABS 1 Main Contents
INTERMEDIATE MACROECONOMICS
INTERMEDIATE MACROECONOMICS LECTURE 6 Douglas Hanley, University of Pittsburgh CONSUMPTION AND SAVINGS IN THIS LECTURE How to think about consumer savings in a model Effect of changes in interest rate
Lecture 4. Finite difference and finite element methods
Finite difference and finite element methods Lecture 4 Outline Black-Scholes equation From expectation to PDE Goal: compute the value of European option with payoff g which is the conditional expectation
Martingale Optimal Transport and Robust Hedging
Martingale Optimal Transport and Robust Hedging Ecole Polytechnique, Paris Angers, September 3, 2015 Outline Optimal Transport and Model-free hedging The Monge-Kantorovitch optimal transport problem Financial
Math 416/516: Stochastic Simulation
Math 416/516: Stochastic Simulation Haijun Li lih@math.wsu.edu Department of Mathematics Washington State University Week 13 Haijun Li Math 416/516: Stochastic Simulation Week 13 1 / 28 Outline 1 Simulation
6. Numerical methods for option pricing
6. Numerical methods for option pricing Binomial model revisited Under the risk neutral measure, ln S t+ t ( ) S t becomes normally distributed with mean r σ2 t and variance σ 2 t, where r is 2 the riskless
Dynamic Hedging in a Volatile Market
Dynamic in a Volatile Market Thomas F. Coleman, Yohan Kim, Yuying Li, and Arun Verma May 27, 1999 1. Introduction In financial markets, errors in option hedging can arise from two sources. First, the option
Introduction to Numerical PDEs
Introduction to Numerical PDEs Varun Shankar February 16, 2016 1 Introduction In this chapter, we will introduce a general classification scheme for linear second-order PDEs, and discuss when they have
1. What is Implied Volatility?
Numerical Methods FEQA MSc Lectures, Spring Term 2 Data Modelling Module Lecture 2 Implied Volatility Professor Carol Alexander Spring Term 2 1 1. What is Implied Volatility? Implied volatility is: the
CS 774 Project: Fall 2009 Version: November 27, 2009
CS 774 Project: Fall 2009 Version: November 27, 2009 Instructors: Peter Forsyth, paforsyt@uwaterloo.ca Office Hours: Tues: 4:00-5:00; Thurs: 11:00-12:00 Lectures:MWF 3:30-4:20 MC2036 Office: DC3631 CS
1 Consumption and saving under uncertainty
1 Consumption and saving under uncertainty 1.1 Modelling uncertainty As in the deterministic case, we keep assuming that agents live for two periods. The novelty here is that their earnings in the second
MODELING COMMODITY PRICES (COPPER)
MODELING COMMODITY PRICES (COPPER) U. (WITH ROGER J-B WETS) UNIVERSIDAD DE CHILE & UNIVERSITY OF CALIFORNIA, DAVIS OUTLINE INTRODUCTION MODELS XIII ISCP, Bergamo 2013 1 INTRODUCTION XIII ISCP, Bergamo
Robust Portfolio Decisions for Financial Institutions
Robust Portfolio Decisions for Financial Institutions Ioannis Baltas 1,3, Athanasios N. Yannacopoulos 2,3 & Anastasios Xepapadeas 4 1 Department of Financial and Management Engineering University of the
Analyzing Pricing and Production Decisions with Capacity Constraints and Setup Costs
Erasmus University Rotterdam Bachelor Thesis Logistics Analyzing Pricing and Production Decisions with Capacity Constraints and Setup Costs Author: Bianca Doodeman Studentnumber: 359215 Supervisor: W.
MATH4143: Scientific Computations for Finance Applications Final exam Time: 9:00 am - 12:00 noon, April 18, Student Name (print):
MATH4143 Page 1 of 17 Winter 2007 MATH4143: Scientific Computations for Finance Applications Final exam Time: 9:00 am - 12:00 noon, April 18, 2007 Student Name (print): Student Signature: Student ID: Question
Lecture 2: Making Good Sequences of Decisions Given a Model of World. CS234: RL Emma Brunskill Winter 2018
Lecture 2: Making Good Sequences of Decisions Given a Model of World CS234: RL Emma Brunskill Winter 218 Human in the loop exoskeleton work from Steve Collins lab Class Structure Last Time: Introduction
King s College London
King s College London University Of London This paper is part of an examination of the College counting towards the award of a degree. Examinations are governed by the College Regulations under the authority
Trust Region Methods for Unconstrained Optimisation
Trust Region Methods for Unconstrained Optimisation Lecture 9, Numerical Linear Algebra and Optimisation Oxford University Computing Laboratory, MT 2007 Dr Raphael Hauser (hauser@comlab.ox.ac.uk) The Trust
Reduced models for sparse grid discretizations of the multi-asset Black-Scholes equation
Reduced models for sparse grid discretizations of the multi-asset Black-Scholes equation The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters.
Scenario tree generation for stochastic programming models using GAMS/SCENRED
Scenario tree generation for stochastic programming models using GAMS/SCENRED Holger Heitsch 1 and Steven Dirkse 2 1 Humboldt-University Berlin, Department of Mathematics, Germany 2 GAMS Development Corp.,
EMH vs. Phenomenological models. Enrico Scalas (DISTA East-Piedmont University)
EMH vs. Phenomenological models Enrico Scalas (DISTA East-Piedmont University) www.econophysics.org Summary Efficient market hypothesis (EMH) - Rational bubbles - Limits and alternatives Phenomenological
MATH6911: Numerical Methods in Finance. Final exam Time: 2:00pm - 5:00pm, April 11, Student Name (print): Student Signature: Student ID:
MATH6911 Page 1 of 16 Winter 2007 MATH6911: Numerical Methods in Finance Final exam Time: 2:00pm - 5:00pm, April 11, 2007 Student Name (print): Student Signature: Student ID: Question Full Mark Mark 1
Contents Critique 26. portfolio optimization 32
Contents Preface vii 1 Financial problems and numerical methods 3 1.1 MATLAB environment 4 1.1.1 Why MATLAB? 5 1.2 Fixed-income securities: analysis and portfolio immunization 6 1.2.1 Basic valuation of
Lecture 17: More on Markov Decision Processes. Reinforcement learning
Lecture 17: More on Markov Decision Processes. Reinforcement learning Learning a model: maximum likelihood Learning a value function directly Monte Carlo Temporal-difference (TD) learning COMP-424, Lecture
Science China Information Sciences
A Simulator with Elastic Guidewire and Vascular for Minimally Invasive Vascular Surgery Xiaoran CHENG, Xiaoliang XIE, Guibin BIAN, Zengguang HOU, Shiqi LIU, and Zhanjie GAO The State Key Laboratory of
Decisional optimality in life reinsurance modeling
Decisional optimality in life reinsurance modeling IAA colloquium - Oslo 2015 Maxence Saunier maxence.saunier@aonbenfield.com 35 rue de la fédération, 75015 Paris, FRANCE Referents Arnaud Chevalier Frédéric
Symmetric Game. In animal behaviour a typical realization involves two parents balancing their individual investment in the common
Symmetric Game Consider the following -person game. Each player has a strategy which is a number x (0 x 1), thought of as the player s contribution to the common good. The net payoff to a player playing
Macroeconomic Analysis and Parametric Control of Economies of the Customs Union Countries Based on the Single Global Multi- Country Model
Macroeconomic Analysis and Parametric Control of Economies of the Customs Union Countries Based on the Single Global Multi- Country Model Abdykappar A. Ashimov, Yuriy V. Borovskiy, Nikolay Yu. Borovskiy
Infinitely Many Solutions to the Black-Scholes PDE; Physics Point of View
CBS 2018-05-23 1 Infinitely Many Solutions to the Black-Scholes PDE; Physics Point of View 서울대학교물리학과 2018. 05. 23. 16:00 (56 동 106 호 ) 최병선 ( 경제학부 ) 최무영 ( 물리천문학부 ) CBS 2018-05-23 2 Featuring: 최병선 Pictures
BROWNIAN MOTION Antonella Basso, Martina Nardon
BROWNIAN MOTION Antonella Basso, Martina Nardon basso@unive.it, mnardon@unive.it Department of Applied Mathematics University Ca Foscari Venice Brownian motion p. 1 Brownian motion Brownian motion plays
Models of the ocean: which ocean?
Models of the ocean: which ocean? Anne Marie Treguier, CNRS, Laboratoire de Physique des Océans, Brest, France Part 1: Some general statements - ocean models - convergence of solution - diffusion equation
AEM Computational Fluid Dynamics Instructor: Dr. M. A. R. Sharif
AEM 620 - Computational Fluid Dynamics Instructor: Dr. M. A. R. Sharif Numerical Solution Techniques for 1-D Parabolic Partial Differential Equations: Transient Flow Problem by Parshant Dhand September
Neural Network Prediction of Stock Price Trend Based on RS with Entropy Discretization
2017 International Conference on Materials, Energy, Civil Engineering and Computer (MATECC 2017) Neural Network Prediction of Stock Price Trend Based on RS with Entropy Discretization Huang Haiqing1,a,
Self-organized criticality on the stock market
Prague, January 5th, 2014. Some classical ecomomic theory In classical economic theory, the price of a commodity is determined by demand and supply. Let D(p) (resp. S(p)) be the total demand (resp. supply)
Modeling of Price. Ximing Wu Texas A&M University
Modeling of Price Ximing Wu Texas A&M University As revenue is given by price times yield, farmers income risk comes from risk in yield and output price. Their net profit also depends on input price, but
A model reduction approach to numerical inversion for parabolic partial differential equations
A model reduction approach to numerical inversion for parabolic partial differential equations Liliana Borcea Alexander V. Mamonov 2, Vladimir Druskin 3, Mikhail Zaslavsky 3 University of Michigan, Ann
Why do Larger Firms Pay Executives More for Performance?
Why do Larger Firms Pay Executives More for Performance? Performance-based versus Market-based incentives QUML Economics and Finance Workshop for PhD and Post-doc Students Bo Hu June 27, 2018 Tinbergen
Eco504 Fall 2010 C. Sims CAPITAL TAXES
Eco504 Fall 2010 C. Sims CAPITAL TAXES 1. REVIEW: SMALL TAXES SMALL DEADWEIGHT LOSS Static analysis suggests that deadweight loss from taxation at rate τ is 0(τ 2 ) that is, that for small tax rates the
Partitioned Analysis of Coupled Systems
Partitioned Analysis of Coupled Systems Hermann G. Matthies, Rainer Niekamp, Jan Steindorf Technische Universität Braunschweig Brunswick, Germany wire@tu-bs.de http://www.wire.tu-bs.de Coupled Problems
Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?
DOI 0.007/s064-006-9073-z ORIGINAL PAPER Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function? Jules H. van Binsbergen Michael W. Brandt Received:
Fast and accurate pricing of discretely monitored barrier options by numerical path integration
Comput Econ (27 3:143 151 DOI 1.17/s1614-7-991-5 Fast and accurate pricing of discretely monitored barrier options by numerical path integration Christian Skaug Arvid Naess Received: 23 December 25 / Accepted:
On the use of time step prediction
On the use of time step prediction CODE_BRIGHT TEAM Sebastià Olivella Contents 1 Introduction... 3 Convergence failure or large variations of unknowns... 3 Other aspects... 3 Model to use as test case...
Economics 2010c: Lecture 4 Precautionary Savings and Liquidity Constraints
Economics 2010c: Lecture 4 Precautionary Savings and Liquidity Constraints David Laibson 9/11/2014 Outline: 1. Precautionary savings motives 2. Liquidity constraints 3. Application: Numerical solution
Package multiassetoptions
Package multiassetoptions February 20, 2015 Type Package Title Finite Difference Method for Multi-Asset Option Valuation Version 0.1-1 Date 2015-01-31 Author Maintainer Michael Eichenberger
,,, be any other strategy for selling items. It yields no more revenue than, based on the
ONLINE SUPPLEMENT Appendix 1: Proofs for all Propositions and Corollaries Proof of Proposition 1 Proposition 1: For all 1,2,,, if, is a non-increasing function with respect to (henceforth referred to as
MATH60082 Example Sheet 6 Explicit Finite Difference
MATH68 Example Sheet 6 Explicit Finite Difference Dr P Johnson Initial Setup For the explicit method we shall need: All parameters for the option, such as X and S etc. The number of divisions in stock,
A simple wealth model
Quantitative Macroeconomics Raül Santaeulàlia-Llopis, MOVE-UAB and Barcelona GSE Homework 5, due Thu Nov 1 I A simple wealth model Consider the sequential problem of a household that maximizes over streams
Energy Systems under Uncertainty: Modeling and Computations
Energy Systems under Uncertainty: Modeling and Computations W. Römisch Humboldt-University Berlin Department of Mathematics www.math.hu-berlin.de/~romisch Systems Analysis 2015, November 11 13, IIASA (Laxenburg,
Modeling Capital Market with Financial Signal Processing
Modeling Capital Market with Financial Signal Processing Jenher Jeng Ph.D., Statistics, U.C. Berkeley Founder & CTO of Harmonic Financial Engineering, www.harmonicfinance.com Outline Theory and Techniques
Lecture outline W.B.Powell 1
Lecture outline What is a policy? Policy function approximations (PFAs) Cost function approximations (CFAs) alue function approximations (FAs) Lookahead policies Finding good policies Optimizing continuous
Conformal Invariance of the Exploration Path in 2D Critical Bond Percolation in the Square Lattice
Conformal Invariance of the Exploration Path in 2D Critical Bond Percolation in the Square Lattice Chinese University of Hong Kong, STAT December 12, 2012 (Joint work with Jonathan TSAI (HKU) and Wang
Well-balanced schemes for the Euler equations with gravitation
Well-balanced schemes for the Euler equations with gravitation Roger Käppeli Joint work with S. Mishra Outline Introduction Well-balanced scheme for HydroStatic Equilibrium (HSE) First order Second order
Trading Financial Market s Fractal behaviour
Trading Financial Market s Fractal behaviour by Solon Saoulis CEO DelfiX ltd. (delfix.co.uk) Introduction In 1975, the noted mathematician Benoit Mandelbrot coined the term fractal (fragment) to define
CS 343: Artificial Intelligence
CS 343: Artificial Intelligence Markov Decision Processes II Prof. Scott Niekum The University of Texas at Austin [These slides based on those of Dan Klein and Pieter Abbeel for CS188 Intro to AI at UC
A numerical analysis of the monetary aspects of the Japanese economy: the cash-in-advance approach
Applied Financial Economics, 1998, 8, 51 59 A numerical analysis of the monetary aspects of the Japanese economy: the cash-in-advance approach SHIGEYUKI HAMORI* and SHIN-ICHI KITASAKA *Faculty of Economics,
Numerical schemes for SDEs
Lecture 5 Numerical schemes for SDEs Lecture Notes by Jan Palczewski Computational Finance p. 1 A Stochastic Differential Equation (SDE) is an object of the following type dx t = a(t,x t )dt + b(t,x t
A model reduction approach to numerical inversion for parabolic partial differential equations
A model reduction approach to numerical inversion for parabolic partial differential equations Liliana Borcea Alexander V. Mamonov 2, Vladimir Druskin 2, Mikhail Zaslavsky 2 University of Michigan, Ann
Research Article Exponential Time Integration and Second-Order Difference Scheme for a Generalized Black-Scholes Equation
Applied Mathematics Volume 1, Article ID 796814, 1 pages doi:11155/1/796814 Research Article Exponential Time Integration and Second-Order Difference Scheme for a Generalized Black-Scholes Equation Zhongdi
Macroeconomics and finance
Macroeconomics and finance 1 1. Temporary equilibrium and the price level [Lectures 11 and 12] 2. Overlapping generations and learning [Lectures 13 and 14] 2.1 The overlapping generations model 2.2 Expectations
Systems of Ordinary Differential Equations. Lectures INF2320 p. 1/48
Systems of Ordinary Differential Equations Lectures INF2320 p. 1/48 Lectures INF2320 p. 2/48 ystems of ordinary differential equations Last two lectures we have studied models of the form y (t) = F(y),
An Introduction to Stochastic Calculus
An Introduction to Stochastic Calculus Haijun Li lih@math.wsu.edu Department of Mathematics Washington State University Week 2-3 Haijun Li An Introduction to Stochastic Calculus Week 2-3 1 / 24 Outline
(Incomplete) summary of the course so far
(Incomplete) summary of the course so far Lecture 9a, ECON 4310 Tord Krogh September 16, 2013 Tord Krogh () ECON 4310 September 16, 2013 1 / 31 Main topics This semester we will go through: Ramsey (check)
Hotelling Under Pressure. Soren Anderson (Michigan State) Ryan Kellogg (Michigan) Stephen Salant (Maryland)
Hotelling Under Pressure Soren Anderson (Michigan State) Ryan Kellogg (Michigan) Stephen Salant (Maryland) October 2015 Hotelling has conceptually underpinned most of the resource extraction literature
Topic 6. Introducing money
14.452. Topic 6. Introducing money Olivier Blanchard April 2007 Nr. 1 1. Motivation No role for money in the models we have looked at. Implicitly, centralized markets, with an auctioneer: Possibly open
AAEC 6524: Environmental Economic Theory and Policy Analysis. Outline. Introduction to Non-Market Valuation Property Value Models
AAEC 6524: Environmental Economic Theory and Policy Analysis to Non-Market Valuation Property s Klaus Moeltner Spring 2015 April 20, 2015 1 / 61 Outline 2 / 61 Quality-differentiated market goods Real
Lecture Quantitative Finance Spring Term 2015
and Lecture Quantitative Finance Spring Term 2015 Prof. Dr. Erich Walter Farkas Lecture 06: March 26, 2015 1 / 47 Remember and Previous chapters: introduction to the theory of options put-call parity fundamentals