BEA514 Topics in Numerical Optimization

• Topics

  It is important to recognize that optimal action in the short run need not be optimal in the long run. This course presents various economics and management science programs from a dynamic perspective. Dynamic optimization, in a deterministic as well as stochastic setting, is an important research tool. To be able to deal with decision-making for real-world problems in economics and management science, the course has a focus on how to solve such optimization challenges in a computational setting, i.e., how to create numerical codes to determine the appropriate dynamic policies/decisions.

  Topics will be lectured in the following sequence:

  • General overview: Difference- and differential equations and stability analysis
  • General overview: Dynamic Optimal Control (OC)
  • Labs on first-order conditions (FOC) and open loop policies (in Matlab)
  • Dynamic programming (DP) and the Hamilton-Jacobi-Bellman (HJB) equation. A general discretization scheme for the HJB.
  • Infinite horizon stochastic optimization and the numerical probability approach.
  • Alternative numerical approaches

• Learning outcome

  After completion of the course, the candidates can:

  Knowledge

  • critically read and comprehend relevant scientific papers addressing dynamic optimization
  • formulate models and propose numerical solution procedures to dynamic challenges in economics and management science using the tools from optimal control theory
  • constructively approach deterministic and stochastic dynamic decision problems (not only limited to linear or linear-quadratic problems)
  • recognize numerical schemes producing decision variables (policies) in a feedback form and their applicability

  Skills

  • formulate and model operational management tasks and assign feasible numerical solution schemes
  • analyze and evaluate potential nonlinear, dynamic, and stochastic effects on economic quantities and resources and how they may depend on policy choices
  • design a probability-based discretization approach to Hamilton-Jacobi-Bellman (HJB) formulated dynamic decision problems to determine the value functions and optimal feedback policies for such projects

  General competence

  • manage complex interdisciplinary research projects involving optimal time-based decisions tasks in an operational setting
  • recognize the potential as well as the limitations of modern numerical solution approaches in the field, particularly the-curse-of-dimensionality and potential workarounds
  • communicate and bridge the gap between theoretical economic modeling and feasible real world approaches

• Teaching

  The course requires physical attendance at NHH. 

• Restricted access

  • PhD candidates at NHH
  • PhD candidates at Norwegian institutions
  • PhD candidates at other institutions
  • PhD candidates from the ENGAGE.EU alliance
  • Motivated master’s students may be admitted after application, but are subject to the approval from the course responsible on a case by case basis

• Recommended prerequisites

  Knowledge of medium-advanced calculus and some familiarity with differential equations in addition to introductory probability theory and vector algebra.

• Required prerequisites

  Knowledge of medium advanced calculus and some familiarity with differential equations and stability analysis and introductory probability theory and vector algebra.

• Credit reduction due to overlap

  None. 

• Compulsory Activity

  • Activity in class
  • 2-4 exercises/assignments during the course

  Compulsory activities (work requirements) are valid for one semester after the semester they were obtained.

• Assessment

  Individual term paper

  Re-take is offered the semester after the course was offered for students with valid compulsory activities (work requirements)

• Grading Scale

  Pass / Fail

• Computer tools

  The use of high-level programming in MatLab will be an integrated part of the course.

• Literature

  All topics in the course are covered by scientific papers and selected parts in the two advanced textbooks 

  • H. J. Kushner and Paul Dupois, Numerical Methods for Stochastic Control Problem in Continuous Time, Springer, 2001.
  • D. Bertsekas, Dynamical Programming in Deterministic and Stochastic Models, Prentice-Hall, NJ, 1987.

  The course material is "handouts" and web links in Canvas.

• This is an ENGAGE-course

  This course is offered to PhD candidates from the ENGAGE.EU alliance.