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Stochastic Optimal Control with Applications in Finance
Last Updated: 2026-02-05 15:06:39
Abstract
In this lecture, the dynamical programming approach and the duality/martingale approach to stochastic optimal control are covered. The running example is the continuous-time consumption-investment problem.
Objective
Aim of this lecture is to enable the students to understand the methods of optimal control in continuous time and continuous state that are being used in the finance literature. Furthermore, they should be able to solve simple unconstrained and constrained optimal control problems themselves.
Content
In this course we give an introduction to the solution of optimisation problems under uncertainty, with a special focus on the solution of consumption / investment problems as they arise in mathematical finance. We present both the “classical” dynamic programming approach based upon Bellman’s equations and the more recent duality approach. Contents. Preliminaries: • Motivation in discrete time • Diffusion processes, Markov processes and generators • The portfolio choice / consumption-investment problem The Dynamic Programming Approach: • Discrete-time motivation • the Bellman equation • verification theorems • application to portfolio choice The Duality Approach • The duality approach • Connection to martingale measure • Examples: Optimal investment under constraints • Optimal stopping problems and American options • Monte-Carlo methods for American Options
General Information
- Language
- English
- Levels
- DR , NDS , MSC
- Frequency
- Yearly recurring
Examination
- Type
- no performance assessment
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Stochastic Optimal Control with Applications in Finance |
|
2 h weekly |
Offered In
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Master of Advanced Studies in Finance (For information and admission see . Abbreviations: O obligatory course; W elective course; E recommended or optional course)
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