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401-4913-00L DR , MSC , NDS D-USYS , D-BAUG , D-MAVT , D-INFK , D-MTEC , D-MATH , D-BIOL , D-GESS , D-ITET , D-ARCH , D-CHAB

Stochastic Optimal Control with Applications in Finance

Lecturers: Prof. Dr. Philipp Schönbucher
VVZ CR n/a

Last Updated: 2026-02-05 15:14:57

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

Stochastic Optimal Control is concerned with the search for optimal strategies under uncertainty. In this lecture we will cover the most common approaches to the analysis and solution of stochastic optimisation problems and apply them to example problems in portfolio optimisation and option pricing. Besides the classical dynamic programming methods, we will also cover the more recently developed duality approaches which frequently admit a deeper insight into the structure of the problem at hand. The aim of this lecture is to enable the audience to understand and apply the most common methods of stochastic optimal control that are used in the recent literature on mathematical finance and financial economics. The aim of this lecture is to enable the students to understand methods of stochastic optimal control that are commonly used in mathematical finance and financial economics, and to apply these methods in their own research.

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 , MSC , NDS
Frequency
Yearly recurring

Examination

Type
no performance assessment

Course Components

Type Title Time & Place Hours
lecture Stochastic Optimal Control with Applications in Finance
  • Wed 13:15-15:00 (HG D 7.2)
2 h weekly

Offered In