## 401-4938-14L | ||

Professor(en):M. Soner |
Betreuer: | |

Vorlesung: |
Link zum KurskatalogSpring 2018 |
Webseite: |

Ziele:Goals are to achieve a deep understanding of 1. Dynamic programming approach to optimal control; 2. Several classes of important optimal control problems and their solutions. 3. To be able to use this models in engineering and economic modeling. |
Vorlesungslevel:D-ITET Master, Systems and Control specialization Supplementary Core Courses | |

Voraussetzungen:Basic knowledge of Brownian motion, stochastic differential equations and probability theory is needed. | ||

Inhalt:In this course, we develop the dynamic programming approach for the stochastic optimal control problems. The general approach will be described and several subclasses of problems will also be discussed in including: 1. Standard exit time problems; 2. Finite and infinite horizon problems; 3. Optimal stoping problems; 4. Singular problems; 5. Impulse control problems. After the general theory is developed, it will be applied to several classical problems including: 1. Linear quadratic regulator; 2. Merton problem for optimal investment and consumption; 3. Optimal dividend problem of (Jeanblanc and Shiryayev); 4. Finite fuel problem; 5. Utility maximization with transaction costs; 6. A deterministic differential game related to geometric flows. Textbook will be Controlled Markov Processes and Viscosity Solutions, 2nd edition, (W.H. Fleming and H.M. Soner) Springer-Verlag, (2005). And lecture notes will be provided. |
Dokumentation:Controlled Markov Processes and Viscosity Solutions, 2nd edition, (W.H. Fleming and H.M. Soner) Springer-Verlag, (2005). And lecture notes will be provided. |