The course covers the classical dynamic programming approach to controlled diffusion
systems, with applications to portfolio and consumption problems in continuous time
finance.
+ Motivation: the Merton problems; finite horizon terminal wealth and consumption objectives; infinite horizon consumption problem; direct solution of some examples;
+ Dynamic programming and the HJB equation; finite horizon controlled diffusion problem; dynamic programming principle; martingale optimality principle; verification theorem; examples; infinite horizon problem; dynamic programming
principle; martingale optimality principle; verification theorem; examples.
Reading List:
Huyen Pham [2] Continuous-time stochastic control and optimization with financial applications (Chapters 2 and 3) Springer 2009
Chris Rogers [3] Optimal Investment (Chapters 1 and 2) Springer 2013
TomasBjork [1] Arbitrage Theory in Continuous Time (Chapter 19) OUP 2009
Please note that e-book versions of many books in the reading lists can be found on SOLO and ORLO
systems, with applications to portfolio and consumption problems in continuous time
finance.
+ Motivation: the Merton problems; finite horizon terminal wealth and consumption objectives; infinite horizon consumption problem; direct solution of some examples;
+ Dynamic programming and the HJB equation; finite horizon controlled diffusion problem; dynamic programming principle; martingale optimality principle; verification theorem; examples; infinite horizon problem; dynamic programming
principle; martingale optimality principle; verification theorem; examples.
Reading List:
Huyen Pham [2] Continuous-time stochastic control and optimization with financial applications (Chapters 2 and 3) Springer 2009
Chris Rogers [3] Optimal Investment (Chapters 1 and 2) Springer 2013
TomasBjork [1] Arbitrage Theory in Continuous Time (Chapter 19) OUP 2009
Please note that e-book versions of many books in the reading lists can be found on SOLO and ORLO
- Lecturer: Hanqing Jin
Course term: Hilary
Course lecture information: 8 lectures
Course overview:
The course covers the classical dynamic programming approach to controlled diffusion systems, with applications to portfolio and consumption problems in continuous time finance.
Course synopsis:
Motivation: the Merton problems; finite horizon terminal wealth and consumption objectives; infinite horizon consumption problem; direct solution of some examples;
Dynamic programming and the HJB equation: finite horizon controlled diffusion problem; dynamic programming principle; martingale optimality principle; verification theorem; examples.
Infinite horizon problem: dynamic programming principle; martingale optimality principle; verification theorem; examples.
Optimal valuation and hedging in an incomplete market.
Dynamic programming and the HJB equation: finite horizon controlled diffusion problem; dynamic programming principle; martingale optimality principle; verification theorem; examples.
Infinite horizon problem: dynamic programming principle; martingale optimality principle; verification theorem; examples.
Optimal valuation and hedging in an incomplete market.