Synopsis for Stochastic Control and Dynamic Asset Allocation

Formulation of stochastic control problems
Maximum principle and backward stochastic dierential equation
Dynamic programming and Hamilton-Jacobi-Bellman (HJB) equation
Continuous-time market and self-nancing strategies
Arbitrage and fundamental theorem of asset pricing
Contingent claims and market completeness
Risk preferences and utility functions
Formulation of Merton problems and their solutions: primal and dual approaches

Further details: - Dr H Jin and Dr M Monoyios - 16 lectures - HT - Core course
Students will learn the important and powerful approach of stochastic control to solving dynamic asset allocation problems, primarily in the continuous time setting. The course consists of two core parts. In the first part, general stochastic control problems for diffusion processes are formulated and basic methodologies introduced. In the second part a continuous-time market together with its key properties is described, and the Merton expected utility maximization problems are solved by the stochastic control approach and the martingale (dual) approach. A course on stochastic analysis (covering the Ito calculus, martingale and stochastic differential equations) is a prerequisite. The assessment will be through a final examination,

The following books are good references:

1. [(1)] H. Pham, Continuous-time Stochastic Control and Optimization with Financial Applications, Springer 2009
2. [(2)] R. Merton, Continuous Time Finance, Blackwell 1990
3. [(3)] W. Fleming and M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer 2006
4. [(4)] J. Yong and X.Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer, New York, 1999.
5. [(4)] I Karatzas, lectures on the mathematics of finance. CRM Monograph Series, 8. American Mathematical Society, Providence, RI, 1997.