We consider the problem of sequentially investing in a set of stocks.
Experts and Bandits (non-stochastic)
- Weighted majority algorithm its variant for Bandit Problems.
More on Merton Portfolio Optimization
Merton Portfolio Optimization
We consider a specific diffusion control problem. We focus on setting where there is one risky asset and one riskless asset, though we will see that much of the analysis passes over to multiple assets.
Diffusion Control Problems
- The Hamilton-Jacobi-Bellman Equation.
- Heuristic derivation of the HJB equation.
- Davis-Varaiya Martingale Prinicple for Optimality
Stochastic Integration – a Heuristic view
Heuristic derivation of
- the Stochastic Integral
- Stochastic Differential Equations
- Ito’s Formula
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Continuous Time Dynamic Programs
- Continuous-time dynamic programs
- The HJB equation; a heuristic derivation; and proof of optimality.
Optimal Stopping
- Optimal Stopping Problems; One-Step-Look-Ahead Rule
- The Secretary Problem.
- Infinite Time Stopping
Algorithms for MDPs
- High level idea: Policy Improvement and Policy Evaluation.
- Value Iteration; Policy Iteration.
- Temporal Differences; Q-factors.
Infinite Time Horizon, MDP
- Positive Programming, Negative Programming & Discounted Programming.
- Optimality Conditions.
Applied Probability Notes 