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Category: MATH69122 Stochastic Control for Finance

More on Merton Portfolio Optimization

Continue reading “More on Merton Portfolio Optimization”

Author appliedprobabilityPosted on March 21, 2018April 11, 2018Categories Control, Control for Finance, MATH69122 Stochastic Control for Finance, Optimization, ProbabilityLeave a comment on 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.

Continue reading “Merton Portfolio Optimization”

Author appliedprobabilityPosted on March 9, 2018July 9, 2018Categories MATH69122 Stochastic Control for Finance1 Comment on Merton Portfolio Optimization

Diffusion Control Problems

  • The Hamilton-Jacobi-Bellman Equation.
  • Heuristic derivation of the HJB equation.
  • Davis-Varaiya Martingale Prinicple for Optimality

Continue reading “Diffusion Control Problems”

Author appliedprobabilityPosted on February 27, 2018February 28, 2018Categories Control, Control for Finance, MATH69122 Stochastic Control for Finance, ProbabilityLeave a comment on Diffusion Control Problems

Stochastic Integration – a Heuristic view


Heuristic derivation of

  • the Stochastic Integral
  • Stochastic Differential Equations
  • Ito’s Formula

 

Continue reading “Stochastic Integration – a Heuristic view”

Author appliedprobabilityPosted on February 27, 2018February 27, 2018Categories Control for Finance, MATH69122 Stochastic Control for Finance, ProbabilityLeave a comment on Stochastic Integration – a Heuristic view

Continuous Time Dynamic Programs

  •  Continuous-time dynamic programs
  • The HJB equation; a heuristic derivation; and proof of optimality.

Continue reading “Continuous Time Dynamic Programs”

Author appliedprobabilityPosted on February 19, 2018February 27, 2018Categories Control, Control for Finance, MATH69122 Stochastic Control for FinanceLeave a comment on Continuous Time Dynamic Programs

Optimal Stopping


  • Optimal Stopping Problems; One-Step-Look-Ahead Rule
  • The Secretary Problem.
  • Infinite Time Stopping

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Author appliedprobabilityPosted on February 19, 2018February 27, 2018Categories Control for Finance, MATH69122 Stochastic Control for Finance, OptimizationLeave a comment on Optimal Stopping

Algorithms for MDPs

  • High level idea: Policy Improvement and Policy Evaluation.
  • Value Iteration; Policy Iteration.
  • Temporal Differences; Q-factors.

Continue reading “Algorithms for MDPs”

Author appliedprobabilityPosted on February 7, 2018February 13, 2018Categories Control, Control for Finance, MATH69122 Stochastic Control for Finance, OptimizationLeave a comment on Algorithms for MDPs

Infinite Time Horizon, MDP

  • Positive Programming, Negative Programming & Discounted Programming.
  • Optimality Conditions.

Continue reading “Infinite Time Horizon, MDP”

Author appliedprobabilityPosted on February 7, 2018February 13, 2018Categories Control, Control for Finance, MATH69122 Stochastic Control for Finance, Optimization, ProbabilityLeave a comment on Infinite Time Horizon, MDP

Markov Decision Processes

  • Markov Decisions Problems; Bellman’s Equation; Two examples

Continue reading “Markov Decision Processes”

Author appliedprobabilityPosted on January 30, 2018February 6, 2018Categories Control, Control for Finance, MATH69122 Stochastic Control for FinanceLeave a comment on Markov Decision Processes

Markov Chains

  • A short introduction to Markov chains for dynamic programming
  • Definition, Markov Property, some Potential Theory.

Continue reading “Markov Chains”

Author appliedprobabilityPosted on January 30, 2018January 30, 2018Categories MATH69122 Stochastic Control for Finance, Probability1 Comment on Markov Chains

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