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Diffusion Control

Here are the slides from Lectures

10_Diffusion Control

Please read Section 2.3 of the notes

Stochastic_Control_2020

 

Author appliedprobabilityPosted on March 9, 2020Categories MATH69122 Stochastic Control for Finance, UncategorizedLeave a comment on Diffusion Control

Stochastic Integration (a quick intro)

Here are the slides from Lectures

9_Stochastic Integration

Please read Section 2.2 of the notes

Stochastic_Control_2020

 

Author appliedprobabilityPosted on March 9, 2020March 9, 2020Categories MATH69122 Stochastic Control for Finance, UncategorizedLeave a comment on Stochastic Integration (a quick intro)

Continuous Time Dynamic Programming

Here are the slides from Lectures

8_Continuous Time Dynamic Programming

Please read Section 2.1 of the notes

Stochastic_Control_2020

 

Author appliedprobabilityPosted on March 9, 2020March 9, 2020Categories MATH69122 Stochastic Control for Finance, UncategorizedLeave a comment on Continuous Time Dynamic Programming

LQR and Kalman Filter

Here are the slides from Lectures

7_LQR_and_Kalman_Filter

Please read these notes [which will be later added to the main set of notes]:

LQR_PDF

 

Author appliedprobabilityPosted on February 27, 2020Categories MATH69122 Stochastic Control for Finance, UncategorizedLeave a comment on LQR and Kalman Filter

ODE method for Stochastic Approximation

We consider the Robbins-Monro update

and argue that this can be approximated by the o.d.e.:

Continue reading “ODE method for Stochastic Approximation”

Author appliedprobabilityPosted on February 27, 2020Categories UncategorizedLeave a comment on ODE method for Stochastic Approximation

Lyapunov Functions

Lyapunov functions are an extremely convenient device for proving that a dynamical system converges. We cover:

  • The Lyapunov argument
  • La Salle’s Invariance Principle
  • An Alternative argument for Convex Functions
  • Exponential Convergence Rates

Continue reading “Lyapunov Functions”

Author appliedprobabilityPosted on February 27, 2020Categories Control, Optimization1 Comment on Lyapunov Functions

Optimal Stopping

Here are the slides from Lectures

6_Optimal Stopping

Please read Section 1.6 from the notes:

Stochastic_Control_2020 [pdf]

Please attempt Ex53, Ex54, Ex56, Ex57.

Author appliedprobabilityPosted on February 17, 2020Categories UncategorizedLeave a comment on Optimal Stopping

Algorithms for MDPs

Here are the slides from Lectures

5_Algorithms for MDPs

Please read Section 1.5 from the notes:

Stochastic_Control_2020 [pdf]

Please attempt Ex39, 40 & 41 [if you can code], 42 and 43.

Author appliedprobabilityPosted on February 16, 2020Categories UncategorizedLeave a comment on Algorithms for MDPs

Infinite Time Horizon MDP

Here are the slides from Lectures

4_Infinite Time Horizon

Please read Section 1.4 from the notes:

Stochastic_Control_2020 [pdf]

Please attempt Ex35, Ex36, Ex37.

Author appliedprobabilityPosted on February 3, 2020February 17, 2020Categories UncategorizedLeave a comment on Infinite Time Horizon MDP

Markov Decision Processes

Here are the slides from Lectures

3_Markov Decision Processes [pdf]

Please read Section 1.3 from the notes:

Stochastic_Control_2020 [pdf]

Please attempt exercises Ex22, Ex23, Ex24, Ex25.

Author appliedprobabilityPosted on February 3, 2020February 3, 2020Categories UncategorizedLeave a comment on Markov Decision Processes

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