Applied Probability Notes

Merton Portfolio Optimization

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Please read Section 2.4 of the notes

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Please read Section 2.3 of the notes

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Please read Section 2.2 of the notes

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Please read Section 2.1 of the notes

Here are the slides from Lectures

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

We consider the Robbins-Monro update

$x_{n+1} = x_n +\alpha_n [g(x_n) + \epsilon_n]$

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

$\frac{dz}{d t} = g(z(t)).$

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