"A conservative is a man who believes that nothing should be done for the first time." - Alfred E. Wiggam

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STOCHASTIC OPTIMAL CONTROL AND INVESTMENT

"As soon as we have finished with the discrete-time theory, a crash-course in continuoustime diffusions (including stochastic integration and the notorious formula of Kiyoshi Ito) is in order to make the transition to continuous time smoother (and, in fact, possible)...

Special emphasis will be given to problems taken from the field of Mathematical Finance, but other fun problems will be considered as well...

Discrete-time models are nice because of the absence of technicalities that sometimes obscure the bigger picture. Continuous-time models are more elegant (also meaning: more delicate and technical to analyze) and sometimes allow for closed-form solutions, or in the absence of the latter for good approximating numerical methods. After the price has been paid of having to go through a rocky mathematical road we shall find that there are rewards in the end of the trip...

We model the preferences of an agent (who is you) via a utility function u — for the economist’s sake we usually assume that u is a concave and increasing function; for the mathematician’s sake we also assume it is smooth...

One can find an inter-relationship between the value functions v(t,x) and finally come up with a non-linear PDE called the Hamilton-Jacobi-Bellman (HJB) equation. Since its particularly scary first sight has sent many-a-nice people to the asylum, we refrain from presenting it at this point and leave the suspense for later...

Optimal consumption. There is a natural tendency of individuals to eat and spend money (rather foolishly, sometimes), instead of waiting for time T to consume the fruit of their investment (which would be even more foolish, admittedly)."


That was amusing, but I still don't know what "q(t) measures the discounted present value from t onwards of the profits from the marginal unit of investment at t" means... Stupid optimal control. Maybe I can form a model of optimal studying using it.

Hmm, I wonder if I should create 2 tags for economics - 'economics' and 'applied maths'.