Re: Stochastic calculus in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg34438] Re: Stochastic calculus in Mathematica
- From: "Jason Cawley" <jasoncawley at prodigy.net>
- Date: Mon, 20 May 2002 04:21:30 -0400 (EDT)
- References: <ac2m3o$3jr$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I'm not sure if I understand, but I can take a stab at it. When you say a "volume process", I assume you mean a trading volume, not a physical 3-D volume. So you are looking for a stochastic "money flow" model, and then want a derivative presumably to look for turning points in a money flow measure. See, the two equations you've got, seen as independent, could give 2-D coordinates of the process (price and volume varying as an X and Y). Then "derivative" would be ambiguous - there would be a partial with respect to volume and a partial with respect to price as well as a total derivative. But the money flow measure is just a straight product of that X and Y (right?), not the 2-D map of independent variations in price and volume. Then what you want would seem to be - take the first and integrate with respect to time, take the second and integrate with respect to time, take the product of the two. That is your total money flow measure. MF = (Integrate [dI, t] * Integrate [dP, t]) You need to put the brownian motion terms in terms of time before you can integrate them, because the dependence of each part of the expression on t has to be explicit. When you have the money flow measure expression, you can differentiate it with respect to any of the variables you care to look at, searching for extrema of the expression with respect to this or that. I hope this helps. Sincerely, Jason Cawley