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Fix this economy model?

philipp.sas Scneider
Posted 10 years ago

Dear all. Im desperately looking for Help. My capacities in Wolfram aren't the biggest and I'm trying to get my Model to run. Can someone Help me? ~ Greetings Philipp. P.S. The Model is attached

(*Clear variables*)

Clear[P, DC, DF, DB, DS, F, ?, ?, ?, ?];
(*Model Equations*)
DC[t_] := DC[t] = ?*(P[t] - F); 
DF[t_] := DF[t] = ?*(F - P[t]);
DB[t_] := DB[t] = ?;
DS[t_] := DS[t] = -?; 
P[t_] := P[t] = 
   P[t - 1] + ?[(?*DC[t - 1] - ?*DF[t - 1])*(P[t - 1] - 
         F) + ? (DB[t - 1] - DS[t - 1])];

(*Abhängikeiten darstellen*)


(*parameter setting*)
? = 0.010;
F = 0;
? = 1.011;
? = 1.000;
? = 0.165;

(*Startwerte setzten*)
P[0] = F; P[1] = F;

logprices = Table[P[i], {i, 1, 5000}];
logreturns = Differences@logprices;

ListLinePlot[Exp@logprices, PlotStyle -> Black, PlotRange -> All, 
 Frame -> True, FrameLabel -> {{"price", None}, {"time", None}}, 
 AspectRatio -> 0.4, GridLines -> {{}, {Exp[F]}}]

(*Entwicklung der log Renditen*)
ListLinePlot[logreturns, 
 PlotStyle -> Black, PlotRange -> All, Frame -> True, 
 FrameLabel -> {{"log returns", None}, {"time", None}}, 
 AspectRatio -> 0.4, Axes -> None]
Attachments:
POSTED BY: philipp.sas Scneider
4 Replies
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Hi,

I think that the model equations for P are incorrect. Just behind the $\mu$ you are using square brackets where you should use round brackets.

P[t_] := P[t] = 
   P[t - 1] + \[Mu] ((\[Chi]*DC[t - 1] - \[Phi]*DF[t - 1])*(P[t - 1] -
           F) + \[Kappa] (DB[t - 1] - DS[t - 1]));

should do. You will still have an overflow when you try to evaluate 

Table[P[i], {i, 1, 5000}]

though. You see that this behaves badly if you use:

logprices = Table[P[i], {i, 1, 450}];
logreturns = Differences@logprices;

ListLinePlot[Exp@logprices, PlotStyle -> Black, PlotRange -> All, 
 Frame -> True, FrameLabel -> {{"price", None}, {"time", None}}, 
 AspectRatio -> 0.4, GridLines -> {{}, {Exp[F]}}]

enter image description here

If you iterate to the first 480 elements you get:

enter image description here

At 481 you get to values of about $10^{183}$.

Cheers,

Marco
POSTED BY: Marco Thiel

Thank you very much,... I'll see if it works better now :)
POSTED BY: philipp.sas Scneider
Eric Meyers
Eric Meyers
Posted 10 years ago

I think it's the [ and ] near the mu in your P function. Also it diverges at around t=450. See if this fixes you up.

Eric

Ps. I see Marco found the same issue before me.

Attachments:
POSTED BY: Eric Meyers

Welcome to Wolfram Community! Please make sure you know the rules: https://wolfr.am/READ-1ST

And please EDIT your post and make your title NOT generic, but about the actual model.
POSTED BY: EDITORIAL BOARD
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