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Science Forum Index » Statistics - Education Forum » Monte Carlo with related variables
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| Author |
Message |
| Jack |
 Posted: Sat Dec 30, 2006 8:18 am |
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Guest
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Hi,
I am a novice re Monte Carlo and would like some help on how to approach and
solve the following problem.
I am trying to work out how to produce a Monte Carlo simulation for a model
where the "input variables" have a relation.
The model is analogous to betting on bookmaker odds.
I have run the model I wish to investigate against actual data to produce
the historical P/L on the model.
Where
Profit = (Odds*stake) if a winner, and
Loss = -stake for loser.
So the variables are
1. The Odds
2. The Stake.
3. The Win %
So the distributions will be empiracally derived from the data.
The Odds seems the obvious "fundamental" variable and I have fitted it to a
distribution (GEV fits it best).
Now, the Win% varies with the odds - lower odds, higher Win% (with a given
ditribution).
Similarly, I work out the stake depending on the "advantage" I see a bet
having.
This seems to vary with odds, so the lower the odds tends to give a bigger
advantage. This advantage parameter will (probably) have its own
distribution for each odds.
So, my question is how can I model/sample the various Advantage & Win%
distributions given the odds?
What I have come up with is using "bins". So for each odds bin, say 5-10%,
11-15% etc I pull out the distributions for Advantage/Stake and Win Rate
that my data analysis suggests and I interpolate for empty bins.
Is this a practical "accepted" method, or are there other (simple)
analytical or other approaches I might use? Can Odds,Advantage and Win% be
modeled together as a single multivariate distribution somehow and sampled
accordingly? - I've no idea :)
I also thought of doing a regression to fit Win% and Advantage (parameters
of regression depending on the empirical distribution of the variables) to
Odds.
Once successful I can use a MC analysis to work out profit % /risk of ruin
etc for various staking strategies.
During my web "research" I have not been able to find any examples where a
model/data analysis is used with dependencies as a basis to develop a MC
simulation - not one I can understand anyway.
Thanks for any help. |
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