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  #1  
Old 03-31-2005, 10:39 AM
elau elau is offline
 
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Default Stochastic vs. Deterministic Models

Can anyone please give me a distinction between the two?
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  #2  
Old 03-31-2005, 10:43 AM
Mobile Actuary Mobile Actuary is offline
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With a deterministic model, the assumptions and equations you select "determine" the results. The only way the outputs change is if you change an assumption (or an equation).

With a stochastic model, an element of randomness is introduced at one or many points of the model. Every time you run the model, you get a different result. If you run it many times, this gives you a measure of variability in the process, as predicted by the model.
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Old 03-31-2005, 05:14 PM
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actuaryalfred actuaryalfred is offline
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A good example of deterministic models can be found in linear programming: if you want to minimize the cost by choosing how you transport the good from places to places, then you are dealing with a determinstic model for every data you have is fixed beforehand.

As for stochastic models, you may consider the following. If you know on average 5 customers come to bank, then how many servers should you provide so that on average the waiting time per customer is less than 5 mins. Since in this case you can never know exactly how many customers will come, you have to make assumptions on the arrival of the customer like what the distribution is, and whether the arrivals are independent, etc. That's one of the stochastic part of this model.
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Old 04-01-2005, 11:16 AM
Russell Frank Russell Frank is offline
 
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- and this is why I don't like the terms deterministic and stochastic models.

We have two answers; both are reasonable, and they don't agree with each other. To highlight why I say they are different, look at Alfred's second example - the queuing theory problem that he says is a stochastic model. It's a stochastic problem, all right - we are looking at a probabilistic situation. I could use a stochastic model to analyze it - do a simulation, etc., but I can also use standard probability theory to solve most queuing theory problems, and come up with a single definite answer, giving the exact probability distribution of waiting time, etc. By most people's definition (specifically Mobile's) this is not a stochastic model, because I have solved the problem exactly, and if you ask me to do it again, I'll give you the exactly the same answer.

For most people, stochastic model means some form of simulation model, for example, a complicated DFA model, or a model for aggregate losses under some set-up that can't be calculated easily by direct methods.

Mobile Actuary gives the answer I think most in the field would agree with, but based on the dictionary definitions of the terms, I think Alfred has a good claim too.
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Old 04-20-2005, 05:27 PM
chapman_kolmogorov chapman_kolmogorov is offline
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You can use standard probability to solve MOST queueing theory problems...that is impressive.
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Old 04-21-2005, 12:29 AM
Russell Frank Russell Frank is offline
 
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Yes, that was pretty stupid of me. I was thinking of simple models with exponential inter-arrival times.

I still want an answer to my basic question.

I toss a coin - it comes up heads with probability 1/2 and tails with probability 1/2. Is this an example of a stochastic model? If not, why not? If yes, why does anybody make an issue of stochastic versus deterministic models?
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Old 04-21-2005, 02:01 AM
elau elau is offline
 
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What are some types of stochastic models an actuary can build (eg. interest rate?)? And in what ways will the actuary approach the problem (ie. how to setup the model, calculations, etc.)?
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Old 04-21-2005, 02:04 AM
elau elau is offline
 
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Quote:
Originally Posted by Russell Frank
I toss a coin - it comes up heads with probability 1/2 and tails with probability 1/2. Is this an example of a stochastic model? If not, why not? If yes, why does anybody make an issue of stochastic versus deterministic models?
Does it depend on how you look at it? If you run a simulation model and simulate a head or tail every time, and you look at the average number of heads or tails you get after n simulations, this would be the stochastic way of approaching the problem? If you go about this problem theoretically, and say it's 1/2 chance of getting a head, then it's deterministic?
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Old 04-21-2005, 10:08 AM
Mobile Actuary Mobile Actuary is offline
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Quote:
Does it depend on how you look at it? If you run a simulation model and simulate a head or tail every time, and you look at the average number of heads or tails you get after n simulations, this would be the stochastic way of approaching the problem? If you go about this problem theoretically, and say it's 1/2 chance of getting a head, then it's deterministic?
If you model 100 tosses of a fair coin in a deterministic model, your answer is 50 heads every time you run it; in a stochastic model run many times you would get an approximation of the results predicted by the binomial distribution.

Quote:
What are some types of stochastic models an actuary can build (eg. interest rate?)? And in what ways will the actuary approach the problem (ie. how to setup the model, calculations, etc.)?
There's a lot of literature on this topic....
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Last edited by Mobile Actuary; 04-21-2005 at 10:11 AM..
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