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> If the problems are different a different utility function may be appropriate. The claim of the paper is that you can derive an appropriate rational solution

by mrow84 6y ago

> If the problems are different a different utility function may be appropriate. The claim of the paper is that you can derive an appropriate rational solution for each problem using a single technique. > How so? EE works only with an infinite number of periods. Afaik this is not correct - EE does not require the problem to have an infinite number of periods, rather it is saying that you cannot assume that the temporal integral is equal to the ensemble integral, and that you must act accordingly. You have to (in principle) integrate the whole time series of interest - this can be done over your uncertainty, but requires no utility function, a simple expectation will do.

kgwgk 6y ago
> The claim of the paper is that you can derive an appropriate rational solution for each problem using a single technique. Can you derive a rational solution for this problem using that technique? "An investor must choose how much to consume and must allocate his wealth between stocks and a risk-free asset" https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem In the problems that EE has actually solved the solution is known and is derived using similar arguments. Note that EUT has two main uses, descriptive (how do people behave?) and normative (what should you do in this situation?). Descriptive: you try to find empirically a utility function that describes people's preferences when facing decisions. Normative: you look at the problem (whether it's portfolio selection or deciding where to construct a dam), make assumptions about the probabilities of outcomes and their desirability and calculate what is the prefer solution that you should take. Optimizing long-term growth because it's the defining property of a multiplicative process is not a new idea. The logarithmic utility function is derived for this problem using those arguments even in undergraduate textbooks. It's discussed for example in pages 232-234 of http://dl.rasabourse.com/Books/Finance%20and%20Financial%20Markets/%5BEdwin_J._Elton%2C_Martin_J._Gruber%2C_Stephen_J._Brow_Modern%20Portfolio%20Theory%20and%20Investment%28rasabourse.com%29.pdf http://dl.rasabourse.com/Books/Finance%20and%20Financial%20M... (I don't necessarily agree with everything said there, it's just an example.) Empricically, though, people don't quite behave as growth-optimizers. They would be leveraged to be invested 200% in equities to have the optimal portfolio. > EE does not require the problem to have an infinite number of periods Ok. But then the infinite repetion where the time-average is justified by the ability of the agent to experience every possible outcome infinite times is just a mental construct without any relation to physical reality. Which is fine for me, mind you. Still, that doesn't explain how this is correct: "With EE you recover different behaviours depending on the structure of the problem, both the reward structure and the temporal structure (e.g. number of periods)" In the question of whether you take that bet, you get the same answer whether you play once, or ten times, or one million. (Or course the same is true when you analyse the problem using logarithmic utility, because it's mathematically equivalent to growth optimization in a multiplicative process).
- mrow84 6y ago
  EUT can be used descriptively because you can just pick any utility function to fit whatever behaviour you are trying to explain, but that doesn't offer any insight. If the theory was good you could find a utility function that fit a range of behaviours, but without it being overfit. Again, the EE claim, and one which is demonstrated for at least some simple cases, is that you can recover a range of behaviours without adding in parameters by considering time explicitly. > In the question of whether you take that bet, you get the same answer whether you play once, or ten times, or one million. If you are only playing one round, you should take the bet, if you are playing more than one round, you shouldn't. EUT requires you to change utility function to recover those two different answers, EE gives you the correct answer however many rounds you choose to play (one, or more) without requiring any additional modification.
  - kgwgk 6y ago
    > EUT can be used descriptively because you can just pick any utility function to fit whatever behaviour you are trying to explain, but that doesn't offer any insight. Well, using EUT descriptively is useful when you're objective is to create a model from empirical observations. I agree that this is irrelevant in this discussion. > Again, the EE claim, and one which is demonstrated for at least some simple cases, is that you can recover a range of behaviours without adding in parameters by considering time explicitly. Sure. You can recover the same using EUT in prescriptive mode. Which is not about fitting observations to a general parametric utility function or anything like that. It's about using a model of the problem (p.ex. multiplicative dynamics) to derive the right utility function to use (p.ex. logarithmic) when possible (just like EE does). And using an approximate model that is hopefully not too wrong when the problem is not so easy. > In the question of whether you take that bet, you get the same answer whether you play once, or ten times, or one million. If you are only playing one round, you should take the bet, if you are playing more than one round, you shouldn't. The question in equation (2) is of the form "you are only playing one round". But the answer is not "you should take the bet", because we're told that to answer you need to consider an hypothetical infinite sequence of bets. If I offer you the possibility to win $10000 or lose $9999 on a coin flip, only once, do you play or not? > EE gives you the correct answer however many rounds you choose to play (one, or more) without requiring any additional modification. So there is one answer for "one" and one answer for "more"? When you said that it could depend on "the number of periods" I thought you meant that the answer could be different for two periods than for seven, for example. (Of course EUT with logarithmic utility is equivalent to EE and won't make a difference between playing twice or seven times either.)

by mrow84 6y ago

kgwgk 6y ago

> The claim of the paper is that you can derive an appropriate rational solution for each problem using a single technique. Can you derive a rational solution for this problem using that technique? "An investor must choose how much to consume and must allocate his wealth between stocks and a risk-free asset" https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem In the problems that EE has actually solved the solution is known and is derived using similar arguments. Note that EUT has two main uses, descriptive (how do people behave?) and normative (what should you do in this situation?). Descriptive: you try to find empirically a utility function that describes people's preferences when facing decisions. Normative: you look at the problem (whether it's portfolio selection or deciding where to construct a dam), make assumptions about the probabilities of outcomes and their desirability and calculate what is the prefer solution that you should take. Optimizing long-term growth because it's the defining property of a multiplicative process is not a new idea. The logarithmic utility function is derived for this problem using those arguments even in undergraduate textbooks. It's discussed for example in pages 232-234 of http://dl.rasabourse.com/Books/Finance%20and%20Financial%20Markets/%5BEdwin_J._Elton%2C_Martin_J._Gruber%2C_Stephen_J._Brow_Modern%20Portfolio%20Theory%20and%20Investment%28rasabourse.com%29.pdf http://dl.rasabourse.com/Books/Finance%20and%20Financial%20M... (I don't necessarily agree with everything said there, it's just an example.) Empricically, though, people don't quite behave as growth-optimizers. They would be leveraged to be invested 200% in equities to have the optimal portfolio. > EE does not require the problem to have an infinite number of periods Ok. But then the infinite repetion where the time-average is justified by the ability of the agent to experience every possible outcome infinite times is just a mental construct without any relation to physical reality. Which is fine for me, mind you. Still, that doesn't explain how this is correct: "With EE you recover different behaviours depending on the structure of the problem, both the reward structure and the temporal structure (e.g. number of periods)" In the question of whether you take that bet, you get the same answer whether you play once, or ten times, or one million. (Or course the same is true when you analyse the problem using logarithmic utility, because it's mathematically equivalent to growth optimization in a multiplicative process).

mrow84 6y ago
EUT can be used descriptively because you can just pick any utility function to fit whatever behaviour you are trying to explain, but that doesn't offer any insight. If the theory was good you could find a utility function that fit a range of behaviours, but without it being overfit. Again, the EE claim, and one which is demonstrated for at least some simple cases, is that you can recover a range of behaviours without adding in parameters by considering time explicitly. > In the question of whether you take that bet, you get the same answer whether you play once, or ten times, or one million. If you are only playing one round, you should take the bet, if you are playing more than one round, you shouldn't. EUT requires you to change utility function to recover those two different answers, EE gives you the correct answer however many rounds you choose to play (one, or more) without requiring any additional modification.
- kgwgk 6y ago
  > EUT can be used descriptively because you can just pick any utility function to fit whatever behaviour you are trying to explain, but that doesn't offer any insight. Well, using EUT descriptively is useful when you're objective is to create a model from empirical observations. I agree that this is irrelevant in this discussion. > Again, the EE claim, and one which is demonstrated for at least some simple cases, is that you can recover a range of behaviours without adding in parameters by considering time explicitly. Sure. You can recover the same using EUT in prescriptive mode. Which is not about fitting observations to a general parametric utility function or anything like that. It's about using a model of the problem (p.ex. multiplicative dynamics) to derive the right utility function to use (p.ex. logarithmic) when possible (just like EE does). And using an approximate model that is hopefully not too wrong when the problem is not so easy. > In the question of whether you take that bet, you get the same answer whether you play once, or ten times, or one million. If you are only playing one round, you should take the bet, if you are playing more than one round, you shouldn't. The question in equation (2) is of the form "you are only playing one round". But the answer is not "you should take the bet", because we're told that to answer you need to consider an hypothetical infinite sequence of bets. If I offer you the possibility to win $10000 or lose $9999 on a coin flip, only once, do you play or not? > EE gives you the correct answer however many rounds you choose to play (one, or more) without requiring any additional modification. So there is one answer for "one" and one answer for "more"? When you said that it could depend on "the number of periods" I thought you meant that the answer could be different for two periods than for seven, for example. (Of course EUT with logarithmic utility is equivalent to EE and won't make a difference between playing twice or seven times either.)