It’s a good result, but I wonder if the standard deviation is the best parameter. Loss-averse agents react differently to asymmetrical distributions allowing large losses than those allowing large gains.
Edit: For example, the mean of an exponential distribution f(x;t) = L e^(-Lx) has mean and standard deviation 1/L, but a loss-averse agent is likely to prefer it to the normal distribution N(1/L, 1/L^2), which has the same mean and standard deviation.
Once you abanndon independence, the possibilities are litteraly infinite—and not just easily controllable infinities, either. I worked with SD as that’s the simplest model I could use; but skewness, kurtosis or, Bayes help us, the higher moments, are also valid choices.
You just have to be careful that your choice of units is consistent; the SD and the mean are in the same unit, the variance is in units squared, the skewness and kurtosis are unitless, the k-th moment is in units to the power k, etc...
That’s true—and it occurred to me after I posted the comment that your criteria don’t define the decision system anyway, so even using some other method you might still be able to prove that it meets your conditions.
See also semivariance in the context of investment (and betting in general). NB: “semivariance” has a different meaning in the context of spatial statistics.
It’s a good result, but I wonder if the standard deviation is the best parameter. Loss-averse agents react differently to asymmetrical distributions allowing large losses than those allowing large gains.
Edit: For example, the mean of an exponential distribution f(x;t) = L e^(-Lx) has mean and standard deviation 1/L, but a loss-averse agent is likely to prefer it to the normal distribution N(1/L, 1/L^2), which has the same mean and standard deviation.
Once you abanndon independence, the possibilities are litteraly infinite—and not just easily controllable infinities, either. I worked with SD as that’s the simplest model I could use; but skewness, kurtosis or, Bayes help us, the higher moments, are also valid choices.
You just have to be careful that your choice of units is consistent; the SD and the mean are in the same unit, the variance is in units squared, the skewness and kurtosis are unitless, the k-th moment is in units to the power k, etc...
That’s true—and it occurred to me after I posted the comment that your criteria don’t define the decision system anyway, so even using some other method you might still be able to prove that it meets your conditions.
See also semivariance in the context of investment (and betting in general). NB: “semivariance” has a different meaning in the context of spatial statistics.