### Generating the unique paths to convert an ascending #permutation into a descending permutation using only adjacent swaps

One way to transform the list [1,2,3] to [3,2,1] is [1,2,3] -> [2,1,3] -> [2,3,1] -> [3,2,1] swapping only items that appear next to each other in the list. An alternate way is [1,2,3] -> [1,3,2] -> [3,1,2] -> [3,2,1] There is only one way to convert the series [1,2] to [2,1] which is by … Continue reading

### Computing the tangent point on the Efficient Frontier

As noted in a previous blog post, an investor’s preferred portfolioÂ on the efficient frontier is determined by the point where the investor’s constant absolve risk aversion (CARA) utility function is tangent to the efficient frontier. The indifference contours of the utility function for any individual are defined by a parameter, A, which maps any … Continue reading

### Gambles with the same Expected return and Kelly bet size

By Elliot Noma, Yu Bai In our previous post we grouped gambles by their optimal bet sizes. Here we consider the subset of these groups in which the gambles share not only an optimal bet size, but also the same expected return. 1. Finding the set of gambles with same expected return and Kelly bet … Continue reading