This program maximizes the expected long term growth rate under the assumption of levy stability and under the assumption that the strategy is followed in perpetuum (redistributing the assets each year).

Example. Start with a risk free 8.2 percent bond, so enter 8.2. Press 'add asset'to add a Levy stable risky asset. First choose alpha. While 2.0 represents log normal changes, 1.7 is considered typical so enter 1.7. Enter 0 for the skewness, beta. Next, c is the volatility, for a normal asset it is the standard deviation of the year-on-year change in the natural log of the price. Choose a high volatility of 0.4. Mu is the growth rate of the risky asset, for 12 percent enter 0.12. The 4 parameters are then 1.7,0,.4, and 0.12. Press calculate to perform the Fourier transform. Move the sliders to select asset levels. Each time the sliders are moved the program integrates the log of the sum of the asset values against the exponentials of the distributions. Set the second slider to 200 which can mean 200,000. Note that with the first slider to 0 the Bernoulli rate is 11.82%, the growth rate of the asset. With the first slider to 400, the Bernoulli rate is 14.23% which is better, and the first slider at 140 gives 15.45%. Thus adding a small amount of a risk free asset at the lower interest rate of 8.2% increases the Bernoulli rate of the risky asset by more than three percent. Caution: The Bernoulli rate is the short term expected log return. In a mathematical sense a portfolio managed with the highest Bernoulli rate -- if the true Bernoulli rate were ever known -- will have best highest long term expected growth, but observe that mathematically the the long term must be allowed to exceed the lifetime of the earth, and an event of of losing all but one millionth of one cent and then regaining it all centuries later must be viewed as equivalent of never having taken a loss. (Read Bernoulli's original article). Bernoulli spoke only of utility but it is clear that maximizing the expected logarithm of growth in each time interval is the same as maximizing the expected long term growth rate of the portfolio.

(Note: this is very much a work in progress. If you'd like to suggest what the next step should be contact goldengemnetwork@gmail.com or visit  GoldenGem neural network).