I'm an accounting student who has taken one university math course (required) so my math skills are not that high. However I do have some knowledge regarding calculus and optimization.
I was looking for a way to select my bet sizes at a horse race assuming a logarithmic utility curve (thus to optimize asset growth). Imagine my surprise when I found an article outlining a step-by-step algorithm to do just that.
Optimal Bets In Pari-Mutuel Systems by Nissan Levin
Efficiency of Racetrack Betting Markets - Google Books
The sad thing is I cannot decipher the logarithmic algorithm. I can solve the example for the linear using the given algorithm but I believe the author did not show the complete work for the logarithmic example.
The paper includes an example with answers which is used for the linear and logarithmic utility sections (the other aspects of the paper-fair game,deserted,stochastic, etc are not relevant for me) as well as the algorithm to solve both.
The log algorithm starts as
Step 0: Let t=0
Step 1: Increase t by 1 and find a and G(t) using (15)-(18)
This is where I don't know what to do. First I don't know why a "t" variable is needed but that is beside the point. Formulas (15) to (18) have variables which refer to each other and I cannot solve for G(t). I think the alternate equations for a(i) (11) and "a" (12) would be useful to substitute in but I'm not sure.
Basically I want to know how to arrive at A(4)=1056.1 and G(4)=0.00072 and the chart on pg 119 (table 2) with the parameters given (w,p(i),b(i),c,Q)
Any help would be greatly appreciated.
P.S. Answering this question is very important to me. My hope is that a qualified individual could read the relevant sections (about six pages) and easily show how to answer the question. If this cannot be done (it is a long process to derive a simpler algorithm) a rough estimate of how long a mathematician would require to solve it and where I could possibly hire someone would be appreciated.