Given future price probability distribution, what is a strategy that maximizes return?

Say I know the price probability distribution, e.g., lognormal(p,s), of a stock X at a future time T that is perhaps one or two years into the future. p is price and s is a standard deviation.

What should I trade to maximize my expected total return at time T?

Should I for example roll over short-term stock options, long-term stock options, buy the stock using some amount of leverage, etc?

Is there some way or tool that calculates this automatically?

How do I need to change this problem or my thinking so that the solution is not to simply use infinite amounts of leverage?

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Edit:

I am assuming I have some positive amount of capital C to invest.

Available instruments are:

• Long and short stocks
• Long and short call and put options
• Stock futures and swaps
• T-Bills, notes and bonds
• (If it makes things easier we can ignore warrants and convertibles)
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the strategy should be self-financing I assume ? Also you have to make some assumptions on the avaliable instruments you are able to trade. –  Probilitator Mar 28 '14 at 7:53
Are you looking for a dynamic or a static one? –  Probilitator Mar 29 '14 at 10:56