Log Optimal Investments

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I am taking an introductory finance class, and am totally lost on our latest assignment.

The question that kills me is as follows: Consider a (single period) market with 2 risky assets, and 2 states of the world(omega). Suppose the given probablity on omega is P, and let Q be the risk neutral probability. Suppose an investment bank offers two products X1 and X2, both with price 1, and with payoffs given by:

Xi(omega j) = { gamma*qi^-1, if i =j, zero if i!=j}

where 0 < gamma < 1. Assuming p1 > q1/gamma, what is the log optimal strategy with initial wealth 1?

So far, I have tried to value the portfolio at time zero (initial wealth) and at the state dependant time 1. By definition, the expectation on Q of the discounted value of S1 equals the discounted value of S0, but I am not sure where to head from here. All suggestions are appreciated.