Consider a single-period binomial model: The price of the stock at time 0 is S(0) = 100. At time 1 it can move up to 110 with probability 1/3, and down to 90 with probability 2/3. There is also a bank account that pays interest r = 5% per period. The agent has exponential utility U(X(1)) = −e−0.03X(1). If the agent has $100 as initial capital, how much should she invest in the stock, in order to maximize her expected utility?