# single period security market with two assets

Consider a single period security market with two assets. Assume the current prices are

There are two states at time one and the payoff matrix is

1.Suppose the investor believes that each state has equal probability. Assume an investor’s initial wealth is w0 = 10, and her utility function is u(x) = log(x). Solve the optimal portfolio selection problem for this agent and verify the optimal solution exists.

2.Find the risk-neutral probability measure for this agent.