Consider a trader with initial fund given by 0 = 15, and the transaction cost function of holding q shares of stock i is C(q) = 10 + q 2 .

The price (xi) at which this trader sells its position is stochastically distributed according to the following probability distribution: P(xi) = ( 0.5, if xi = $8 0.5, if xi = $2 Let a random variable be the profit of trading at each time t, t = 1, 2, . . . , T,

. If the traders utility function is given by u() = () 1 9 (), where () is the mean and () is the variance, determine the traders optimal level of position, and the associated equilibrium profits from liquidate the complete position.

. Consider now that the traders utility function is described by u() = (). What is now the optimal level of position and the associated equilibrium profits?