FIN 539 Practice Questions
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Practice Questions
FIN 539
1. Consider a one-period model with two states: u happens with probability 0.6 and d happens with probability 0.4. Consider the following stock: S0 = 10, S1(u) = 15, S1(d) = 5. Suppose that the risk free rate is r = 0% and the agent’s time discount factor is β = 0. The agent’s utility function over wealth is u(x) = 1 − e −0.2x . The agent’s initial wealth is X0 = $20. State and solve both the primal and dual problems to find the agent’s optimal stock holding.
2. Under the same assumptions as those covered in class for the one stock case, use both the direct approach (as in Chapter 1) and the duality approach (as in Chapter 2) to solve for the optimal consumption and optimal trading strategy for the case u1 (c) = c − and u2 (x) = x − . Recover the value function V (t, x) for the dual problem.
2023-02-25