ECON3006/4437/8037: Financial Economics
Assignment 1
金融经济学代写 General Information: PLEASE READ CAREFULLY 100 % = 24 points. Maximal 3 students can submit one solution of Assignment 1.
General Information: PLEASE READ CAREFULLY
- 100 % = 24 points.
- Maximal 3 students can submit one solution of Assignment 1. All students within the group receive the same grade. Only 1 student of the group submit the solution WITH uni-ids of students within the group. The other student(s) submits his/her uni id and the uni id of students within the group.
- Name the uploaded file, if possible as a pdf, in the form of “uni id-A1”.
- Only working within each group is allowed. Please use wattle to build groups. Try to be precise in your argumentation. Please keep a copy of your solutions.
- Due on Friday August 20th 2021 by 23:55 PM (GMT+10). Late assignment will not be accepted.
Solve the following 3 problems.
1.3+6+4+2+1=16 points 金融经济学代写
Let T and there is consumption only at T = 1.
(a) Let wealth at time 0 be w = 612 AUD and endowment at time 1 be ω = 0.
- Formulate the budget set with prices p0= 1 and p1= (2, 1, 2).
- Specify an endowment ω with w = 0 that gives the same budget set.
- Draw the budget set.
- Is it (= U) continuous?
- Is it strictly increasing?
- Is it smooth?
- Is it concave?
- Explain the second equality in [◦◦].
Give a short formal argument for each answer.
(c) Take part a. and b.: formulate the corresponding maximization problem with with p1 = (2, 1, 2) and solve it. Also formulate the optimal solution as a lottery.
(d) Compute the certainty equivalent of the optimal solution and draw an illustrating picture with the risk premium.
(e) Compute and plot the Absolute Risk Aversion of the present utility index as a function of wealth.
2.3+3+2=8 points 金融经济学代写
Suppose Question 1 is based on throwing a dice (Throwing 1 is state s = 1 throwing 2, 3 is state s = 2 and 4, 5, 6 is state s = 3.)
Now, suppose the dice is thrown twice, a time t = 1 and time t = 2.
(a) i. Draw the corresponding tree,
ii. formulate the information structure of the tree
iii. compute the probability of each state at time T = 2.
(b) Reformulate the model from question 1 with T = 2, w.r.t. commodity space, budget set and the additive von Neumann Morgenstern (vNM) utility model (no discounting) with consumption at time 1, 2 and price at time T = 2 given by p2 = (p1 , p1 , p1 ) where p1 is from question 1.
Hint: formulating the utility model is conceptually the most difficult part.
(c) Answer then the 5 questions from 1 (b) in the present case.
(d) (EXTRA no points) Solve the new constrained problem
3.EXTRA Question for practice (no points) 金融经济学代写
(a) Specify the commodity space and the assets.
(b) Calculate (not with a computer) the state prices p with a technique of your choice.
(c) Is p unique? Why? Is the market arbitrage free?
(d) Compute the state prices risk neutral probabilities
