Hallo zusammen :)
Ich wäre sehr dankbar, wenn jemand mit diesen Aufgaben mir helfen kann
Danke im Voraus :)
Aufgaben:
(13 )Petersburg game: Bernoulli found out that everybody would invest only a small
amount for this game. For this reason, he looked for an utility function U, where the marginal utility U′(x) is indirect proportional to the value x. Show that this means that he considered the logarithmic utility and calculate the expected utility for this utility function.
(15) Petersburg game: Consider that the decision maker follows the following rule: It is only allowed to bid for the game (the feasible bids), if the probability of a loss is smaller than 80%. Find the maximal possible bid under this constraint.
(16) Consider the lottery
| payment | 0 | 1 | 2 | 3 | 4 |
| probability | 1/2 | 1/4 | 1/8 | 1/16 | 1/16 |
For bidding 1,2,3 units calculate the expected profit and its variance. Show the result in a return/risk diagram.
(17) How to find out individual utility functions?
Howard Raiffa (1961): Decision makers have to indicate their certainty equivalents for the lottery
Show that given the constraints U(0) = 0, U(1) = 1, if we know the certainty equivalents for all p, 0 ≤ p ≤ 1, we know the utility function U for all values between 0 and 1.
