Decision Analysis, Value of Information, Monte Carlo Simulation, Regression Analysis

.QUESTION 1: DECCISION ANALYSIS
a. Utility function is a twice differentiable function of wealth which satisfies the principle of non-
satiation and risk aversion. We can assess the utility function by mainly two methods, that is
interview method and probability encoding. In interview method, a person is asked a series of
questions from which his/her utility function is assessed while in probability encoding
probabilities are attached to uncertain possible outcomes depending on an individual’s
preference.
A standard gamble is a technique for managing outcomes by attaching probability values to an
individual’s preferences. The standard gamble is used in determining utility values by asking a
series of leading questions the answer to which will help determine the utility values of the
individual as they indicate an individual’s attitude towards a particular risk.
1. Decision matrix
Good Fair Bad
Share market 11400 10800 10000
Government bonds 10900 10900 10900
2. Optimist criterion
Good Fair Bad Maximum outcome
Share market 11400 10800 10000 11400
Government bonds 10900 10900 10900 10900
The optimist will take the option of the maximum outcome which is to trade shares under good market
which its outcome is $11400
3. Pessimist criterion
Good Fair Bad Minimum
outcome
Share market 11400 10800 10000 10000
Government bonds 10900 10900 10900 10900
The pessimist will take the option of maximum in the possible minimum outcome which is to trade
in government bond in all seasons which results in $10900

4. Regret criterion
Good Fair Bad Minimum
outcome
Maximum
outcome
Share market 11400 10800 10000 10000 11400
Government bonds 10900 10900 10900 10900 10900
Regret criterion can choose to go for both the minimax and maximin take the option of trading in
government bond which gives $10900.
5. Expected monetary value
Good Fair Bad
Share market 11400 10800 10000
Government bonds 10900 10900 10900
Probability 0.4 0.2 0.4
EMV ( Share market )=11400 ×0.4+ 10800× 0.2+10000 ×0.4
¿ $ 10720
EMV ( government bond )=10900 × 0.4+10900 × 0.2+10900 × 0.4
¿ $ 10900
The optimal action in the expected monetary value will be to trade in government bond which its
outcome is $10900.
6. Expected value of perfect information
Good Fair Bad
Share market 11400 10800 10000
Government bonds 10900 10900 10900
Probability 0.4 0.2 0.4
The highest expected monetary value is $10900
Expectation for maximizing profit
EV ∨PI =0.4 × 11400+10900 × 0.2+ 10900× 0.4
¿ $11100

EVPI=11100−10900
¿ $ 200
Knowing the direction the market will go is worth $200
QUESTION 2 VALUE OF INFORMATION
a. The probability of unfavorable market is 0.5
EVP=0.5 ×100000−0.5 ×60000=$ 20000
Since the expected monetary value is $20000 he can go ahead and start the producing new type of
razor.
b. The friend’s probability
Favorable Unfavorable
Correct prediction 0.7 0.2
Incorrect prediction 0.3 0.8
The prior probabilities are 0.5 for favorable market and 0.5 for unfavorable market
The joint and marginal probability will be;
Favorable Unfavorable
Correct prediction 0.35 0.1 0.45
Incorrect prediction 0.15 0.4 0.55
0.5 0.5
Posterior probability
Favorable Unfavorable
Correct prediction 0.78 0.73
Incorrect prediction 0.22 0.27
c. Posterior probability
Posterior probability when the friend predict unfavorable market is 0.22