dr. y. İlker topcu · decision-making under risk ... risk premium. dr. y. İlker topcu () & dr....

Dr. Y. İlker TOPCUwww.ilkertopcu.net www.ilkertopcu.org www.ilkertopcu.info

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Dr. Özgür KABAKweb.itu.edu.tr/kabak/

http://www.ilkertopcu.net/http://www.ilkertopcu.org/http://www.ilkertopcu.info/http://www.facebook.com/yitopcuhttps://twitter.com/yitopcuhttp://web.itu.edu.tr/kabak/

Introduction One dimensional (single criterion) decision

making Single stage vs. multi stage decision making

Decision analysis is an analytical and systematic way to tackle problems

A good decision is based on logic: rational decision maker (DM)

Dr. Y. İlker Topcu (www.ilkertopcu.n ) & Dr. Özgür Kabak ([email protected])et 2

http://www.ilkertopcu.info/mailto:[email protected]

Components of Decision Analysis A state of nature is an actual event that may occur in

the future. A payoff matrix (decision table) is a means of

organizing a decision situation, presenting the payoffs from different decisions/alternatives given the various states of nature.



Basic Steps in Decision Analysis1) Clearly define the problem at hand2) List the possible alternatives3) Identify the possible state of natures4) List the payoff (profit/cost) of alternatives

with respect to state of natures5) Select one of the mathematical decision

analysis methods (models)6) Apply the method and make your decision



Decision-Making Environments Type 1: Decision-making under certainty

DM knows with certainty the payoffs of every alternative .

Type 2: Decision-making under uncertainty

DM does not know the probabilities of the various states of nature. Actually s/he knows nothing!

Type 3: Decision-making under risk

DM does know the probabilities of the various states of nature.



Decision Making Under Certainty Instead of state of natures, a true state is known

to the decision maker before s/he has to make decision

The optimal choice is to pick an alternative with the highest payoff



Decision Making Under Uncertainty Maximax

Maximin

Criterion of Realism

Equally likelihood

Minimax



Decision Table / Payoff Matrix

STATES OF NATURE

ALTERNATIVESFavorable

marketUnfavorable

marketConstruct large plant $200,000 ($180,000)Construct small plant $100,000 ($20,000)Do nothing $0 $0



STATES OF NATURE

ALTERNATIVESFavorable marketUnfavorable market

Construct large plant$200,000($180,000)

Construct small plant$100,000($20,000)

Do nothing$0$0

PROBABILITIES0.60.4

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Maximin

STATES OF NATURE

ALTERNATIVESFavorable marketUnfavorable marketMinimum in row

Construct large plant$200,000($180,000)($180,000)

Construct small plant$100,000($20,000)($20,000)

Do nothing$0$0$0

MAXIMIN =$0

DECISION :Do nothing

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Maximax

STATES OF NATURE

ALTERNATIVESFavorable marketUnfavorable marketMaximum in row

Construct large plant$200,000($180,000)$200,000

Construct small plant$100,000($20,000)$100,000

Do nothing$0$0$0

MAXIMAX =$200,000

DECISION :Construct large plant

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Hurwicz criterion

STATES OF NATURE

ALTERNATIVESFavorable marketUnfavorable marketWEIGHTED AVERAGE



Do nothing$0$0$0

Optimism-pessimism index (a)0.9MAX. W.A.=$162,000


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Minimax regret

STATES OF NATURE




Do nothing$0$0

REGRET VALUESMaximum in row

$0$180,000$180,000

$100,000$20,000$100,000

$200,000$0$200,000

MINIMAX =$100,000

DECISION :Construct small plant

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Laplace's

STATES OF NATURE

ALTERNATIVESFavorable marketUnfavorable marketRow average



Do nothing$0$0$0

MAX. R.A. =$40,000


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EMV

STATES OF NATURE

ALTERNATIVESFavorable marketUnfavorable marketExpected Monetary Value



Do nothing$0$0$0

PROBABILITIES0.60.4

MAX. EMV =$52,000


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EOL

STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4

REGRET VALUESExpected Opportunity Loss

$0$180,000$72,000

$100,000$20,000$68,000

$200,000$0$120,000

MIN. EOL =$68,000


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MaximaxChoose the alternative with the maximum optimistic

level

ok = {oi} = { {vij}}

STATES OF NATURE


marketUnfavorable

marketMaximum in

row (ok)Construct large plant $200,000 ($180,000) $200,000Construct small plant $100,000 ($20,000) $100,000Do nothing $0 $0 $0

m

i 1max

=

m

i 1max

=

m

j 1max

=



MaximinChoose the alternative with the maximum security

level

sk = {si} = { {vij}}m

i 1max

=

m

i 1max

=

m

j 1min

=

STATES OF NATURE


marketUnfavorable

marketMinimum in

row (sk)Construct large plant $200,000 ($180,000) ($180,000)Construct small plant $100,000 ($20,000) ($20,000)Do nothing $0 $0 $0



Criterion of RealismHurwicz suggested to use the optimism-pessimism index (α)Choose the alternative with the maximum weighted average

of optimistic and security levels

{α oi + (1 – α) si} where 0≤α≤1m

i 1max

=

STATES OF NATURE


marketUnfavorable

marketWeighted average α=0.7

Construct large plant $200.000 ($180.000) 380α-180 86Construct small plant $100.000 ($20.000) 120α-20 64Do nothing $0 $0 $0 0



STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4

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Maximin

STATES OF NATURE




Do nothing$0$0$0

MAXIMIN =$0


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Maximax

STATES OF NATURE




Do nothing$0$0$0

MAXIMAX =$200,000


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Hurwicz criterion

STATES OF NATURE

ALTERNATIVESFavorable marketUnfavorable marketWeighted averagea=0.7

Construct large plant$200,000($180,000)380a-18086

Construct small plant$100,000($20,000)120a-2064

Do nothing$0$0$00

Optimism-pessimism index (a)0.9MAX. W.A.=$0


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Minimax regret

STATES OF NATURE




Do nothing$0$0


$0$180,000$180,000

$100,000$20,000$100,000

$200,000$0$200,000

MINIMAX =$100,000


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Laplace's

STATES OF NATURE




Do nothing$0$0$0

MAX. R.A. =$40,000


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EMV

STATES OF NATURE




Do nothing$0$0$0

PROBABILITIES0.60.4

MAX. EMV =$52,000


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EOL

STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4


$0$180,000$72,000

$100,000$20,000$68,000

$200,000$0$120,000

MIN. EOL =$68,000


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-200000-150000-100000

-500000

50000100000150000200000250000

0 0.2 0.4 0.6 0.8 1

α

Payo

ff

Point 1Small Plant

Large Plant Point 2



Criterion of Realism

120α-20 = 0 ⇒ α = 0.1667380α-180 = 120α-20 ⇒ α = 0.6154

0 ≤ α ≤ 0.1667 ⇒ “Do nothing”0.1667 ≤ α ≤ 0.6154 ⇒ “Construct small plant”0.6154 ≤ α ≤ 1 ⇒ “Construct large plant”



Equally LikelihoodLaplace argued that “knowing nothing at all about the

true state of nature” is equivalent to “all states having equal probability”

Choose the alternative with the maximum row average (expected value)

STATES OF NATURE


marketUnfavorable

marketRow

averageConstruct large plant $200,000 ($180,000) $10,000Construct small plant $100,000 ($20,000) $40,000Do nothing $0 $0 $0



STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4

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Maximin

STATES OF NATURE




Do nothing$0$0$0

MAXIMIN =$0


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Maximax

STATES OF NATURE




Do nothing$0$0$0

MAXIMAX =$200,000


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Hurwicz criterion

STATES OF NATURE




Do nothing$0$0$0



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Minimax regret

STATES OF NATURE




Do nothing$0$0


$0$180,000$180,000

$100,000$20,000$100,000

$200,000$0$200,000

MINIMAX =$100,000


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Laplace's

STATES OF NATURE




Do nothing$0$0$0

MAX. R.A. =$40,000


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EMV

STATES OF NATURE




Do nothing$0$0$0

PROBABILITIES0.60.4

MAX. EMV =$52,000


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EOL

STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4


$0$180,000$72,000

$100,000$20,000$68,000

$200,000$0$120,000

MIN. EOL =$68,000


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MinimaxSavage defined the regret (opportunity loss) as the difference

between the value resulting from the best action given that state

of nature j is the true state and the value resulting from alternative i with respect to state

of nature jChoose the alternative with the minimum worst

(maximum) regretRegret Values STATES OF NATURE


marketUnfavorable

marketMaximum in

rowConstruct large plant $0 $180,000 $180,000Construct small plant $100,000 $20,000 $100,000Do nothing $200,000 $0 $200,000



STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4

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Maximin

STATES OF NATURE




Do nothing$0$0$0

MAXIMIN =$0


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Maximax

STATES OF NATURE




Do nothing$0$0$0

MAXIMAX =$200,000


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Hurwicz criterion

STATES OF NATURE


Construct large plant$200,000($180,000)$54,0800.1666666667

Construct small plant$100,000($20,000)$53,9200.6153846154

Do nothing$0$0$0



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Minimax regret

$200,000($180,000)

$100,000($20,000)

$0$0

Regret ValuesSTATES OF NATURE


Construct large plant$0$180,000$180,000

Construct small plant$100,000$20,000$100,000

Do nothing$200,000$0$200,000

MINIMAX =$100,000


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Laplace's

STATES OF NATURE




Do nothing$0$0$0

MAX. R.A. =$40,000


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EMV

STATES OF NATURE




Do nothing$0$0$0

PROBABILITIES0.60.4

MAX. EMV =$52,000


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EOL

STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4


$0$180,000$72,000

$100,000$20,000$68,000

$200,000$0$120,000

MIN. EOL =$68,000


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Results of the Example

METHOD DECISION

Maximax “Construct large plant”

Maximin “Do nothing”

Criterion of Realism depends on α

Equally likelihood “Construct small plant”

Minimax “Construct small plant”

The appropriate method is dependent on the personality and philosophy of the DM.



Additional Example

Alternative

State of NatureGood

Market(TL)

Average Market

(TL)

Poor Market

(TL)Large Coffee House 75,000 25,000 -40,000

Small Coffee House 100,000 35,000 -60,000

Do nothing 0 0 0


PresenterPresentation NotesMaximax: 75, 100*, 0Maximin: -40, -60, 0*Hurwicz: (a=0.6) 29, 36*, 0Eq. Like.: 20, 25*, 0Regret: 40*, 60, 100


Solutions with QM for Windows



Decision Making Under RiskProbability

Objective Subjective

Expected (Monetary) ValueExpected Value of Perfect Information

Expected Opportunity Loss Utility Theory

Certainty EquivalenceRisk Premium



Probability

A probability is a numerical statement about the likelihood that an event will occur

The probability, P, of any event occurring is greater than or equal to 0 and less than or equal to 1:

0 ≤ P(event) ≤ 1 The sum of the simple probabilities for all possible

outcomes of an activity must equal 1



Objective Probability

Determined by experiment or observation: Probability of heads on coin flip Probability of spades on drawing card from deck

P(A): probability of occurrence of event An(A): number of times that event A occursn: number of independent and identical repetitions

of the experiments or observations

P(A) = n(A) / n∞→n

limit



Subjective Probability Determined by an estimate based on the expert’s

personal belief, judgment, experience,

and existing knowledge of a situation


PresenterPresentation Notes Subjective Probability is associated not with the system under observation, but with the observer of that systemDifferent DMs can assign different probabilities to the same event.


Payoff Matrix with Probabilities

STATES OF NATURE


marketUnfavorable

marketProbabilites 60% 40%Construct large plant $200,000 ($180,000)Construct small plant $100,000 ($20,000)Do nothing $0 $0



STATES OF NATURE


Probabilites60%40%



Do nothing$0$0

PROBABILITIES0.60.4

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Maximin

STATES OF NATURE




Do nothing$0$0$0

MAXIMIN =$0


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Maximax

STATES OF NATURE




Do nothing$0$0$0

MAXIMAX =$200,000


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Hurwicz criterion

STATES OF NATURE




Do nothing$0$0$0



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Minimax regret

STATES OF NATURE




Do nothing$0$0


$0$180,000$180,000

$100,000$20,000$100,000

$200,000$0$200,000

MINIMAX =$100,000


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Laplace's

STATES OF NATURE




Do nothing$0$0$0

MAX. R.A. =$40,000


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EMV

STATES OF NATURE




Do nothing$0$0$0

PROBABILITIES0.60.4

MAX. EMV =$52,000


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EOL

STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4


$0$180,000$72,000

$100,000$20,000$68,000

$200,000$0$120,000

MIN. EOL =$68,000


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STATES OF NATURE


marketUnfavorable

marketExpected

ValueConstruct large plant $200,000 ($180,000) $48,000Construct small plant $100,000 ($20,000) $52,000Do nothing $0 $0 $0PROBABILITIES 0.6 0.4

Expected (Monetary) ValueChoose the alternative with the maximum weighted row

averageEV(ai) = vij P(θj)∑

j



STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4

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Maximin

STATES OF NATURE




Do nothing$0$0$0

MAXIMIN =$0


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Maximax

STATES OF NATURE




Do nothing$0$0$0

MAXIMAX =$200,000


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Hurwicz criterion

STATES OF NATURE




Do nothing$0$0$0



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Minimax regret

$200,000($180,000)

$100,000($20,000)

$0$0

REGRET VALUESSTATES OF NATURE




Do nothing$200,000$0$200,000

MINIMAX =$100,000


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Laplace's

STATES OF NATURE




Do nothing$0$0$0

MAX. R.A. =$40,000


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EMV

STATES OF NATURE

ALTERNATIVESFavorable marketUnfavorable marketExpected Value



Do nothing$0$0$0

PROBABILITIES0.60.4

MAX. EMV =$52,000


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EOL

STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4


$0$180,000$72,000

$100,000$20,000$68,000

$200,000$0$120,000

MIN. EOL =$68,000


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Sensitivity Analysis

EV (Large plant) = $200,000P – $180,000 (1 – P)

EV (Small plant) = $100,000P – $20,000(1 – P)

EV (Do nothing) = $0P + $0(1 – P)



Sensitivity Analysis

-200000-150000-100000

-500000

50000100000150000200000250000

0 0.2 0.4 0.6 0.8 1

P

EV

Point 1Small Plant

Large Plant Point 2



Expected Value of Perfect Information A consultant or a further analysis can aid the decision

maker by giving exact (perfect) information about the true state: the decision problem is no longer under risk; it will be under certainty.

Is it worthwhile for obtaining perfectly reliable information: is EVPI greater than the fee of the consultant (the cost of the analysis)?

EVPI is the maximum amount a decision maker would pay for additional information



Expected Value of Perfect InformationEVPI is the increase in EMV that results from having

perfect informationEVPI = EV with PI – Maximum EV under risk

EV with Perfect Information: 200*.6+0*.4=120Maximum EV under risk: 52 EVPI = 120 – 52 = 68

STATES OF NATURE


marketUnfavorable

marketExpected

ValueConstruct large plant $200,000 ($180,000) $48,000Construct small plant $100,000 ($20,000) $52,000Do nothing $0 $0 $0PROBABILITIES 0.6 0.4



STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4

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Maximin

STATES OF NATURE




Do nothing$0$0$0

MAXIMIN =$0


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Maximax

STATES OF NATURE




Do nothing$0$0$0

MAXIMAX =$200,000


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Hurwicz criterion

STATES OF NATURE




Do nothing$0$0$0



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Minimax regret

$200,000($180,000)

$100,000($20,000)

$0$0





Do nothing$200,000$0$200,000

MINIMAX =$100,000


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Laplace's

STATES OF NATURE




Do nothing$0$0$0

MAX. R.A. =$40,000


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EMV

STATES OF NATURE




Do nothing$0$0$0

PROBABILITIES0.60.4

MAX. EMV =$52,000


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EOL

STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4


$0$180,000$72,000

$100,000$20,000$68,000

$200,000$0$120,000

MIN. EOL =$68,000


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Regret Values STATES OF NATURE


marketUnfavorable

marketConstruct large plant $0 $180,000 $72,000Construct small plant $100,000 $20,000 $68,000Do nothing $200,000 $0 $120,000PROBABILITIES 0.6 0.4

Expected Opportunity

Loss

Expected Opportunity LossChoose the alternative with the minimum weighted row

average of the regret matrixEOL(ai) = rij P(θj)∑

j



STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4

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Maximin

STATES OF NATURE




Do nothing$0$0$0

MAXIMIN =$0


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Maximax

STATES OF NATURE




Do nothing$0$0$0

MAXIMAX =$200,000


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Hurwicz criterion

STATES OF NATURE




Do nothing$0$0$0



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Minimax regret

$200,000($180,000)

$100,000($20,000)

$0$0





Do nothing$200,000$0$200,000

MINIMAX =$100,000


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Laplace's

STATES OF NATURE




Do nothing$0$0$0

MAX. R.A. =$40,000


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EMV

STATES OF NATURE




Do nothing$0$0$0

PROBABILITIES0.60.4

MAX. EMV =$52,000


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EOL

$200,000($180,000)

$100,000($20,000)

$0$0

Regret ValuesSTATES OF NATUREExpected Opportunity Loss




Do nothing$200,000$0$120,000

PROBABILITIES0.60.4

MIN. EOL =$68,000


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Additional Example

Alternative

State of NatureGood

Market(TL)

Average Market

(TL)

Poor Market

(TL)Large Coffee House 75,000 25,000 -40,000

Small Coffee House 100,000 35,000 -60,000

Do nothing 0 0 0Probability 0.25 0.50 0.25


PresenterPresentation NotesEMV: 21.25, 27.5*, 0EVPI: 42.5 – 27.5 = 15EOL: 21.25, 15*, 42.5


«Deal or no Deal» TV Game Show The game revolves around the opening of a set of

numbered briefcases (or boxes), each of which contains a different cash.

The contents (i.e., the values) of all of the cases are known at the start of the game, but the specific location of any prize is unknown.

The contestant claims (or is assigned) a case to begin the game.

The case's value is not revealed until the conclusion of the game.



The contestant then begins choosing cases that are to be removed from play.

The amount inside each chosen case is immediately revealed

Throughout the game, after a predetermined number of cases have been opened, the banker offers the contestant an amount of money to quit the game

The offer based roughly on the amounts remaining in play and the contestant's demeanor, the bank tries to 'buy' the contestant's case for a lower price than what's inside the case.


«Deal or no Deal» TV Game Show

PresenterPresentation NotesDemeanor -> attitude, behaviour


The player then answers "Deal or no deal" question, choosing: "Deal", accepting the offer and ending the game "No Deal", rejecting the offer and continuing

This process of removing cases and receiving offers continues, until either the player accepts an offer to 'deal', or all offers have been rejected and player wins the cash

inside her/his case. To lengthen games, the banker's offer is usually less

than the expected value, particularly early in the game


«Deal or no Deal» TV Game Show


Utility Theory Utility assessment may assign the worst payoff a utility

of 0 and the best payoff a utility of 1. A standard gamble is used to determine utility values:

When DM is indifferent between two alternatives, the utility values of them are equal.

Choose the alternative with the maximum expected utility

EU(ai) = u(ai) = u(vij) P(θj)∑j



Standard Gamble for Utility AssessmentBest payoff (v*)u(v*) = 1

Worst payoff (v–)u(v–) = 0

Certain payoff (v)u(v) = 1*p+0*(1–p)

(p)

(1–p)



Utility Assessment (1st approach)v*u(v*) = 1

x1u(x1) = 0.5

x2u(x2) = 0.75

(0.5)

(0.5)

Best payoff (v*)u(v*) = 1


Certain payoff (x1)u(x1) = 0.5

(0.5)

(0.5)

x1u(x1) = 0.5

v–u(v–) = 0

x3u(x3) = 0.25

(0.5)

(0.5)

In the example:u(-180) = 0 and u(200) = 1x1= 100 ⇒ u(100) = 0.5x2 = 175 ⇒ u(175) = 0.75x3 = 5 ⇒ u(5) = 0.25

I II

III

0

0.2

0.4

0.6

0.8

1

-200 -150 -100 -50 0 50 100 150 200Dr. Y. İlker Topcu (www.ilkertopcu.n ) & Dr. Özgür Kabak ([email protected])et 36
Sheet: Sheet1

Sheet: Sheet2

Sheet: Sheet3

Getiri

Fayda E?risi

-180.0

5.0

100.0

175.0

200.0

0.0

0.25

0.5

0.75

1.0

Expected Utility (Example 1)v ij u(v ij ) 200 1175 0.75100 0.55 0.250

-20-180 0

v ij u(v ij ) 5 0.250 0.2432

-20 0.2162-180 0

Utilities STATES OF NATURE


marketUnfavorable

marketExpected

UtilityConstruct large plant 1 0 0.6Construct small plant 0.5 0.2162 0.3865Do nothing 0.2432 0.2432 0.2432PROBABILITIES 0.6 0.4



fayda değerleriOLAYLAR

SEÇENEKLERYüksek TalepDüşük TalepBeklenen

Olasılıklar%60%40Fayda

Büyük fabrika kurma100.60200-180

Küçük fabrika kurma0.50.21620.3865100-20

Yatırım yapmama0.24320.24320.243200

viju(vij)

2001

1750.75

1000.5

50.25

0

-20

-1800

viju(vij)

50.25

00.24320.0270270270.027027

-200.21620.13513513510.135135

-1800

Sheet1

fayda değerleriOLAYLAR

SEÇENEKLERYüksek TalepDüşük TalepBeklenen

Olasılıklar%60%40Fayda

Büyük fabrika kurma100.60200-180

Küçük fabrika kurma0.50.21620.3865100-20

Yatırım yapmama0.24320.24320.243200

viju(vij)

2001

1750.75

1000.5

50.25

0

-20

-1800

viju(vij)

50.25

00.24320.0270270270.0272

-200.21620.13513513510.1352

-1800

Input

STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4

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Maximin

STATES OF NATURE




Do nothing$0$0$0

MAXIMIN =$0


&A

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Maximax

STATES OF NATURE




Do nothing$0$0$0

MAXIMAX =$200,000


&A

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Hurwicz criterion

STATES OF NATURE




Do nothing$0$0$0



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Minimax regret

$200,000($180,000)

$100,000($20,000)

$0$0





Do nothing$200,000$0$200,000

MINIMAX =$100,000


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Laplace's

STATES OF NATURE




Do nothing$0$0$0

MAX. R.A. =$40,000


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EMV

UtilitiesSTATES OF NATURE

ALTERNATIVESFavorable marketUnfavorable marketExpected Utility

Construct large plant100.6

Construct small plant0.50.21620.3865

Do nothing0.24320.24320.2432

PROBABILITIES0.60.4

MAX. EMV =$0


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EOL

STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4


$0$180,000$72,000

$100,000$20,000$68,000

$200,000$0$120,000

MIN. EOL =$68,000


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Utility Assessment (2nd approach)

Best payoff (v*)u(v*) = 1


Certain payoff (vij)u(vij) = p

(p)

(1–p)

In the example:u(-180) = 0 and u(200) = 1For vij=–20, p=%70 ⇒ u(–20) = 0.7For vij=0, p=%75 ⇒ u(0) = 0.75For vij=100, p=%90 ⇒ u(100) = 0.9

0

0.2

0.4

0.6

0.8

1

-200 -150 -100 -50 0 50 100 150 200

Sheet: Sheet1

Sheet: Sheet2

Sheet: Sheet3

Getiri

Fayda E?risi

-180.0

-20.0

0.0

100.0

200.0

0.0

0.7

0.75

0.9

1.0

Expected Utility (Example 2)

Utilities STATES OF NATURE


marketUnfavorable

marketExpected

UtilityConstruct large plant 1 0 0.6Construct small plant 0.9 0.7 0.82Do nothing 0.75 0.75 0.75PROBABILITIES 0.6 0.4



STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4

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Maximin

STATES OF NATURE




Do nothing$0$0$0

MAXIMIN =$0


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Maximax

STATES OF NATURE




Do nothing$0$0$0

MAXIMAX =$200,000


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Hurwicz criterion

STATES OF NATURE




Do nothing$0$0$0



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Minimax regret

$200,000($180,000)

$100,000($20,000)

$0$0





Do nothing$200,000$0$200,000

MINIMAX =$100,000


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Laplace's

STATES OF NATURE




Do nothing$0$0$0

MAX. R.A. =$40,000


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EMV

UtilitiesSTATES OF NATURE

ALTERNATIVESFavorable marketUnfavorable marketExpected Utility

Construct large plant100.6

Construct small plant0.90.70.82

Do nothing0.750.750.75

PROBABILITIES0.60.4

MAX. EMV =$0


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EOL

STATES OF NATURE




Do nothing$0$0

PROBABILITIES0.60.4


$0$180,000$72,000

$100,000$20,000$68,000

$200,000$0$120,000

MIN. EOL =$68,000


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Preferences for Risk

Monetary outcome

Util

ity



Certainty Equivalence If a DM is indifferent between accepting a lottery

ticket and accepting a sum of certain money, the monetary sum is the Certainty Equivalent (CE) of the lottery

Z is CE of the lottery (Y>Z>X).

X

Y

Z

p

1–p



Risk Premium Risk Premium (RP) of a lottery is the difference between

the EV of the lottery and the CE of the lottery If the DM is risk averse (avoids risk), RP > 0

S/he prefers to receive a sum of money equal to expected value of a lottery than to enter the lottery itself

If the DM is risk prone (seeks risk), RP < 0S/he prefers to enter a lottery than to receive a sum of money equal to its expected value

If the DM is risk neutral, RP = 0S/he is indifferent between entering any lottery and receiving a sum of money equal to its expected value



Decision Analysis�(Decision Tables, Utility)IntroductionComponents of Decision AnalysisBasic Steps in Decision Analysis�Decision-Making EnvironmentsDecision Making Under CertaintyDecision Making Under UncertaintyDecision Table / Payoff MatrixMaximaxMaximinCriterion of RealismSlide Number 12Criterion of RealismEqually LikelihoodMinimaxResults of the ExampleAdditional ExampleSolutions with QM for WindowsDecision Making Under RiskProbabilityObjective ProbabilitySubjective ProbabilityPayoff Matrix with ProbabilitiesExpected (Monetary) ValueSensitivity AnalysisSensitivity AnalysisExpected Value of Perfect InformationExpected Value of Perfect InformationExpected Opportunity LossAdditional Example«Deal or no Deal» TV Game Show«Deal or no Deal» TV Game Show«Deal or no Deal» TV Game ShowUtility TheoryStandard Gamble for Utility AssessmentUtility Assessment (1st approach)Expected Utility (Example 1)Utility Assessment (2nd approach)Expected Utility (Example 2)Preferences for RiskCertainty EquivalenceRisk Premium

dr. y. İlker topcu · decision-making under risk ... risk premium. dr. y. İlker topcu () & dr....

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