QMB midterm

risk-averse

(The utility function is concave.)

Payoff matrix

- a table that summarizes the final outcome (or payoff) for each decision alternative under each possible state of nature

Construct Utility Table

A 1 0 0.500 B 0.8 0.65 0.725 maximum Prob 0.5 0.5

Decision Node

A decision node (a square) represents a choice to be made

Rolling back procedure

A systematic way of calculating EMVs in a decision tree and thereby identifying the best decision strategy.The process starts on the right on the tree and works back

AHP ( analytic Hierarchy Process)

AHP provides a more structured approach for determining the scores and weights for the multicriteria scoring model.

1) Buy the parcel of land at location A. 2) Buy the parcel of land at location B. 3) Buy both parcels. 4) Buy nothing.

Alternatives

Three characteristics of Decision tree

Alternatives Criteria States of Nature

1) Financial payoff.

Criteria

Branches leading out of a _________ represent the __________; the decision maker can choose the preferred branch.

Decision Node; Possible Decisions

Non-Probabilistic

Do not assume that the probabilities of occurrence can be assigned to the states of nature. These rules help to enhance our insight and sharpen our intuition about decision problems so that we can make more informed decisions: Maximax (Optimistic criteria) Maximin (Conservative criteria) Minimax regret

Terminal Nodes

Dots (triangles in ASP) value or Payoffs

Risk premium equation

EMV of an uncertain situation - certainty equivalent of the same uncertain situation

common utility rule

Each decision maker has his or her own utility function

utility matrix slove : For Expected utitliy A (prob.: 0.4) B (prob.: 0.6 U(13)=0.96 U(-12)=-19.08

Expected Utility 0.4*0.96+0.6*(-19.08) = -11.06

State of Nature

Future events not under the decision makers control

multi-stage decision problems

Many problems involve a series of decisions. These can be analyzed via decision trees. Each intermediate decision branches off

Probabilistic method

Objective probabilities are often assigned based on interviews with one or more domain experts.

Branches leading out of __________ represent the ___________ of uncertain events; the decision maker has no control over which of these will occur

Probability Nodes; Possible Outcomes

EOL Expected Regret or Opportunity Loss

Selects alternative with the smallest expected regretor opportunity loss

The new airport is built at location A. 2) The new airport is built at location B.

States of nature

risk seeking

The utility function is convex

risk neutral

The utility function is linear

The decision with the largest EMV will also have the smallest EOL - Always

True

The expected monetary value (EMV) and expected opportunity loss (EOL) decision rules always result in the selection of the same decision alternative.

True

the risk neutral decision maker follows the expected monetary value (EMV) decision rule

True

Regret

True payoff under the same state of nature

Exponential Utility Function

Used to model classic risk averse behaviorU(x) = 1 - e^(-x/R)R = risk tolerancex = monetary payoff you want to find utility for

Decision State of Nature 1 2. EMV A 150,000. -30,000 60,000 <--maximum B 70,000. 40,000. 55,000 Prob. 0.5. 0.5

Utility Theory incorporates the decision maker's attitudesand preferences toward risk and return in the decision-making process.

criteria

Various factors that are important to the decision maker and influenced by alternatives salary career potential location

Multicriteria Scoring Model

We score (or rate) each alternative in a decision problem based on each criterion. The value of score is from 0 to1. These scores can be thought of as subjective aassessments of the utility that each alternative provide son the various criteria. Assign weights to the criterion which reflect their relative importance.

Minimax Regret

Weakness: Adding another alternative could change the outcome

Maximin

Weakness: Does not consider states of nature, and sometimes there can only be marginal differences in the mins we select from

Maximax

Weakness: does not take into account different states of nature and always assumes the best outcome

what is R u (x)= 1-e^-x/4

a parameter that controls the shape of the utility function according to decision make's risk tolerance

Event nodes

circles value cash flow from data

Radar chart

compares aggregate values of three or more variables represented on axes starting from the same point

risk-averse definition

decision maker assigns the largest relative utility toany payoff, but has a diminishing marginal utility for increasedpayoffs - every additional dollar in payoff results in smallerincreases in utility

Risk seeking (definition)

decision maker assigns the smallest relative utility to any payoff, but has an increasing marginal utility for increased payoffs - every additional dollar in payoff results in larger increases in utility

Risk neutral definition

decision maker falls in between these two extremes, and has a constant marginal utility for increased payoffs - every additional dollar in payoff results in the same amount of increases in utility

which decision rule is most approiate for analyzing multi-stage decision problems

decision tree

Alternatives

different courses of action intended to solve a problem. -Work for company A -Work for company B -Reject both offers and keep searching A choice limited to one of two possibilities, as of things, propositions, or coursed of action.

good decision always result in good outcomes

false

Weakness of EMV

if EMV is between 5000 and 4500 we pick maximum is 5000 (to risky ) with caution in one-time decision problems

utility function that translates each of the possible monetary payoffs in a decision problem

into a non-monetary measure known as a utility

utility of a payoff

represents the total worth, value,or desirability of the outcome of a decision alternative tothe decision maker.

if Risk premium > 0 decision maker is

risk averse

u (x)= 1-e^-x/4 Exponential utility function is often used to model

risk averse behavior

if risk premium = 0 decision maker is

risk neutral

if risk premium < 0 decision maker is

risk seeking

In Multicriteria repersent for (X) and (Y)

scores and weights sij = score for alternative j on criterion iwi = weight for criterion Select the alternative with largest weighted average score

Risk premium definition

the EMV that a decision maker is willing to give up or pay to avoid a risky decision

Certainty equivalent

the amount of money that is equivalent in a decision makers mind to a situation involving uncertainty

what is x u (x)= 1-e^-x/4

the monetary payoff you want t find the utility for

As R increase what happens

the shape of utility curve becomes flatter or less risk-averse

Decision trees can be used for both single stage and multi stage decision

true

a structured approach to decision making can help us make good decisions cannot guarantee good outcomes

true

square nodes in decision tree indicate a decision must be made

true

Payoff matrix solve for utility matrix using:u (x)= 1-e^-x/4 $13 ($12)

utility matrix U(13)=0.96 U(-12)=-19.08