# Decision Theory Essay

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Quantitative Methods
Fenway & Backbay cohorts
Sri Krishnamurthy, CFA, CAP
Hult.quant.fenway@gmail.com
Hult.quant.backbay@gmail.com
QuantUniversity LLC.

Session 4 - Part 1
Copyright 2014 QuantUniversity LLC. Cannot be reproduced or used without written permission from
QuantUniversity LLC.

Elements of Decision
Analysis
 Although decision making under uncertainty occurs in a wide

variety of contexts, all problems have three common elements: The set of decisions (or strategies) available to the decision maker, 2. The set of possible outcomes and the probabilities of these outcomes, and
3. A value model that prescribes monetary values for the various decision-outcome combinations.
1.

Once these elements are known, the decision maker can find an optimal decision, depending on the optimality criterion chosen.

Elements of Decision
Analysis Continued
 A payoff table lists the payoff for each decision-outcome pair. Positive

values correspond to rewards (or gains), and negative values correspond to costs (or losses).

Elements of Decision
Analysis Continued
 The maximin criterion finds the worst payoff in each row of the

payoff table and chooses the decision corresponding to the best of these. ( Risk averse)
 The maximax criterion finds the best payoff in each row of the payoff table and chooses the decision corresponding to the best of these. (Risk Taker)
 The expected monetary value, or EMV, for any decision is a weighted average of the possible payoffs for this decision, weighted by the probabilities of the outcomes.

Coin toss

EMV for the payoff table
Let’s say the probabilities of realizing the payoffs are as below
O1

O2

O3

D2

.3

.5

.2

D3

.5

.2

.3

Sensitivity Analysis
 In sensitivity analysis, we systematically vary inputs to the

problem to see how (or if) the outputs – the EMVs and the best decision – change.
 Some of the quantities in a decision analysis, particularly the probabilities, are often intelligent guesses at best.
 Therefore, it is important, especially in real-world business problems, to accompany any decision analysis with a sensitivity analysis.

Decision Tree for the simple example
 Decision tree for a simple decision problem:

Decision Trees
 Decision trees are composed of nodes (circles, squares, and

triangles) and branches (lines).
 The nodes represent points in time. A decision node (a square) represents a time when the decision maker makes a decision.  A probability node (a circle) represents a time when the result of an uncertain outcome becomes known.
 An end node (a triangle) indicates that the problem is completed - all decisions have been made, all uncertainty has been resolved, and all payoffs and costs have been incurred.

Decision Trees Continued
 Time proceeds from left to right. This means that any

branches leading into a node (from the left) have already occurred. Branches leading out of a decision node represent the possible decisions; the decision maker can choose the preferred branch.
Probabilities are listed on probability branches. These probabilities are conditional on the events that have already been observed (those to the left).
Monetary values are shown to the right of the end nodes.
EMVs are calculated through a “folding-back” process.

Folding-Back Procedure
 Starting from the right of the decision tree and working back

to the left:
 At each probability node, calculate an EMV – a sum of products of monetary values and probabilities.
 At each decision node, take a maximum of EMVs to identify the optimal decision.

Risk Profiles
 The risk profile for a decision is a “spike” chart that

represents the probability distribution of monetary outcomes for this decision.
 By looking at the risk profile for a particular decision, you can see the risks and rewards involved. By comparing risk profiles for…