Leonard Savage’s Decision Theory
Meriem ELKHAL
November 1, 2023
Meriem ELKHAL
Leonard Savage’s Decision Theory
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1 / 19
Introduction
Decision-making is a vital responsibility for managers.
Many decisions involve uncertainty, and managers need to choose the
best option.
Leonard Savage’s work has significantly contributed to understanding
decision-making under uncertainty.
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Who was Leonard Savage?
Leonard Jimmie Savage (1917-1971)
American mathematician and
statistician
Pioneer in the field of decision theory
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Savage’s Contributions
Leonard Savage made significant contributions to the field of decision
theory, particularly in the context of decision-making under
uncertainty.
He introduced several key concepts and methodologies that continue
to be influential in decision analysis.
Some of his notable contributions include the development of the
Expected Utility Theory and the concept of subjective probability.
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Expected Utility Theory
One of Leonard Savage’s most prominent contributions was the
development of the Expected Utility Theory.
This theory provides a framework for rational decision-making under
uncertainty.
It suggests that individuals make decisions by maximizing their
expected utility, which combines the desirability of an outcome with
the probability of that outcome occurring.
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Subjective Probability
Savage’s work emphasized the role of subjective probability in
decision theory.
He argued that individuals often lack objective data to estimate
probabilities, so they rely on their personal beliefs and judgments.
Subjective probability allows decision-makers to incorporate their own
assessments of uncertainty into the decision-making process.
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Decision Theory: Definition
Decision theory is a process of selecting an act out of several available
alternative courses of action judged to be the best action according to
predetermined criteria.
Its objective is to help decision-makers select the best course of action
from available options.
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Key Components in Decision Theory
Decision Maker: The individual or group responsible for choosing
the best course of action from the available alternatives.
Courses of Action: These are the alternative strategies or actions
available to the decision-maker. For example, the quantity of a
particular stock to be ordered.
States of Nature: These represent external events outside the
decision-maker’s control that influence the success of a chosen action.
For instance, market demand for a particular product.
Payoff Values: Each combination of a course of action and state of
nature is associated with a payoff, representing the net benefit to the
decision-maker.
Bayes’ Rule: Used to calculate payoffs for each combination of
courses of action and states of nature.
Regrets or Opportunity Loss: Regret measures the difference
between the maximum possible profit for a state of nature and the
actual profit obtained due to the decision.
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Decision-Making Under Uncertainty
In finance, decision-makers often face uncertainty with no historical
data available to estimate probabilities.
For example, when launching a new financial product, historical data
may not be applicable.
This lack of data leads to decision-making under uncertainty.
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Minimax Regrets Criteria
The Minimax Regrets Criteria, introduced by Leonard Savage, helps
identify opportunity loss or regrets associated with each state of
nature.
It quantifies the difference between the maximum possible payoff for a
state of nature and the actual payoff due to the chosen decision.
Decision-makers aim to minimize regrets by choosing actions that
result in the least amount of opportunity loss.
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Minimax Regret Strategy in Finance
The Minimax Regret Strategy is employed by risk-neutral
decision-makers in finance who want to minimize their maximum
regret.
’Regret’ is defined as the opportunity loss resulting from making the
wrong financial decision.
To implement this strategy, a table is constructed to show the size of
regret, calculated as the difference between the maximum possible
profit for a state of nature and the actual profit obtained due to the
chosen financial decision.
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Example: Minimax Regret Strategy in Finance
Imagine a financial manager choosing where to invest money: in
bonds, stocks, or mutual funds.
We’re not sure about the economy, so we need to consider different
scenarios.
Let’s look at the profits in three different economic scenarios: growing
economy, stable economy, declining economy.
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Step 1: Create a Payoff Table
Action
Bonds
Stocks
Mutual Funds
Meriem ELKHAL
Growing
40
70
53
Stable
40
30
45
Leonard Savage’s Decision Theory
Declining
5
-13
-5
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Step 2: Create a Regret Table
First, we calculate regrets for each action in each state of nature.
Regret = Maximum possible profit - Actual profit
Action
Bonds
Stocks
Mutual Funds
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Growing
40
70
53
Stable
45
30
45
Leonard Savage’s Decision Theory
Declining
5
-13
-5
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Step 2: Create a Regret Table
Action
Bonds
Stocks
Mutual Funds
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Growing
70 - 40 = 30
70 - 70 = 0
70 - 53 = 17
Stable
45 - 45 = 0
45 - 30 = 15
45 - 45 = 0
Leonard Savage’s Decision Theory
Declining
5-5=0
5 -(-13) = 18
5 -(-5) = 10
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Step 3: Find the maximum regret
Action
Bonds
Stocks
Mutual Funds
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Growing
70 - 40 = 30
70 - 70 = 0
70 - 53 = 17
Stable
45 - 45 = 0
45 - 30 = 15
45 - 45 = 0
Declining
5-5=0
5 - (-13) = 18
5 - (-5) = 10
Leonard Savage’s Decision Theory
Max Regret
30
18
17
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Step 4: Minimize Maximum Regret
The goal is to choose the action with the smallest maximum regret.
In this example, the decision is to invest in mutual funds.
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Conclusion
Leonard Savage’s Decision Theory helps us make better financial
decisions when we’re not sure about the outcomes.
The Minimax Regret Strategy is a simple way to make decisions in
finance while minimizing regret.
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Conclusion
Thank you!
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