Decision under uncertainty

The decisions under uncertainty is part of decision theory . There are decision-making situations in which the occurrence of future environmental conditions cannot be predicted with certainty. Thus, when selecting possible alternatives, their effects are not fully known. In contrast to this, the environmental conditions and their probabilities of occurrence are known when making decisions under safety .

Degrees of uncertainty

Even if no uniform linguistic usage has developed yet, Wolfgang Müller distinguishes between the following two degrees of uncertainty, depending on whether the occurrence probabilities for the environmental conditions are known:

The decision maker has the choice between various alternatives , which are dependent on the possible environmental conditions s _j . ${\displaystyle a_{i}}$

1. Decision-making under risk : The decision-maker is aware of the probability of occurrence of the environmental conditions s _j , which depends on his decision, objectively (e.g. with the lottery) or subjectively (based on estimates or historical values). The sum of the probabilities must be 1: = 1 ${\displaystyle w_{j}}$ ${\displaystyle \quad \sum _{j}w_{j}}$
2. Decision under uncertainty : The decision maker only knows the possible environmental states s _j that are dependent on his decision , but he cannot make a statement about the probabilities with which these environmental states will occur.

Frank Knight (1921) in his book Risk, Uncertainty and Profit distinguishes a further escalation level of uncertainty:

3. Decision under complete uncertainty ( Knight's uncertainty ): The decision-maker is not aware of either the probability of occurrence of the environmental conditions dependent on his decision or the possible environmental conditions dependent on his decision . For these decision-making situations , Sarasvathy suggests the decision logic Effectuation as a decision aid . ${\displaystyle w_{j}}$ ${\displaystyle s_{j}}$ ${\displaystyle s_{j}}$

According to the economist Hans-Werner Sinn , the two decision-making situations mentioned can also be subdivided while taking into account probability hierarchies. With probability hierarchies it is meant that there are alternative probability distributions for all states. Thus, risk and uncertainty can be distinguished as follows:

1. Decision under risk: The probabilities can be determined with certainty and there is a completely known probability hierarchy.
2. Decision under uncertainty: The probabilities are completely unknown and the probability hierarchies can only be partially represented. According to Sinn, these two degrees can always be traced back to a “certain known objective probability”. This can then be used for further analyzes and decisions. With the help of subjectively estimated probabilities, a transition from uncertainty to risk can also be made.

Insufficient Reason Principle

If there are no probabilities whatsoever or if the occurrence of one condition is not more credible than that of another, the principle of insufficient reason can be followed. Here all possible states are considered to be equally likely. The states thus occur with the same probability and the probability is regarded as a safe objective variable. This corresponds to the decision criterion using the expected value. This rule is called Laplace's rule . A distinction between the terms uncertainty and risk would therefore not be necessary.

A simple example of this principle is the drawing of red and blue balls from an urn. If the balls are completely evenly spaced, there is no incentive for one color to be drawn sooner than another. So pulling the color red is just as likely as pulling a blue ball.

Risk in risk management

In common parlance, risk is often understood as the risk of failure of an action or activity. In the business management focus, the risk results in both positive (= opportunities) and negative deviations (= losses). Different risks can compensate each other. This possible compensation must be taken into account in a general risk definition. For this reason, Werner Gleißner defines the concept of risk in the company as follows:

"Risk is the possibility, resulting from an uncertainly foreseeable future, caused by 'accidental' disruptions, of deviating from the planned goal."

In risk management, therefore, there is often no division into uncertainty and risk, but the term risk here clarifies the entire uncertainty. The justification for this is that, in situations of uncertainty, probabilities can be estimated with the best available information, whereby a transition to the risk situation is made.

Decision rules

Rules for making decisions under risk

Bayes' rule

Since the probability of occurrence of the environmental conditions is known when making a decision under risk, Bayes' rule (also called the μ rule) can be applied here. With this rule, the action alternative is chosen which has the greatest mathematical expected value.

μ-σ rule

The μ-σ rule takes into account both the expected value and the risk attitude of the decision maker. The standard deviation σ is used. If the decision maker is willing to take risks , he will choose the alternative with the same expected value μ, which has a higher σ. If the decision maker is risk averse , he will rather choose the alternative which has the lower standard deviation for the same μ. With a risk-neutral decision maker, the rule corresponds to Bayes' rule. Before the μ-σ rule can be applied, it should always be checked whether the prerequisites for normal distribution are met.

μ-R rule

With this generalized rule, the decision is made dependent on what a certain expected value μ and any risk measure R in principle is present. The μ-σ principle is a special case of this rule.

Bernoulli principle

In the Bernoulli principle, the action results are calculated into utility values ​​with the help of risk benefit functions. Each decision maker has an individual risk benefit function that reflects his risk preference. Convex function curves represent a risk-averse decision maker and concave curves represent a risk- taking decision maker. However, it should be noted that everyone does not always react to risks in the same way in different situations. The individual risk function can therefore represent both courses, depending on the environmental conditions.

Rules for making decisions under uncertainty

In decision theory, numerous procedures have been developed in order to be able to apply suitable decision rules despite the uncertainty . These often reflect a certain preference for risk. The best-known rules are:

Maximin rule (after A. Wald)

This rule is based on a pessimistic decision maker. The value chosen is always the one that is greatest when the most unfavorable environmental condition occurs.

Maximax rule (after A. Wald)

This rule is based on an optimistic decision maker. The value chosen is always the one that is greatest when the most favorable environmental condition occurs.

Further rules are the Hurwicz rule (after Leonid Hurwicz ) and the Laplace rule mentioned above .

Safety-first approach

One approach in the area of risk and portfolio management (the safety-first approach English to put safety first '). This approach limits the risk so that it does not exceed a set upper limit. Constraints of business decisions play a central role. Thus, in the safety-first approach, risk is defined as the risk of loss. This approach is used in decision-making where a choice is to be made between risky alternative courses of action (e.g. insurance companies).

For example, a company sets a maximum probability of loss or a maximum permitted probability of insolvency for a specific time horizon. The risk is thus limited upwards. The so-called shortfall probability plays an important role here. This quantifies the risk of falling below (= negative deviation) from certain target values. An example of a connection between the shortfall probability and the insolvency probability would be the specification of a minimum rating for a company. This corresponds to the accepted insolvency probability and it can also be interpreted as an application of the shortfall probability for ancillary conditions specified by the company.

There are three types of safety-first approach:

1. The shortfall probability of the portfolio is minimized.
2. There is a maximum accepted shortfall probability of the portfolio. Now the maximum expected return is selected without exceeding the set limit.
3. A maximum accepted shortfall probability and a targeted minimum return are set. From the portfolios that meet both requirements, the one with the highest return is selected.

When looking at the three types, it becomes clear that the safety-first approaches do not follow the expected utility maximization of the general expected utility theory. Rather, a risk / return combination is derived from portfolios that offer the required minimum security requirement.

See also

• Decision under security
• Decision under risk
• Ellsberg paradox
• Decision-making function
• Statistical decision problem

Web links

• Modeling Society's Capacity to Manage Extraordinary Events (PDF; 241 kB) From the Swedish Morphological Society (PDF file; 337 kB)
• Strategic Decision Support using Computerized Morphological Analysis (PDF file; 208 kB)

Individual evidence

1. ↑ Wolfgang Müller: Risk and Uncertainty . In: Waldemar Wittmann u. a. (Ed.): Concise dictionary of business administration (=  Encyclopedia of Business Administration . Volume 1 ). 5th edition. Schaffer-Pöschel, Stuttgart 1993, ISBN 3-7910-8033-4 .
2. ^ Frank Knight: Risk, Uncertainty and Profit . University of Chicago Press, Chicago 1971, ISBN 0-226-44690-5 (English, first edition: 1921).
3. ^ Saras D. Sarasvathy: Effectuation. Elements of Entrepreneurial Expertise . Edward-Elgar, Cheltenham 2008, ISBN 1-84844-572-5 (English).
4. ↑ ^{a b c} Hans-Werner Sinn: Economic decisions in the event of uncertainty . JCB Mohr (Paul Siebeck), Tübingen 1980, ISBN 3-16-942702-4 , p. 22 ( limited preview in Google Book Search - dissertation).
5. ↑ ^{a b} Werner Gleißner: Fundamentals of Risk Management. With well-founded information for better decisions . 3. Edition. Franz Vahlen, Munich 2017.
6. ↑ Hans-Werner Sinn: Economic decisions in the event of uncertainty . JCB Mohr (Paul Siebeck), Tübingen 1980, ISBN 3-16-942702-4 , p. 32 ( limited preview in Google Book Search - dissertation).
7. ↑ ^{a b} Werner Gleißner: Fundamentals of Risk Management. With well-founded information for better decisions . 3. Edition. Franz Vahlen, Munich 2011, p. 17 .
8. ↑ Werner Gleißner: Risk analysis and replication for company valuation and value-oriented company management . In: Economics Studies . No. 7 , July 2011, p. 345–352 ( werner-gleissner.de [PDF; accessed on October 7, 2019]).
9. ↑ JV Kaduff, K. Spremann: Security and Diversification in Shortfall Risk . In: Journal for Business Research (ZfbF) . 1996, p. 779-802 .
10. ↑ ^{a b} Werner Gleißner: Risk measures and evaluation - basics, downside measures and capital market models . In: Risk Manager Yearbook 2008 . Bank-Verlag, Cologne 2008, p. 107–126 ( werner-gleissner.de [PDF; accessed October 17, 2019]).
11. ↑ ^{a b} shortfall risk. In: Gabler Wirtschaftslexikon. Springer Gabler Verlag, accessed in 2017 . 
12. ↑ [1]
13. ^ A. Roy: Safety first and the holding of assets . In: Econometrica . tape 20 , 1952, pp. 434-449 (English).
14. ^ S. Kataoka: A Stochastic Programming Model . In: Econometrica . tape 31 , 1963, pp. 181-196 (English).
15. ^ L. Tesla: Safety first and Heding . In: Review of Economic Studies . tape 23 , 1955, pp. 1-16 (English).