Prospect theory is a theory of behavioral economics, judgment and decision making that was developed by Daniel Kahneman and Amos Tversky in 1979. The theory was cited in the decision to award Kahneman the 2002 Nobel Memorial Prize in Economics.
Based on results from controlled studies, it describes how individuals assess their loss and gain perspectives in an asymmetric manner (see loss aversion). For example, for some individuals, the pain from losing $1,000 could only be compensated by the pleasure of earning $2,000. Thus, contrary to the expected utility theory (which models the decision that perfectly rational agents would make), prospect theory aims to describe the actual behavior of people.
In the original formulation of the theory, the term prospect referred to the predictable results of a lottery. However, prospect theory can also be applied to the prediction of other forms of behaviors and decisions.
Prospect theory challenges the expected utility theory developed by John von Neumann and Oskar Morgenstern in 1944 and constitutes one of the first economic theories built using experimental methods.
History
In the draft received by the economist Richard Thaler in 1976, the term "Value Theory" was used instead of Prospect Theory. Later on, Kahneman and Tversky changed the title to Prospect Theory to avoid possible confusions. According to Kahneman, the new title was 'meaningless.'
Overview
Prospect theory stems from loss aversion, the observation that agents asymmetrically feel losses more acutely than equivalent gains. It centers on the idea that people evaluate the utility of gains and losses relative to a certain "neutral" reference point regarding their current individual situation. Thus, rather than rationally maximizing a fixed expected utility, value decisions are made relative to the current neutral situation and not following any absolute measure of utility.
Consider two choice scenarios:
a 100% chance of gaining $450 or a 50% chance of gaining $1000 a 100% chance of losing $500 or a 50% chance of losing $1100
It is assumed that the agent's individual utility is proportional to the dollar amount (e.g. $1000 would be twice as useful as $500). Prospect theory suggests that:
When faced with a risky choice leading to gains, agents are risk averse, preferring a certain outcome with a lower expected utility (i.e., the value function is concave). In the example, agents will choose the certain $450 even though the expected utility of the risky gain is higher. When faced with a risky choice leading to losses, agents are risk seeking, preferring the outcome that has a lower expected utility but the potential to avoid losses (i.e., the value function is convex). Agents will choose the 50% chance of losing $1100 even though the expected utility is lower, due to the chance that they lose nothing at all.
These two examples are thus in contradiction with the theory of expected utility, which leads only to choices which maximize utility. Also, the concavity of gains and the convexity of losses implies diminishing marginal utility with increasing gains or losses. In other words, someone who has more money has a lower desire for a fixed amount of gain (and lower aversion to a fixed amount of loss) than someone who has less money.
The theory continues with a second concept, based on the observation that people attribute excessive weight to events with low probability and insufficient weight to events with high probability. For example, individuals may unconsciously treat an outcome with a probability of 99% as if its probability were 95%, and an outcome with probability of 1% as if it had a probability of 5%. Under- and over-weighting of probabilities is importantly distinct from under- and over-estimating probabilities, a different type of cognitive bias which is observed for example in the overconfidence effect.
Model The theory describes the decision processes in two stages: During an initial phase termed editing, outcomes of a decision are ordered according to a certain heuristic. In particular, people decide which outcomes they consider equivalent, set a reference point and then consider lesser outcomes as losses and greater ones as gains. The editing phase aims to alleviate any framing effects. It also aims to resolve isolation effects stemming from individuals' propensity to often isolate consecutive probabilities instead of treating them together. The editing process can be viewed as composed of coding, combination, segregation, cancellation, simplification and detection of dominance. In the subsequent evaluation phase, people behave as if they would compute a value (utility), based on the potential outcomes and their respective probabilities, and then choose the alternative having a higher utility.
The formula that Kahneman and Tversky assume for the evaluation phase is (in its simplest form) given by:
where is the overall or expected utility of the outcomes to the individual making the decision, are the potential outcomes and their respective probabilities and is a function that assigns a value to an outcome. The value function that passes through the reference point is s-shaped and asymmetrical. Losses hurt more than gains feel good (i.e., there is loss aversion). This differs from expected utility theory, in which a rational agent is indifferent to the reference point, i.e. does not care how the outcome of losses and gains are framed. The function is a probability weighting function and captures the idea that people tend to overreact to small probability events, but underreact to large probabilities. Let denote a prospect with outcome with probability and outcome with probability , and nothing with probability . If is a regular prospect (i.e., either , or , or ), then:
However, if and either or , then:
It can be deduced from the first equation that and . The value function is thus defined on deviations from the reference point, generally concave for gains and commonly convex for losses and steeper for losses than for gains. If is equivalent to then is not preferred to , but from the first equation it follows that , which leads to , therefore:
This means that for a fixed ratio of probabilities the decision weights are closer to unity when probabilities are low than when they are high. In prospect theory, is never linear. In the case that , and prospect dominates prospect , which means that , therefore:
As , , but since , it would imply that must be linear; however, dominated alternatives are brought to the evaluation phase since they are eliminated in the editing phase. Although direct violations of dominance never happen in prospect theory, it is possible that a prospect A dominates B, B dominates C but C dominates A.
Value function The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. These geometric properties indicate risk-aversion for gains and risk-seeking for losses, thereby characterizing loss aversion. These properties were derived inductively from experimental observations. The first purely deductive, mathematical proof of the value function's properties is presented after decades. The proof Ka Yee Yeung. A Minimal-assumption Approach to Deriving a Unique Utility Function: Measuring the Psychological Utility of COVID-19 Vaccinations Worldwide, 23 September 2025, PREPRINT (Version 1) available at Research Square demonstrates a first-principles derivation of the S-shape, loss-averse value function using a partial differential equation (PDE) . This provides a microfoundation to shed light on the empirical rule.
Example To see how prospect theory can be applied, consider the decision to buy insurance. Assume the probability of the insured risk is 1%, the potential loss is $1,000 and the premium is $15. If we apply prospect theory, we first need to set a reference point. This could be the current wealth or the worst case (losing $1,000). If we set the frame to the current wealth, the decision would be to either
1. Pay $15 for insurance, which yields a prospect-utility of ,
OR
2. Enter a lottery with possible outcomes of $0 (probability 99%) or −$1,000 (probability 1%), which yields a prospect-utility of .
According to prospect theory,
, because low probabilities are usually overweighted; , by the convexity of value function in losses.
The comparison between and is not immediately evident. However, for typical value and weighting functions, , and hence . That is, a strong overweighting of small probabilities is likely to undo the effect of the convexity of in losses, making the insurance attractive.
If we set the frame to -$1,000, we have a choice between and . In this case, the concavity of the value function in gains and the underweighting of high probabilities can also lead to a preference for buying the insurance.
The interplay of overweighting of small probabilities and concavity-convexity of the value function leads to the so-called fourfold pattern of risk attitudes: risk-averse behavior when gains have moderate probabilities or losses have small probabilities; risk-seeking behavior when losses have moderate probabilities or gains have small probabilities.
Below is an example of the fourfold pattern of risk attitudes. The first item in each quadrant shows an example prospect (e.g. 95% chance of winning $10,000 is high probability and a gain). The second item in the quadrant shows the focal emotion that the prospect is likely to evoke. The third item indicates how most people would behave given each of the prospects (either Risk Averse or Risk Seeking). The fourth item states expected attitudes of a potential defendant and plaintiff in discussions of settling a civil suit.
Example Gains Losses High probability (certainty effect) 95% chance of winning $10,000 or 100% chance of obtaining $9,499. So, 95% × $10,000 = $9,500 > $9,499. Fear of disappointment. Risk averse. Accept unfavorable settlement of 100% chance of obtaining $9,499 95% chance of losing $10,000 or 100% chance of losing $9,499. So, 95% × −$10,000 = −$9,500 < −$9,499. Hope to avoid loss. Risk seeking. Rejects favorable settlement, chooses 95% chance of losing $10,000 Low probability (possibility effect) 5% chance of winning $10,000 or 100% chance of obtaining $501. So, 5% × $10,000 = $500 < $501. Hope of large gain. Risk seeking. Rejects favorable settlement, chooses 5% chance of winning $10,000 5% chance of losing $10,000 or 100% chance of losing $501. So, 5% × −$10,000 = −$500 > −$501. Fear of large loss. Risk averse. Accept unfavorable settlement of 100% chance of losing $501
Probability distortion is that people generally do not look at the value of probability uniformly between 0 and 1. Lower probability is said to be over-weighted (that is, a person is overly concerned with the outcome of the probability) while medium to high probability is under-weighted (that is, a person is not concerned enough with the outcome of the probability). The exact point in which probability goes from over-weighted to under-weighted is arbitrary, but a good point to consider is probability = 0.33. A person values probability = 0.01 much more than the value of probability = 0 (probability = 0.01 is said to be over-weighted). However, a person has about the same value for probability = 0.4 and probability = 0.5. Also, the value of probability = 0.99 is much less than the value of probability = 1, a sure thing (probability = 0.99 is under-weighted). A little more in depth when looking at probability distortion is that π(p) + π(1 − p) < 1 (where π(p) is probability in prospect theory).
Myopic Loss Aversion (MLA)