European option pricing under cumulative prospect theory with constant relative sensitivity probability weighting functions

2018 ◽  
Vol 16 (1-2) ◽  
pp. 249-274 ◽  
Author(s):  
Martina Nardon ◽  
Paolo Pianca
Keyword(s):  
Option Pricing ◽  
Prospect Theory ◽  
Relative Sensitivity ◽  
Cumulative Prospect Theory ◽  
Probability Weighting ◽  
European Option ◽  
Weighting Functions ◽  
European Option Pricing

scholarly journals Dynamic prospect theory - two core economic decision theories coexist in the gambling behavior of monkeys

2021 ◽  
Author(s):  
Agnieszka Tymula ◽  
Yuri Imaizumi ◽  
Takashi Kawai ◽  
Jun Kunimatsu ◽  
Masayuki Matsumoto ◽  
...  
Keyword(s):  
Reinforcement Learning ◽  
Prospect Theory ◽  
Weighting Function ◽  
Gambling Behavior ◽  
Theory Model ◽  
Probability Weighting ◽  
Choice Data ◽  
Mathematical Functions ◽  
Weighting Functions ◽  
Dynamic Function

Research in behavioral economics and reinforcement learning has given rise to two influential theories describing human economic choice under uncertainty. The first, prospect theory, assumes that decision-makers use static mathematical functions, utility and probability weighting, to calculate the values of alternatives. The second, reinforcement learning theory, posits that dynamic mathematical functions update the values of alternatives based on experience through reward prediction error (RPE). To date, these theories have been examined in isolation without reference to one another. Therefore, it remains unclear whether RPE affects a decision-maker's utility and/or probability weighting functions, or whether these functions are indeed static as in prospect theory. Here, we propose a dynamic prospect theory model that combines prospect theory and RPE, and test this combined model using choice data on gambling behavior of captive macaques. We found that under standard prospect theory, monkeys, like humans, had a concave utility function. Unlike humans, monkeys exhibited a concave, rather than inverse-S shaped, probability weighting function. Our dynamic prospect theory model revealed that probability distortions, not the utility of rewards, solely and systematically varied with RPE: after a positive RPE, the estimated probability weighting functions became more concave, suggesting more optimistic belief about receiving rewards and over-weighted subjective probabilities at all probability levels. Thus, the probability perceptions in laboratory monkeys are not static even after extensive training, and are governed by a dynamic function well captured by the algorithmic feature of reinforcement learning. This novel evidence supports combining these two major theories to capture choice behavior under uncertainty.

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