Is there time discounting for risk premium?

Neural Dynamics of the Combined Discounting of Delay and Probability During the Evaluation of a Delayed Risky Reward

Delay discounting and probability discounting are two important processes, but in daily life there are many more situations that involve delayed risky outcomes. Although neuroscience research has extensively investigated delay and probability discounting in isolation, little research has explored the neural correlates of the combined discounting of delay and probability. Using the event-related brain potentials (ERPs) technique, we designed a novel paradigm to investigate neural processes related to the combined discounting of delay and probability during the evaluation of a delayed risky reward. ERP results suggested distinct temporal dynamics for delay and probability processing during combined discounting. Both the early frontal P200 and the N2 reflected only probability, not delay, while the parietal P300 was sensitive to both probability and delay. Furthermore, the late positive potential (LPP) was sensitive to probability, but insensitive to delay. These results suggest that probability has a prolonged modulatory effect on reward evaluation in the information processing stream. These findings contribute to an understanding of the neural processes underlying the combined discounting of delay and probability. The limitation of this study is to only consider four delay and probability combinations. Future studies can explore the combined discounting of more probability and delay combinations to further test the robustness of the conclusion.

Path Dependency in the Discounting of Delayed and Probabilistic Gains and Losses

Human decision making often involves outcomes that are both risky and delayed. In such delayed lottery scenarios, the question of how such prospects are evaluated arises. An individual can arrive at their choice by following three different subjective value elicitation paths: (1) a direct path by considering the delay and risk of an outcome simultaneously; (2) a delay-probability path by first considering the delay and then the risk of an outcome; and (3) a probability-delay path by first considering the probability and then the delay of an outcome. Using a discounting framework, we conducted an experiment to investigate whether individual choices are path dependent, i.e., if the three paths elicit different subjective values of risky and delayed gains or losses. The experiment included an arbitrary selection of delays and individual probability estimates corresponding to each delay, obtained in an additional delay-probability trade-off task. Such approach ensured the equal individual decision factor strength of each outcome delay and probability. Our findings demonstrate that the human choice of risky and delayed gains or losses is indeed path dependent, which contrasts with the normative view. Furthermore, we present evidence that human choice more closely follows the delay-probability elicitation path than the probability-delay path in the domain of gains.

Risk inherent in delay accounts for magnitude effects in intertemporal decision making

If the future is indeed uncertain, then is the subjective riskiness of future gains and losses amount-dependent? To address this question, we performed two experiments, one regarding hypothetical monetary gains and the other regarding hypothetical monetary losses. Our main objective was to determine whether the magnitude effect observed in delay discounting can be explained by the subjective probability of receiving a future outcome. We employed a well-grounded discounting paradigm with a fixed-sequence procedure and the Subjective Probability Questionnaire across different magnitudes of gains and losses. We replicated prior findings indicating that the magnitude effect (observed in delay discounting) or the reverse magnitude effect (observed in probability discounting) are present for monetary gains but not for monetary losses. We found that the subjective probability of receiving future outcomes is amount-dependent for gains but not for losses. We propose that the magnitude effect can be a by-product of the risk associated with future payoffs of different magnitudes, as shown by mediation analysis. Our secondary goal was to investigate the form of the subjective probability function over time to determine if the change in risk inherent in delay is best described by the hyperbolic or exponential equations. We demonstrate that delay and probability discounting, as well as the subjective probability function, are best described by a simple hyperbolic model.