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<p>The motivation of this research is a classical problem in financial mathematics, namely, the subjective valuation of rewards earned in future periods. Various additive formulas have been proposed and criticized both theoretically and experimentally. We start from the premise that interaction among the periods affecting this subjective assessment is allowed. Dispensing with the additive form of time discounting leads to a Choquet evaluation defined from a capacity that encapsulates the interactions and at the same time, coincides with standard evaluations at any single time period. This consideration raises the general capacity compliance problem. We formally pose this question and motivated by computational tractability, we investigate the main traits of its 2-additive configuration. Then we apply our conclusions to two specific statements respectively suggested by the exponential and hyperbolic discounted utility formulas.</p>

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The capacity compliance problem: refinements of time discounting to Choquet integrals with 2-additive fuzzy measures

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  • 发表日期：

    2025年8月31日

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  • José Carlos R. Alcantud

摘要

The motivation of this research is a classical problem in financial mathematics, namely, the subjective valuation of rewards earned in future periods. Various additive formulas have been proposed and criticized both theoretically and experimentally. We start from the premise that interaction among the periods affecting this subjective assessment is allowed. Dispensing with the additive form of time discounting leads to a Choquet evaluation defined from a capacity that encapsulates the interactions and at the same time, coincides with standard evaluations at any single time period. This consideration raises the general capacity compliance problem. We formally pose this question and motivated by computational tractability, we investigate the main traits of its 2-additive configuration. Then we apply our conclusions to two specific statements respectively suggested by the exponential and hyperbolic discounted utility formulas.