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<p>We study a dynamic decision problem within a binomial tree framework, where the decision maker holds a subjective belief about the probabilities of upward and downward movements. Our analysis focuses on whether key stochastic dominance relations among prior beliefs—specifically, first-order, likelihood-ratio, hazard-rate, and reverse hazard-rate dominance—are preserved after conditioning on observed histories. We further identify conditions under which the distributions over specific sets of histories induced by different priors satisfy first-order stochastic dominance. As an application, we examine how these dominance relations influence the subjective valuation of European and American options. We show that first-order and (reverse) hazard-rate dominance are closely associated with higher expected payoffs from European options, while likelihood-ratio dominance leads to higher continuation values and increased exercise patience in the context of American options.</p>

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Learning and stochastic dominance with applications to subjective valuation of options

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • Ehud Lehrer,
  • Tao Wang

摘要

We study a dynamic decision problem within a binomial tree framework, where the decision maker holds a subjective belief about the probabilities of upward and downward movements. Our analysis focuses on whether key stochastic dominance relations among prior beliefs—specifically, first-order, likelihood-ratio, hazard-rate, and reverse hazard-rate dominance—are preserved after conditioning on observed histories. We further identify conditions under which the distributions over specific sets of histories induced by different priors satisfy first-order stochastic dominance. As an application, we examine how these dominance relations influence the subjective valuation of European and American options. We show that first-order and (reverse) hazard-rate dominance are closely associated with higher expected payoffs from European options, while likelihood-ratio dominance leads to higher continuation values and increased exercise patience in the context of American options.