The St. Petersburg paradox is the oldest paradox in decision theory and has played a pivotal role in the introduction of increasing concave utility functions embodying risk aversion and decreasing marginal utility of gains. All attempts to resolve it have considered some variants of the original set-up, but the original paradox has remained unresolved, while the proposed variants have introduced new complications and problems. Here a rigorous mathematical resolution of the St. Petersburg paradox is suggested based on a probabilistic approach to decision theory.

中文翻译：

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圣彼得堡悖论的解决

圣彼得堡悖论是决策理论中最古老的悖论，在引入体现风险规避和收益边际效用递减的渐增凹效用函数方面发挥了关键作用。解决它的所有尝试都考虑了原始设置的一些变体，但最初的悖论仍未解决，而提议的变体引入了新的并发症和问题。在这里，基于决策理论的概率方法，提出了对圣彼得堡悖论的严格数学解决方案。