This study investigates the influence of risk tolerance on the expected utility in the long run. We estimate the extent to which the expected utility of optimal portfolios is affected by small changes in the risk tolerance. For this purpose, we adopt the Malliavin calculus method and the Hansen–Scheinkman decomposition, through which the expected utility is expressed in terms of the eigenvalues and eigenfunctions of an operator. We conclude that the influence of risk aversion on the expected utility is determined by these eigenvalues and eigenfunctions in the long run.

中文翻译：

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风险承受能力对长期投资的影响：Malliavin 演算方法

本研究调查了风险承受能力对长期预期效用的影响。我们估计最优投资组合的预期效用受风险承受能力微小变化影响的程度。为此，我们采用 Malliavin 演算方法和 Hansen-Scheinkman 分解，通过它，预期效用用算子的特征值和特征函数来表示。我们得出结论，从长远来看，风险厌恶对预期效用的影响是由这些特征值和特征函数决定的。