论文标题
一系列二项式模型的最佳预期效用的收敛
Convergence of Optimal Expected Utility for a Sequence of Binomial Models
论文作者
论文摘要
我们通过二项式模型分析了黑色 - choles模型近似值下预期实用性的收敛性。在D. Kreps和W. Schachermayer最近的一篇论文中，给出了一个令人惊讶且有些反直觉的例子：这种融合一般而言可能无法实现。该反例基于i.i.d.的二项式模型。对数的一步增量具有严格的积极的第三刻。情况是这种情况，当log-price的上踢大于下踢时。在D. Kreps和W. Schachermayer的论文中，这是一个悬而未决的问题，当下脚踢大于上踢大于上踢的情况下，在对称的二线模型的情况下，情况如何，而高脚踢等于下脚。在这种情况下，预期效用的融合是否有积极的结果？在本说明中，我们为这个问题提供了积极的答案。它基于对中心极限定理中产生的收敛性的一些相当精细的估计。
We analyze the convergence of expected utility under the approximation of the Black-Scholes model by binomial models. In a recent paper by D. Kreps and W. Schachermayer a surprising and somewhat counter-intuitive example was given: such a convergence may, in general, fail to hold true. This counterexample is based on a binomial model where the i.i.d. logarithmic one-step increments have strictly positive third moments. This is the case, when the up-tick of the log-price is larger than the down-tick. In the paper by D. Kreps and W. Schachermayer it was left as an open question how things behave in the case when the down-tick is larger than the up-tick and -- most importantly -- in the case of the symmetric binomial model where the up-tick equals the down-tick. Is there a general positive result of convergence of expected utility in this setting? In the present note we provide a positive answer to this question. It is based on some rather fine estimates of the convergence arising in the Central Limit Theorem.
