论文标题
Föllmer-Schweizer分解有限概率空间的稳定性和渐近分析
Stability and asymptotic analysis of the Föllmer-Schweizer decomposition on a finite probability space
论文作者
论文摘要
首先，我们考虑在完整的二项式模型中对冲的问题。使用离散时间föllmer-Schweizer分解，我们证明了向后诱导和顺序回归方法的等效性。其次，在不完整的三项式模型中，我们研究了顺序回归方法的扩展，以近似或有索赔。然后，在有限的概率空间上，我们研究了离散时间föllmer-Schweizer分解在股票价格动态的扰动方面的稳定性，最后，在同时对潜在的折扣价折扣价的漂移和波动性的同时扰动下进行了渐近分析，我们会证明稳定的稳定性和典型的绩效较高的条件。
First, we consider the problem of hedging in complete binomial models. Using the discrete-time Föllmer-Schweizer decomposition, we demonstrate the equivalence of the backward induction and sequential regression approaches. Second, in incomplete trinomial models, we examine the extension of the sequential regression approach for approximation of contingent claims. Then, on a finite probability space, we investigate stability of the discrete-time Föllmer-Schweizer decomposition with respect to perturbations of the stock price dynamics and, finally, perform its asymptotic analysis under simultaneous perturbations of the drift and volatility of the underlying discounted stock price process, where we prove stability and obtain explicit formulas for the leading order correction terms.
