金融建模中期望随机积分的三重比较
A triple comparison between anticipating stochastic integrals in financial modeling
摘要：
我们考虑金融市场中内幕交易问题的简化版本。我们通过预测随机分析来接近它，并在此背景下比较使用Hitsuda-Skorokhod，Ayed-Kuo和Russo-Vallois向前积分。我们的研究结果给出了一些迹象表明，虽然远期积分产生的结果具有适当的金融意义，Hitsuda-Skorokhod和Ayed-Kuo积分不提供一个适当的制定这个问题。关于使用的Ayed-Kuo积分在这种情况下，还提供了进一步的结果，包括证明的事实，即期望的Russo-Vallois解决方案是严格大于，Ayed-Kuo解决方案。最后，我们猜想了具有有限概率不连续样本路径的Ayed-Kuo随机微分方程的显式解。
英文摘要：
We consider a simplified version of the problem of insider trading in a financial market. We approach it by means of anticipating stochastic calculus and compare the use of the Hitsuda-Skorokhod, the Ayed-Kuo, and the Russo-Vallois forward integrals within this context. Our results give some indication that, while the forward integral yields results with a suitable financial meaning, the Hitsuda-Skorokhod and the Ayed-Kuo integrals do not provide an appropriate formulation of this problem. Further results regarding the use of the Ayed-Kuo integral in this context are also provided, including the proof of the fact that the expectation of a Russo-Vallois solution is strictly greater than that of an Ayed-Kuo solution. Finally, we conjecture the explicit solution of an Ayed-Kuo stochastic differential equation that possesses discontinuous sample paths with finite probability.
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