A triple comparison between anticipating stochastic integrals in financial modeling
Abstract
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.
Cite
@article{arxiv.1801.03351,
title = {A triple comparison between anticipating stochastic integrals in financial modeling},
author = {Joan C. Bastons and Carlos Escudero},
journal= {arXiv preprint arXiv:1801.03351},
year = {2018}
}