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arXiv · 1801.03351

A triple comparison between anticipating stochastic integrals in financial modeling

Joan C. Bastons·Carlos Escudero
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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.

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Joan C. Bastons, Carlos Escudero. 2018-01-10. A triple comparison between anticipating stochastic integrals in financial modeling. https://arxiv.org/abs/1801.03351

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