Chances for the honest in honest versus insider trading

Mauricio Elizalde and Carlos Escudero

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Abstract: We study a Black-Scholes market with a finite time horizon and two investors: an honest and an insider trader. We analyze it with anticipating stochastic calculus in two steps. First, we recover the classical result on portfolio optimization that shows that the expected logarithmic utility of the insider is strictly greater than that of the honest trader. Then, we prove that, whenever the market is viable, the honest trader can get a higher logarithmic utility, and therefore more wealth, than the insider with a strictly positive probability. Our proof relies on the analysis of a sort of forward integral variant of the Dol\'eans-Dade exponential process. The main financial conclusion is that the logarithmic utility is perhaps too conservative for some insiders.

Date: 2021-06, Revised 2022-05
New Economics Papers: this item is included in nep-upt
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Published in SIAM J. Financial Math., Vol. 13, No. 2, pp. SC39-SC52 (2022)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2106.10033

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