Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs
نویسندگان
چکیده
The present paper accomplishes a major step towards a reconciliation of two conflicting approaches in mathematical finance: on the one hand, the mainstream approach based on the notion of no arbitrage (Black, Merton & Scholes); and on the other hand, the consideration of non-semimartingale price processes, the archetype of which being fractional Brownian motion (Mandelbrot). Imposing (arbitrarily small) proportional transaction costs and considering logarithmic utility optimisers, we are able to show the existence of a semimartingale, frictionless shadow price process for an exponential fractional Brownian financial market. MSC 2010 Subject Classification: 91G10, 93E20, 60G48 JEL Classification Codes: G11, C61
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ورودعنوان ژورنال:
- Finance and Stochastics
دوره 22 شماره
صفحات -
تاریخ انتشار 2018