Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs
نویسندگان
چکیده
منابع مشابه
Shadow prices, fractional Brownian motion, and portfolio optimisation under transaction costs
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 (arbitrari...
متن کاملPortfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion∗
While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. In this paper, we show, for a class of price processes which are not necessarily semimartingales, the existence of an optimal trading strategy for utility m...
متن کاملOn using shadow prices in portfolio optimization with transaction costs
In frictionless markets, utility maximization problems are typically solved either by stochastic control or by martingale methods. Beginning with the seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676–713], stochastic control theory has also been used to solve various problems of this type in the presence of proportional transaction costs. Martingale methods, on the other hand, h...
متن کاملDuality Theory for Portfolio Optimisation under Transaction Costs
For portfolio optimisation under proportional transaction costs, we provide a duality theory for general càdlàg price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised sense. This shadow price is defined via a “sandwiched” process consisting of a predictable and an optional strong supermartingale and pertains to all strateg...
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The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, th...
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ژورنال
عنوان ژورنال: Finance and Stochastics
سال: 2017
ISSN: 0949-2984,1432-1122
DOI: 10.1007/s00780-017-0351-5