Portfolio Optimization with Consumption in a Fractional Black-scholes Market
نویسنده
چکیده
We consider the classical Merton problem of finding the optimal consumption rate and the optimal portfolio in a Black-Scholes market driven by fractional Brownian motion B with Hurst parameter H > 1/2. The integrals with respect to B are in the Skorohod sense, not pathwise which is known to lead to arbitrage. We explicitly find the optimal consumption rate and the optimal portfolio in such a market for an agent with logarithmic utility functions. A true self-financing portfolio is found to lead to a consumption term that is always favorable to the investor. We also present a numerical implementation by Monte Carlo simulations.
منابع مشابه
Numerical Solution of Fractional Black Scholes Equation Based on Radial Basis Functions Method
Options pricing have an important role in risk control and risk management. Pricing discussion requires modelling process, solving methods and implementing the model by real data in a given market. In this paper we show a model for underlying asset based on fractional stochastic models which is a particular type of behavior of stochastic assets changing. In addition a numerical method based on ...
متن کاملBarrier options pricing of fractional version of the Black-Scholes model
In this paper two different methods are presented to approximate the solution of the fractional Black-Scholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...
متن کاملEuropean option pricing of fractional Black-Scholes model with new Lagrange multipliers
In this paper, a new identification of the Lagrange multipliers by means of the Sumudu transform, is employed to btain a quick and accurate solution to the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Undoubtedly this model is the most well known model for pricing financial derivatives. The fractional derivatives is described in Caputo sen...
متن کاملNumerical Solutions for Fractional Black-Scholes Option Pricing Equation
In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.
متن کاملShadow 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007