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Transfer Principle for nth order Fractional Brownian Motion with Applications to Prediction and Equivalence in Law
The n-th order fractional Brownian motion was introduced by Perrin et al. . It is the (up to a multiplicative constant) unique self-similar Gaussian process with the Hurst index H∈(n-1,n), having n-th order stationary ...
Subdiffusive fractional Black–Scholes model for pricing currency options under transaction costs
(Cogent OA, an imprint of Taylor & Francis, 2018-05-29)
A new framework for pricing European currency option is developed in the case where the spot exchange rate follows a subdiffusive fractional Black–Scholes. An analytic formula for pricing European currency call option is ...
Divisible skylines : exploring least common multiples and divisibility through visual art
(Tessellations Publishing, 2019)
We present an alternative way to consider number theoretic concepts through visual art. Our visualization method, Divisible Skylines, is an artistically motivated study of least common multiples. It demonstrates how beauty ...
Passive discrete-time systems with a Pontryagin state space
Passive discrete-time systems with Hilbert spaces as an incoming and outgoing space and a Pontryagin space as a state space are investigated. A geometric characterization when the index of the transfer function coincides ...
Fractional delta hedging strategy for pricing currency options with transaction costs
(Scientific Press, 2017)
This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional ...
Stieltjes and inverse Stieltjes holomorphic families of linear relations and their representations
(Polish Academy of Sciences, Institute of Mathematics, 2019-12-20)
We study analytic and geometric properties of Stieltjes and inverse Stieltjes families defined on a separable Hilbert space and establish various minimal representations for them by means of compressed resolvents of various ...
Conditional-mean hedging under transaction costs in Gaussian models
(World Scientific Publishing Company, 2018-04-02)
We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian ...
Hedging in fractional Black-Scholes model with transaction costs
We consider conditional-mean hedging in a fractional Black–Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the ...
Factorized sectorial relations, their maximal-sectorial extensions, and form sums
In this paper we consider sectorial operators, or more generally, sectorial relations and their maximal-sectorial extensions in a Hilbert space H. Our particular interest is in sectorial relations S, which can be expressed ...
Long-range dependence in the returns and volatility of the Finnish housing market
Purpose - The purpose of this paper is to examine the evidence of long-range dependence behaviour in both house price returns and volatility for fifteen main regions in Finland over the period of 1988:Q1 to 2018:Q4. These ...