Upper classes for the increments of the fractional Wiener process

1991 ◽  
Vol 87 (4) ◽  
pp. 411-416 ◽  
Author(s):  
Karl Grill
Keyword(s):  
Wiener Process ◽  
Fractional Wiener Process

On large increments of a two-parameter fractional Wiener process

2001 ◽  
Vol 44 (9) ◽  
pp. 1115-1125 ◽  
Author(s):  
Lixin Zhang ◽  
Chuanrong Lu ◽  
Yaohong Wang
Keyword(s):  
Wiener Process ◽  
Fractional Wiener Process ◽  
Large Increments ◽  
Two Parameter

ON OPTIMAL CONTROL OF A STOCHASTIC EQUATION WITH A FRACTIONAL WIENER PROCESS

2021 ◽  
Vol 6 ◽  
pp. 5-12
Author(s):  
Pavel Knopov ◽  
◽  
Tatyana Pepelyaeva ◽  
Sergey Shpiga ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Existence Theorem ◽  
Wiener Process ◽  
Strong Dependence ◽  
Strong Mixing ◽  
Fractional Wiener Process

In recent years, a new direction of research has emerged in the theory of stochastic differential equations, namely, stochastic differential equations with a fractional Wiener process. This class of processes makes it possible to describe adequately many real phenomena of a stochastic nature in financial mathematics, hydrology, biology, and many other areas. These phenomena are not always described by stochastic systems satisfying the conditions of strong mixing, or weak dependence, but are described by systems with a strong dependence, and this strong dependence is regulated by the so-called Hurst parameter, which is a characteristic of this dependence. In this article, we consider the problem of the existence of an optimal control for a stochastic differential equation with a fractional Wiener process, in which the diffusion coefficient is present, which gives more accurate simulation results. An existence theorem is proved for an optimal control of a process that satisfies the corresponding stochastic differential equation. The main result was obtained using the Girsanov theorem for such processes and the existence theorem for a weak solution for stochastic equations with a fractional Wiener process.

Forecasting based on spectral time series analysis: prediction of the Aurubis stock price

2020 ◽  
Vol 17 (4) ◽  
pp. 215-227
Author(s):  
Julia Babirath ◽  
Karel Malec ◽  
Rainer Schmitl ◽  
Kamil Maitah ◽  
Mansoor Maitah
Keyword(s):  
Time Series ◽  
Risk Management ◽  
Time Series Analysis ◽  
Wiener Process ◽  
Stock Price ◽  
Percentage Error ◽  
Portfolio Performance ◽  
Stock Price Prediction ◽  
Series Analysis ◽  
Augmented Dickey Fuller

The attempt to predict stock price movements has occupied investors ever since. Reliable forecasts are a basis for investment management, and improved forecasting results lead to enhanced portfolio performance and sound risk management. While forecasting using the Wiener process has received great attention in the literature, spectral time series analysis has been disregarded in this respect. The paper’s main objective is to evaluate whether spectral time series analysis can produce reliable forecasts of the Aurubis stock price. Aurubis poses a suitable candidate for an investor’s portfolio due to its sound economic and financial situation and the steady dividend policy. Additionally, reliable management contributes to making Aurubis an investment opportunity. To judge if the achieved forecast results can be considered satisfactory, they are compared against the simulation results of a Wiener process. After de-trending the time series using an Augmented Dickey-Fuller test, the residuals were compartmentalized into sine and cosine functions. The frequencies, amplitude, and phase were obtained using the Fast Fourier transform. The mean absolute percentage error measured the accuracy of the stock price prediction, and the results showed that the spectral analysis was able to deliver superior results when comparing the simulation using a Wiener process. Hence, spectral time series can enhance stock price forecasts and consequently improve risk management.

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