Nonnegative, additive functionals of a Wiener process

1965 ◽  
pp. 246-281
Author(s):  
E. B. Dynkin
Keyword(s):  
Wiener Process ◽  
Additive Functionals

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.

Exact solutions to the homing problem for a Wiener process with jumps

Optimization ◽  
2020 ◽  
pp. 1-13
Author(s):  
Mario Lefebvre ◽  
Abderrazak Moutassim
Keyword(s):  
Exact Solutions ◽  
Wiener Process

Limit distribution of additive functionals of diffusion processes

1968 ◽  
Vol 4 (5) ◽  
pp. 850-856
Author(s):  
R. Z. Khas'minskii
Keyword(s):  
Limit Distribution ◽  
Diffusion Processes ◽  
Additive Functionals

Evaluations of absorption probabilities for the Wiener process on large intervals

1980 ◽  
Vol 17 (02) ◽  
pp. 363-372 ◽  
Author(s):  
C. Park ◽  
F. J. Schuurmann
Keyword(s):  
Stochastic Processes ◽  
Wiener Process ◽  
Standard Wiener Process ◽  
Computationally Efficient ◽  
The Past ◽  
Gaussian Stochastic Processes ◽  
Absorption Probabilities

Let {W(t), 0≦t<∞} be the standard Wiener process. The computation schemes developed in the past are not computationally efficient for the absorption probabilities of the type P{sup0≦t≦T W(t) − f(t) ≧ 0} when either T is large or f(0) > 0 is small. This paper gives an efficient and accurate algorithm to compute such probabilities, and some applications to other Gaussian stochastic processes are discussed.

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