Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation

Bright O. Osu; Joy Ijeoma Adindu-Dick

doi:doi:10.11648/j.ml.20160202.11

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Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation

Bright O. Osu, Joy Ijeoma Adindu-Dick

Published in Mathematics Letters (Volume 2, Issue 2)

Received: 7 July 2016 Accepted: 27 July 2016 Published: 11 October 2016

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Abstract

Assessing the stock price indices is the foundation of forecasting the market risk. In this paper, we derived a seemingly Black-Scholes parabolic equation. We then solved this equation under given conditions for the optimal prediction of the expected value of assets.

Published in	Mathematics Letters (Volume 2, Issue 2)
DOI	10.11648/j.ml.20160202.11
Page(s)	19-24
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fractal Scaling Exponent, Black-Scholes Equation, Assets Price Return, Optimal Value, Parabolic Equation

References

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[4]	Cheung, Y. W., Lai, K. S., & Lai, M. (1994). Are there long cycles in foreign stock returns? Journal of International Financial Markets, Institutions and Money, 3 (1), 33-48.
[5]	Cutland, N., Kopp, P., & Willinger, W. (1995). Stock price returns and the Joseph effect: A fractal version of the Black-Scholes model. Progress in Probability, 36, 327-351.
[6]	Fang, H., Lai, K., & Lai, M. (1994). Fractal structure in currency futures price dynamics. The Journal of Futures Markets, 14, 169-181.
[7]	Greene, M. T., & Fielitz B. D. (1997). Long term dependence in common stock returns. Journal of Financial Economics, 5, 339-349.
[8]	Hurst, H. E., (1951). Long term storage capacity of reservoir. Transactions of the American Society of Civil Engineers, 116, 770-799.
[9]	Lo, A. W., (1991). Long term memory in stock market prices. Econometrica, 59, 1279-1313.
[10]	Mandelbrot, B. B., (1982). The fractal geometry of nature. New York: Freeman.
[11]	Mandelbrot, B. B., (1997). Fractals and scaling in finance:Discontinuity, Concentration, Risk. New York: Springer-Verlag.
[12]	Mandelbrot, B. B., & Wallis, J. R. (1969). Robustness of the rescaled range in the measurement of non-cyclic long-run statistical dependence. Water Resources Research, 5, 967-988.
[13]	Muzy, J., Delour, J., & Bacry, E., (2000). Modelling fluctuations of financial time series: from cascade process to stochastic volatility Model. Euro. Phys. Journal B, 17, 537-548.
[14]	Shiryaev, A. N., (1999). Essentials of stochastic finance. Singapore: World Scientific.
[15]	Teverovsky, V., Taqqu, M., & Willinger, W., (1999). A critical look at Lo’s modified R/S statistic. Journal of statistical planning and inference, 80, 211-227.
[16]	Tokinaga, S., Moriyasu, H., Miyazaki, A, & Shimazu, N. (1997). Forecasting of time series with fractal geometry by using scale transformations and parameter estimations obtained by the wavelet transform. Electronics and Communications in Japan, 80 (3), 8-17.
[17]	Wallis, J. R., & Matalas, N. C., (1970). Small sample properties of H and K-estimators of the Hurst coefficient. Water Resources Research, 6, 1583-1594.
[18]	Willinger, W., Taqqu, M., & Teverovsky, V., (1999). Stock market prices and long-range dependence. Finance and Stochastic, 3, 1-13.
[19]	Xiong, Z., (2002). Estimating the fractal dimension of financial time Series by wavelets systems. Engineering-Theory and Practice, 12, 48-53.

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Bright O. Osu, Joy Ijeoma Adindu-Dick. (2016). Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation. Mathematics Letters, 2(2), 19-24. https://doi.org/10.11648/j.ml.20160202.11

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ACS Style

Bright O. Osu; Joy Ijeoma Adindu-Dick. Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation. Math. Lett. 2016, 2(2), 19-24. doi: 10.11648/j.ml.20160202.11

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AMA Style

Bright O. Osu, Joy Ijeoma Adindu-Dick. Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation. Math Lett. 2016;2(2):19-24. doi: 10.11648/j.ml.20160202.11

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@article{10.11648/j.ml.20160202.11,
  author = {Bright O. Osu and Joy Ijeoma Adindu-Dick},
  title = {Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation},
  journal = {Mathematics Letters},
  volume = {2},
  number = {2},
  pages = {19-24},
  doi = {10.11648/j.ml.20160202.11},
  url = {https://doi.org/10.11648/j.ml.20160202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20160202.11},
  abstract = {Assessing the stock price indices is the foundation of forecasting the market risk. In this paper, we derived a seemingly Black-Scholes parabolic equation. We then solved this equation under given conditions for the optimal prediction of the expected value of assets.},
 year = {2016}
}

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TY  - JOUR
T1  - Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation
AU  - Bright O. Osu
AU  - Joy Ijeoma Adindu-Dick
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T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
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VL  - 2
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Author Information

Bright O. Osu

Department of Mathematics, College of Physical and Applied Sciencs, Michael Okpara University of Agriculture, Umudike, Nigeria
Joy Ijeoma Adindu-Dick

Department of Mathematics, Faculty of Physical and Biological Sciences, Imo State University, Owerri, Imo State, Nigeria

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APA Style

Bright O. Osu, Joy Ijeoma Adindu-Dick. (2016). Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation. Mathematics Letters, 2(2), 19-24. https://doi.org/10.11648/j.ml.20160202.11

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ACS Style

Bright O. Osu; Joy Ijeoma Adindu-Dick. Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation. Math. Lett. 2016, 2(2), 19-24. doi: 10.11648/j.ml.20160202.11

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AMA Style

Bright O. Osu, Joy Ijeoma Adindu-Dick. Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation. Math Lett. 2016;2(2):19-24. doi: 10.11648/j.ml.20160202.11

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@article{10.11648/j.ml.20160202.11,
  author = {Bright O. Osu and Joy Ijeoma Adindu-Dick},
  title = {Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation},
  journal = {Mathematics Letters},
  volume = {2},
  number = {2},
  pages = {19-24},
  doi = {10.11648/j.ml.20160202.11},
  url = {https://doi.org/10.11648/j.ml.20160202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20160202.11},
  abstract = {Assessing the stock price indices is the foundation of forecasting the market risk. In this paper, we derived a seemingly Black-Scholes parabolic equation. We then solved this equation under given conditions for the optimal prediction of the expected value of assets.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Optimal Prediction of Expected Value of Assets Under Fractal Scaling Exponent Using Seemingly Black-Scholes Parabolic Equation
AU  - Bright O. Osu
AU  - Joy Ijeoma Adindu-Dick
Y1  - 2016/10/11
PY  - 2016
N1  - https://doi.org/10.11648/j.ml.20160202.11
DO  - 10.11648/j.ml.20160202.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 19
EP  - 24
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20160202.11
AB  - Assessing the stock price indices is the foundation of forecasting the market risk. In this paper, we derived a seemingly Black-Scholes parabolic equation. We then solved this equation under given conditions for the optimal prediction of the expected value of assets.
VL  - 2
IS  - 2
ER  -

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