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Stochastic Analysis of the Effect of Asset Prices to a Single Economic Investor

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In this paper, we propose a single economic investor whose asset follows a geometric Brownian motion process. Our objective therefore is to obtain the fair price and the present market value of the asset with an infinitely horizon expected discounted investment output. We apply dynamic programming principle to derive the Hamilton Jacobi Bellman (HJB)-equation associated with the problem which is found to be equivalent to the famous Black-Scholes Model under no risk neutrality. In addition, for a complete market under equilibrium, we obtained the value of the present asset with risk neutrality and its fair price.


Bulletin of Mathematical Sciences and Applications (Volume 17)
E. Ekuma-Okereke et al., "Stochastic Analysis of the Effect of Asset Prices to a Single Economic Investor", Bulletin of Mathematical Sciences and Applications, Vol. 17, pp. 33-39, 2016
Online since:
November 2016

[1] A.D. Andricopoulos, Option Pricing Using Quadrature and other Numerical Methods, Ph.D. thesis, Department of Mathematics, Manchester United, (2002).

[2] J. Busca, Introduction to Financial Mathematics UNICAMP, Campinas, Brazil, (2002).

[3] J.C. Hull, Options, Futures, and other derivatives, Prentice Hall, New York, (1997).

[4] R.J. Kruizenga, Put and call options: A theoretical and market analysis, Ph.D. Thesis, Cambridge, MA: MIT, (1956).

[5] R.C. Merton, The theory of rational option pricing, The Bell Journal of Economics and Management Science. 4 (1973) 141–183.

[6] S.E. Onah, O.O. Ugbebor, Solution of a Two-dimensional Stochastic Investment Problem, J. App. Math. Comp. 98 (1999) 75-82.

[7] M. F. M. Osborne, Brownian motion in the stock market, Operations Research. 7(2) (1959) 145-173.

[8] B.O. Osu, G.U. Achi, C.A. Emereuwa, Stochastic (Multiplicative) Effect of Government Policy on the income of individuals, J. Modern Mathematics and Statistics. 5(1) (2011) 3-8.


[9] C. W. Smith, Option pricing: a review, Journal of Financial Economics. 3 (1976) 3-52.

[10] S.R. Straja, Stochastic Modeling of Stock Prices, Montgomery Investment Technology, Inc, Camden, NJ 08103, (1997).

[11] R. Cont, Empirical Properties of Asset Returns. Stylized facts and Statistical Issues, Quantitative Finance. 1 (2001) 223 -236.


[12] W. Huang, et al., The optimal Fuzzy Portfolio Strategy with Hedging, Theoretical Mathematics and Application. 2(1) (2012) 1-12.

[13] A.C. Okoroafor, B.O. Osu, A Stochastic iteration Method for the Solution of finite dimensional variation inequalities, J. Nig. Association of Mathematical Physics. 8 (2004) 301-304. MR 1952680.


[14] E. Ekuma-Okereke, B.O. Osu, Dynamic Optimization of Portfolios with Tail Conditional Expectations (TCE) Constraints, Asian Journal of Mathematics and Applications. 2013 (2013).

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