MEAN VARIANCE OF FRACTIONAL STOCHASTIC MODEL AND LOGARITHM UTILITY OPTIMIZATION OF A PENSION FUND WITH TAX AND TRANSACTION COST
This work looked at the mean-variance of fractional continuous time stochastic model for the dynamics of a pension fund with tax and transaction cost, where the effect of tax and transaction cost charging makes on the expected logarithmic utility of the pensioner was established. The associated H-J-B equation in the optimization problem is obtained using lto’s lemma. An explicit solution to the pensioners’ problems was derived under stated condition.
 A. Zhang. A secret to create a complete market from an incomplete market, Applied Mathematics and Computation, Vol.191, No.1, 253–262, 2007
. C. Olunkwa ,B. O. Osu and Carlos Granados ,Mean variance portfolio selection problem with multiscale stochastic volatility, PROSPECTIVA VOL. 20 N° 2 – 2022
4] C. Irgens and J. Paulsen. Optimal control of risk exposure, reinsurance and investments for insurance portfolios. Insurance: Mathematics & Economics, vol. 35, no. 1, 21–51, 2004.
. D. Li and W. L. Ng, Optimal dynamic portfolio selection: multi period mean-variance formulation, Mathematical Finance, vol. 10, pp. 387-406, 2000.
. H. L. Wu and Z. F. Li, Asset and liability management for an insurer with jump-diffusion surplus process under mean-variance criterion, Proceedings - 3rd International Conference on Business Intelligence and Financial Engineering, IEEE Computer Society, pp. 209-213, 2010. 578
 I. Karatzas, J.P. Lehoczky, S.E. Shreve. Optimal portfolio and consumption decisions for a ‘small investor’ on a finite horizon, SIAM Journal on Control and Optimization, Vol.25, No.6, 1557–1586, 1987
 L. Bai and J. Guo. Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint. Insurance: Mathematics & Economics, vol. 42, no. 3, 968–975, 2008.
 L. Bai and H. Zhang. Dynamic mean-variance problem with constrained risk control for the insurers. Mathematical Methods of Operations Research, vol. 68, no. 1, 181–205, 2008.
 N. Bauerle. Benchmark and mean-variance problems for insurers. Mathematical Methods of Operations Research, vol. 62, no. 1, pp. 159–165, 2005.
 R.C. Merton. Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, Vol.3, No.4, 373-413, 1971
 S. Asmussen, B. Højgaard, and M. Taksar. Optimal risk control and dividend distribution policies. Example of excessof-loss reinsurance for an insurance corporation,” Finance and Stochastics, vol. 4, no. 3, 299–324, 2000.
 S. Pliska, A stochastic calculus model of continuous trading: optimal portfolios, Mathematics of Operations Research, Vol.11, No.2, 371–382, 1986
. S. X. Xie, Z. F. Li and S. Y. Wang, Continuous-time portfolio selection with liability: mean-variance model and stochastic LQ approach, Insurance: Mathematics and Economics, vol. 42, pp. 943-953, 2008
.X. Y. Zhou and D. Li, Continuous-time mean-variance portfolio selection: a stochastic LQ framework, Applied Mathematics and Optimization, vol. 42, pp. 19-33, 2000.
 X. Zhang, M. Zhou, and J. Guo. Optimal combinational quota share and excess-of-loss reinsurance policies in a dynamic setting. Applied Stochastic Models in Business and Industry, vol. 23, no. 1, 63–71, 2007.
 Y. Cao and N. Wan. Optimal proportional reinsurance and investment based on Hamilton-Jacobi-Bellman equation. Insurance: Mathematics & Economics, vol. 45, no. 2, 157–162, 2009.
 Z. Liang, K. C. Yuen, and J. Guo. Optimal proportional reinsurance and investment in a stock market with OrnsteinUhlenbeck process. Insurance: Mathematics & Economics, vol. 49, no. 2, 207–215, 2011.
 Z. Li, Y. Zeng, and Y. Lai. Optimal time-consistent investment and reinsurance strategies for insurers under Heston’s SV model. Insurance: Mathematics & Economics, vol. 51, no. 1, 191–203, 2012.
 Y. Zeng, Z. Li, and Y. Lai. Time-consistent investment and reinsurance strategies for mean-variance insurers with jumps. Insurance: Mathematics & Economics, vol. 52,no. 3, 498–507, 2013.
 Y. Zeng and Z. Li. Optimal time-consistent investment and reinsurance policies for mean-variance insurers,” Insurance: Mathematics & Economics, vol. 49, no. 1, pp. 145–154, 2011.
S. A. Ihedioh and C. Olunkwa .Logarithmic Utility optimization of an Insurance Company’s Wealth with Consumption and Dividends under Proportional Reinsurance.: The impact of mode of charging Tax and Transaction cost.Universal Journal of Mathematics Vol. 1, Number 4ISSN 2456-1312 2016.
P. Grimberg and Z. Schuss∗Stochastic model of a pension plan. Department of Applied Mathematics, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel July 3, 2014
Copyright (c) 2023 Chidinma Olunkwa, Bright O. Osu, Kevin N. C. Njoku and Onwuegbulam C.Chisom
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Author(s) and co-author(s) jointly and severally represent and warrant that the Article is original with the author(s) and does not infringe any copyright or violate any other right of any third parties, and that the Article has not been published elsewhere. Author(s) agree to the terms that the GPH Journal will have the full right to remove the published article on any misconduct found in the published article.