MEAN VARIANCE OF FRACTIONAL STOCHASTIC MODEL AND LOGARITHM UTILITY OPTIMIZATION OF A PENSION FUND WITH TAX AND TRANSACTION COST
Keywords:
Mean-variance portfolio selection, Brownian motion, H-J-B Equation, Pensioner logarithmic utility, mode of taxation, transaction cost, consumption, reinsurance
Abstract
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.
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References
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[16] 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.
[17] 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.
[18] 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.
[19] 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.
[20] 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.
[21] 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.
[22]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.
[23]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
[2] A. Zhang. A secret to create a complete market from an incomplete market, Applied Mathematics and Computation, Vol.191, No.1, 253–262, 2007
.[3] 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.
.[5] D. Li and W. L. Ng, Optimal dynamic portfolio selection: multi period mean-variance formulation, Mathematical Finance, vol. 10, pp. 387-406, 2000.
.[6] 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
[7] 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
[8] 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.
[9] 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.
[10] N. Bauerle. Benchmark and mean-variance problems for insurers. Mathematical Methods of Operations Research, vol. 62, no. 1, pp. 159–165, 2005.
[11] R.C. Merton. Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, Vol.3, No.4, 373-413, 1971
[12] 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.
[13] S. Pliska, A stochastic calculus model of continuous trading: optimal portfolios, Mathematics of Operations Research, Vol.11, No.2, 371–382, 1986
.[14] 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
.[15]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.
[16] 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.
[17] 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.
[18] 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.
[19] 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.
[20] 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.
[21] 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.
[22]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.
[23]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
Published
2023-09-08
How to Cite
Olunkwa, C., O. Osu, B., N. C. Njoku, K., & C. Chisom, O. (2023). MEAN VARIANCE OF FRACTIONAL STOCHASTIC MODEL AND LOGARITHM UTILITY OPTIMIZATION OF A PENSION FUND WITH TAX AND TRANSACTION COST. GPH - International Journal of Mathematics, 6(08), 01-18. https://doi.org/10.5281/zenodo.8330632
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Articles
Copyright (c) 2023 Chidinma Olunkwa, Bright O. Osu, Kevin N. C. Njoku and Onwuegbulam C.Chisom
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