Optimal Debt Ratio And Consumption Plan For An Investor In The Presence Of Inflation Risk And Corporate Tax
DOI:
https://doi.org/10.60787/tnamp.v21.509Keywords:
Optimal Debt Ratio, Corporation Tax, Inflation Risk, Optimal ControlAbstract
In this paper, we derive the optimal debt ratio and optimal consumption strategy for an investor in the presence of inflation risk and corporate taxation. The investor is assumed to pay tax on income generated by its asset. The investor’s income is assumed to grow at rate that satisfy a diffusion process. The aim of the investor is to derive the real wealth process which is nominal wealth adjusted for inflation. The resulting real wealth process was solved using dynamic programming approach. As a result, we derive the optimal debt ratio and optimal consumption rate for the investor over time by assuming that the investor chooses a power utility function. We found that the debt ratio depends positively on the corporate tax rate, debt servicing and the volatility of the inflation index. Also, we found that as the risk aversion coefficient increases, the optimal debt ratio will decrease and vice versa. Also, we found that the relationship between the coefficient of risk aversion and the optimal consumption rate is positive.
Downloads
References
Z. Jin, Optimal Debt Ratio and Consumption Strategies in Financial Crisis. J. Optim. Theory Appl. (2014). DOI.10.1007/s10957-014-0629-0.
W. Liu and Z. Jin, Analysis of optimal debt ratio in a Markov regime-switching model. Working paper, Department of finance, La Trobe University, Melbourne, Australia, 2014.
C.I. Nkeki, Optimal pension fund management in a jump diffusion environment: theoretical and empirical study. Journal of Computational and Applied Mathematics. 330(2018), 228-252.
Q. Zhao, Z. Jin and J. Wie, Optimal investment and dividend payment strategies with debt management and reinsurance. Journal of Industrial and management optimization. (2018). 14(4):1323-1348. doi:10.3934/jimo.2018009.
L. Qian, L. Chen, Z. Jin and R. Wang, Optimal liability ratio and dividend payment strategies under catastrophic risk. Journal of Industrial and management optimization. (2018). 14(4):1443-1461. doi:10.3934/jimo.2018015.
Z. Jin, H. Yang and G. Yin, Optimal debt ratio and dividend payment strategies with reinsurance. Insurance: Mathematics and Economics 64(2015) 351-363.
C.I. Nkeki, K.P. Modugu, Optimal investment in the presence of intangible assets and collateralized optimal debt ratio in jump-diffusion models. Math Sci 14,309-334 (2020). https://doi.org/10.1007/s40096-020-00343-8.
A. Abid, F. Abid, A Methodology to estimate the optimal debt ratio when asset return and default probability follow a stochastic process. Journal of Industrial and management optimization, 2023, vol. 19, issue 10.
M.J. Brennan, Y. Xia, Dynamic asset allocation under inflation, J. Finance 57 (2002)1201–1238.
P. Battocchio, F. Menoncin, Optimal pension management in a stochastic framework, Insurance Math. Econom. 34 (2004) 79–95.
R. Korn, S. Kruse, Einfache verfahren zur Bewertung von inflationsgekoppeiten Finanzprodukten, Bl. DGVFM XXVI (3) (2004) 351–367.
A. Zhang, R. Korn, E. Christian-Oliver, Optimal management and inflation protection for defined contribution pension plan. MPRA paper no. 3300, 2009.
C.I. Nkeki, Optimal pension fund management in a jump-diffusion environment: Theoretical and empirical studies, J. Comput. Appl. Maths (2017).
Downloads
Published
Issue
Section
License
Copyright (c) 2025 The Transactions of the Nigerian Association of Mathematical Physics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
