OPTIMAL INVESTMENT STRATEGY AND CAPITAL MANAGEMENT IN A BANK UNDER STOCHASTIC INTEREST RATE AND STOCHASTIC VOLATILITY

Authors

  • Theophilus Danjuma
  • H. C. Chinwenyi
  • Richard K. Tyokyaa

Keywords:

Financial Institution, Investment Strategy, Stochastic Optimization Theory, Stochastic Interest Rate, Stochastic Volatility

Abstract

In this research work, we have looked at how a financial institution can optimally allocate its wealth among three assets namely: treasury, security and loan, and also manage it assets in stochastic interest rate and stochastic volatility setting. We derived the optimal investment policy through the application of dynamic programming principle for the case of constant relative risk aversion (CRRA) utility function. Furthermore, we derived the Stochastic Differential Equation (SDE) for the capital adequacy ratio under Basel Accord, the SDE for the Total Risk – Weighted Assets (TRWA), SDE for the capital required to maintain the capital adequacy ratio under Basel II and Central Bank of Nigeria (CBN) standards and solve the SDEs numerically to study how the financial institution can manage its assets. We also presented numerical examples to illustrate the dynamics of the optimal investment policy, TRWA SDE and SDE of the capital required to maintain the capital adequacy ratio under Basel II and Nigeria CBN standards.

References

Dehghan, M. and Hajarian, M. (2009). Improving preconditioned SOR-type iterative methods for L-matrices. International Journal for Numerical Methods in Biomedical Engineering, 27:774-784.

Gunawardena, A. D., Jain, S. K. and Snyder, L. (1991). Modified iterative methods for consistent linear systems. Linear Algebra and its Applications, 154-156: 123-143.

Kohno, T., Kotakemori, H., Niki, H. and Usui, M. (1997). Improving modified Gauss–Seidel method for Z-matrices. Linear Algebra Appl., 267: 113–123.

Kotakemori, H., Harada, K., Morimoto, M. and Niki, H. (2002). A comparison theorem for the iterative method with the preconditioner (I+S_max). Journal of Computational and Applied Mathematics, 145: 373-378.

Kotakemori, H., Niki, H. and Okamoto, N. (1996). Accelerated iteration method for Z-matrices. Journal of Computational and Applied Mathematics, 75: 87–97.

Li, W. and Sun, W. (2000). Modified Gauss–Seidel type methods and Jacobi type methods for Z - matrices. Linear Algebra and its Applications, 317: 227-240.

Milaszewicz, J. P. (1987). Improving Jacobi and Gauss-Seidel iterations. Linear Algebra and its Applications, 93: 161-170.

Morimoto, M., Harada, K., Sakakihara, M. and Sawami, H. (2004). The Gauss–Seidel iterative method with the preconditioning matrix (I+S_max+S_m). Japan J. Indust. Appl. Math., 21: 25-34.

Ndanusa, A. and Adeboye, K. R. (2012). Preconditioned SOR iterative methods for L-matrices. American Journal of Computational and Applied Mathematics, 2(6): 300-305.

Niki, H., Harada, K., Morimoto, M. and Sakakihara, M. (2004). The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method. Journal of Computational and Applied Mathematics, 164-165: 587-600.

Varga, R. S. (1981). Matrix iterative analysis (2nd ed.). Englewood Cliffs, New Jersey: Prentice-Hall. pp 358.

Published

2020-04-14

How to Cite

Danjuma, T., Chinwenyi, H. C., & Tyokyaa, R. K. (2020). OPTIMAL INVESTMENT STRATEGY AND CAPITAL MANAGEMENT IN A BANK UNDER STOCHASTIC INTEREST RATE AND STOCHASTIC VOLATILITY. FUDMA JOURNAL OF SCIENCES, 4(1), 528 - 538. Retrieved from https://fjs.fudutsinma.edu.ng/index.php/fjs/article/view/78