# Asset Optimization Problem In A Financial Institution

### Abstract

This paper looked at how a financial institution could optimally allocate its total wealth among three assets namely; treasury, security and loan in a stochastic interest rate setting. The optimal investment strategy was derived through the application of a stochastic optimization theory for the case of constant relative risk aversion (CRRA) utility function. Next,numerical examples using published data obtained from CBN statistical bulletin and Nigeria Stock Exchange Fact Book was presented to illustrate the dynamics of the optimal investment strategy. From the results it was seen that the optimal investment strategy was to shift the financial institution investment away from the risky assets (security and loan) toward the riskless asset (treasury). Also the investment in security and loan was observed to be more risky as the volatility increased.The results further showed that there is increased investment in the risky assets as the investor became less risk averse.

### References

Fatma, C. & Fathi, A. A methodology to estimate the interest rate yield curve in illiquid market the Tunisian case. Journal of Emerging Market Finance. 13(5) , 1-9 (2014).

Grant, E. M. & Peter, J. W. An optimal portfolio and capital management strategy for Basel III compliant commercial banks. Journal of Applied Mathematics. 2014 , 1-11 (2014).

Zhang, C. & Rong, X. Optimal investment strategies for DC pension with stochastic salary under the affine interest rate model. Discrete Dynamics in Nature and Society. 2013 , 1-11 (2013).

Fouche, C. H., Mukuddem Petersen, J. & Petersen, M. A. Continuous time stochastic modeling of capital adequacy ratio for banks. Applied Stochastic Model in Business and Industry. 22(1) , 41-71 (2006).

Merton, R. C. Lifetime portfolio selection under uncertainty. The Continuous Case. Review of Economics and Statistics. 51, 247-257 (1969).

Merton, R. C. Optimal consumption and portfolio rules in a continuous time model. Journal of Economic Theory. 3, 373-413 (1971).

Chakroun, F., & Abid, F. An application of stochastic control theory to bank portfolio choice problem.. Statistics and its Interface. 9(1), 69-77 (2016).

Van Schalkwyk, G. J. & Witbooi, P. J. An optimal strategy for liquidity management in banking. Applied Mathematical Science. 2, 275-297 (2017).

Zhang, X. On optimal proportional reinsurance and investment in a partial Markovian regime switching economy. Communication on Stochastic Analysis. 7(3), 481-492 (2013).

Astic, F., & Tourin, A. Optimal bank management under capital and liquidity constraints. Journal of Financial Engineering. 1(3), 1-21 (2014).

Central Bank of Nigeria. Statistical Bulletin. (2019).

Nigeria Stock Exchange Fact Book , (2010).

Jungbacker, B., Koopman, S. J. & VanderWel, M. Maximum likelihood estimation for dynamic factor models with missing data. Journal of Economic Dynamics and Control. 35(8), 1358-1368 (2011).

Vaughan, V. A. Estimation of discretely sampled continuous diffusion processes with application to short-term interest rate models. PhD Thesis, University of Johannesburg,J ohannesburg, South Africa. (2014).

*International Journal of Mathematical Analysis and Optimization: Theory and Applications*,

*2019*(2), 581 - 591. Retrieved from http://jsrd.unilag.edu.ng/index.php/ijmao/article/view/562