Solving a fractional programming problem in a commercial bank

Ankhbayar Chuluunbaatar; Enkhbat Rentsen

doi:10.3934/jimo.2021153

Article Contents

2022, Volume 18, Issue 6: 4183-4190. Doi: 10.3934/jimo.2021153

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Solving a fractional programming problem in a commercial bank

Ankhbayar Chuluunbaatar^1, , and
Enkhbat Rentsen^2,

1.
School of Business, National University of Mongolia, Ulaanbaatar, PC 14200, Mongolia
2.
Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences, Ulaanbaatar, PC 13330, Mongolia

^* Corresponding author: Ankhbayar Chuluunbaatar
^* Corresponding author: Ankhbayar Chuluunbaatar

Received: March 2021

Revised: June 2021

Early access: September 2021

Published: September 2022

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Abstract

We formulate a new optimization problem which arises in the Bank Asset and Liability Management (ALM). The problem is a fractional programming which belongs to a class of global optimization. Most of optimization problems in the Bank Asset and Liability Management are return maximization or risk minimization problems. For solving the fractional programming problem, we propose curvilinear multi-start algorithm which finds the best local solutions to the problem. Numerical results are given based on the balance sheets of 5 commercial banks of Mongolia.

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Mathematics Subject Classification: Primary: 90C26, 90C32; Secondary: 91B05.

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Table 1. The decision variables

$Assets$	$Liabilities$
$A_1: \text{Cash and cash equivalents}$	$L_1: \text{Current account}$
$A_2: \text{Deposits to the Bank of Mongolia}$	$L_2: \text{Time deposit}$
$A_3: \text{Deposits at other banks}$	$L_3: \text{Demand deposit}$
$A_4: \text{Financial investments}$	$L_4: \text{Placements by other banks}$
$A_5: \text{Loans and advances}$	$L_5: \text{Other deposits}$
$A_6: \text{Other financial assets}$	$L_6: \text{Other liabilities}$
$A_7: \text{Fixed assets}$	$E: \text{Equity}$
$A: \text{Total assets}$	$L+E = A: \text{Total assets}$

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Table 2. nitial values of $v$ for banks

$ Ratio $	$ Khan $	$ TDB $	$ XAC $	$ State $	$ Golomt $	$ Mean $	$ Stdev $
$ v_1 $	$ 0.564 $	$ 0.520 $	$ 0.545 $	$ 0.409 $	$ 0.528 $	$ 0.513 $	$ 0.061 $
$ v_2 $	$ 0.457 $	$ 0.403 $	$ 0.442 $	$ 0.599 $	$ 0.445 $	$ 0.469 $	$ 0.075 $
$ v_3 $	$ 0.405 $	$ 0.253 $	$ 0.358 $	$ 0.496 $	$ 0.412 $	$ 0.385 $	$ 0.089 $
$ v_4 $	$ 0.477 $	$ 0.452 $	$ 0.483 $	$ 0.362 $	$ 0.472 $	$ 0.449 $	$ 0.050 $
$ v_5 $	$ 0.202 $	$ 0.203 $	$ 0.413 $	$ 0.181 $	$ 0.186 $	$ 0.237 $	$ 0.099 $
$ v_6 $	$ 0.998 $	$ 1.648 $	$ 1.522 $	$ 0.988 $	$ 0.859 $	$ 1.203 $	$ 0.356 $
$ v_7 $	$ 0.150 $	$ 0.296 $	$ 0.206 $	$ 0.064 $	$ 0.118 $	$ 0.166 $	$ 0.089 $
$ v_8 $	$ 0.300 $	$ 0.232 $	$ 0.116 $	$ 0.251 $	$ 0.311 $	$ 0.242 $	$ 0.078 $
$ v_9 $	$ 0.228 $	$ 0.232 $	$ 0.446 $	$ 0.197 $	$ 0.201 $	$ 0.260 $	$ 0.103 $
$ v_{10} $	$ 0.129 $	$ 0.140 $	$ 0.070 $	$ 0.089 $	$ 0.081 $	$ 0.102 $	$ 0.031 $
Source: Audited report of individual commercial bank

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