### MATHEMATICAL MODEL AND SIMULATION ON ASSET AND LIABILITIES OF SHARIA BANKING

The development of sharia banking continues to increase in Indonesia. The profit-sharing system in this banking, as a substitution of the interest rate in conventional banking, is interesting for Muslims community who want to avoid Riba, a prohibition in Islamic law. Having short existence in operation, there are procedures in the sharia bank system that are not understood enough by Muslims. In this research, we identify the volumes of funding and financing funds from the balance sheet of five sharia banks from January 2015 to February 2017. Funding fund is money raised by banks from customers or called Third Party Fund (TPF). This TPF should be distributed to business persons who need fund for their investment projects. This fund is classified as Financing fund. A bank gains profit from the cost of this fund management. Meanwhile, the customers can withdraw their money based on the provided scheme of the funding, so the bank should anticipate by providing some amount of cash daily.

Data of five banks, named ABC, DEF, GHI, JKL and MNO, are obtained from the OJK (Otoritas Jasa Keuangan) website. Banks GHI (established in 1999) and JKL (established in 1995) are as parts of conventional banks. Banks ABC (established in 2010) and DEF (established in 2002) are relatively new banks. Bank MNO is a pure sharia bank, not from a conventional bank, which has long been established in Indonesia.

After obtaining the results of funding, financing and equivalent rate, the next step is to present the results of Monti Klein profit and loss calculation in each sharia bank. Furthermore, profit and loss from Monti Kleinini calculation will be used as initial data to project or forecast profit obtained by each syariah bank for one year ahead by using decomposition method.

Having calculated the absolute errors of Monti Klein’s profit and loss to the profit and loss of the report data, assuming a reasonable error occurs if the error -1≤error≤1, it appears that Monti Klein’s profit loss on ABC bank, DEF bank, GHI bank and JKL Bank close to the value of profit and loss Data Report. While at Bank MNO the resulting error is too large, so the value of profit loss Monti Klein at MNO bank is not close to the value of profit and loss Data Report. The bank that has the smallest error value is the bank ABC. So ABC bank has the value of profit loss Monti Klein the closest to the value of profit and loss report data.

The relationship between Monti Klein’s profit and loss on the Report Data, the income of Monti Klein at Bank ABC, Bank DEF and JKL Bank tends to have the same pattern with the profit and loss of Report Data, resulting in Monti Klein’s profit on the three Banks is close to the value of profit and loss Data Report. In contrast, at Bank GHI and Bank MNO, there is no relationship between Monti Klein’s profit and loss and the Report Data Loss, so that the Monti Klein’s profit and loss profit is not close to Profit and Loss Report Data.

Profit loss Monti Klein can be projected by using additive decomposition method.While in profit and loss Data Projection report can be done by using multiplicative decomposition method, except in Bank MNO using multiplicative decomposition.

The results of Monti Klein’s profit projection on Bank ABC, Bank DEF and Bank JKL tend to have the same pattern with the result of projection of Profit and Loss Data Report. Meanwhile, the result of Klein monti profit loss projection at Bank GHI and Bank MNO does not have the same relationship pattern with the result of profit and loss project data projection.

**LIST OF RESEARCH OUTPUT**

- N. Sumarti, D. Rantini, E. Yunita, VA Andriani, HR Widyani, 2017. Selecting Potential Cities for the Silicon Valley of Indonesia using a Mathematical Model, Proceeding of International Conference on Computational Modelling and Simulation 2017, University of Colombo, Sri Lanka.
- KA Sidarto, A Kania, N Sumarti, 2017. Finding multiple solutions of multimodal optimization using spiral optimization algorithm with clustering. MENDEL — Soft Computing Journal 1, ppp. 95 – 102.
- Novriana Sumarti, 2017. A Mathematics Model for Determinating the Value of Ijarah Contract. Proceeding of the 2nd Annual Applied Science and Engineering Conference (AASEC 2017).
- Rio N. Arifin, Dean Andrean, Novriana Sumarti, 2017. Penerapan Metode Learning Options pada Real Options Menggunakan Lattice, prodising Seminar Nasional Matematika Universitas Katholik Parahiyangan, Bandung 23 September 2017.
- Dean Andrean, Rio Nur Arifin, Novriana Sumarti , 2017. Penerapan Real Option Analysis dengan Perubahan Volatilitas dalam Menentukan Nilai Proyek Pertambangan, Bunga Rampai ForMIND 2017.
- Novriana Sumarti, 2017. Penentuan Porsi dalam Skema Profit-Loss Sharing Investasi Syariah, Bunga Rampai ForMIND 2017.
- Novriana Sumarti, Nidya Inayatul Ghaida, Suryani Putri, 2017. Mathematical model on Sharia Bank Balance Sheet with Monti Klein Profit Method, draft.

**HEAD OF RESEARCH TEAM :** Novriana Sumarti, Ph.D

**TEAM MEMBERS** : Dr. Kuntjoro Adji Sidarto, Dr. M. Syamsuddin

**OFFICIAL ADDRESS :** Industrial and Financial Mathematics Research Group, ITB 4th Floor Mathematics, CAS Building, Jl. Ganesha 10 Bandung

**EMAIL :** novriana@math.itb.ac.id

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