Developing a two-stage multi-period stochastic model for asset and liability management: A real case study in a commercial bank of Iran

Document Type : Article


Department of Industrial Engineering and Management Systems, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran


In this paper, a novel two-stage multi-period stochastic model is developed to obtain a comprehensive plan. This plan aims to manage the assets and liabilities such that all legal and budget constraints are satisfied. Assets in the model include short- and long-term loans with reasonable interest rates, investments in the stock market, varied bonds with different expirations, investments in other banks, and the legal budget in the Central Bank. However, liabilities encompass all types of sight and investment deposits with different maturities. In the model, each type of deposit's amount is considered a decision variable, while its total amount is assumed to be stochastic. The mathematical model is constructed in an innovative way such that all previous loans and bonds with possible transactions in the planning horizon could be considered initial parameters. Real data for a commercial bank in Tehran, the Islamic Republic of Iran capital, are used to construct and check the optimization model. The total revenues obtained through the mathematical model and one achieved based on the experiences of financial experts in the commercial bank for four years are compared.


  • References

    • Josa-Fombellida, R., & Rincón-Zapatero, J. P. “Stochastic pension funding when the benefit and the risky asset follow jump diffusion processes”. European Journal of Operational Research220(2), 404-413 (2012).
    • Gülpinar, N., & Pachamanova, D. “A robust optimization approach to asset-liability management under time-varying investment opportunities”. Journal of Banking & Finance37(6), 2031-2041 (2013).
    • Frangos, C., Zenios, S. A., & Yavin, Y “Computation of feasible portfolio controlstrategies for an insurance company using a discrete time asset/liability model”. Mathematical and computer modelling40(3-4), 423-446 (2004).
    • Consiglio, A., Saunders, D., & Zenios, S. “A. Asset and liability management for insurance products with minimum guarantees: The UK case”. Journal of Banking & Finance30(2), 645-667 (2006).
    • Asimit, A. V., Badescu, A. M., Siu, T. K., & Zinchenko, Y. “Capital requirements and optimal investment with solvency probability constraints”. IMA Journal of Management Mathematics26(4), 345-375 (2015).
    • Asanga, S., Asimit, A., Badescu, A., & Haberman, S. “Portfolio optimization under solvency constraints: a dynamical approach”. North American Actuarial Journal18(3), 394-416 (2014).
    • Rao, H. V., Dutta, G., & Basu, S.”New asset liability management model with decision support system for life insurance companies: interface design issues for database and mathematical models”. International Journal of Revenue Management10(3-4), 259-289 (2018).
    • Dutta, G., Rao, H. V., Basu, S., & Tiwari, M. K. “Asset liability management model with decision support system for life insurance companies: Computational results”. Computers & Industrial Engineering128, 985-998 (2019).
    • Mukuddem-Petersen, J., & Petersen, M. A. “Optimizing asset and capital adequacy management in banking”. Journal of Optimization Theory and Applications137(1), 205-230 (2008).
    • Uryasev, S., Theiler, U. A., & Serraino, G. “Risk‐return optimization with different risk‐aggregation strategies”. The journal of risk finance (2010).
    • Date, P., Canepa, A., & Abdel-Jawad, M. “A mixed integer linear programming model for optimal sovereign debt issuance”. European Journal of Operational Research214(3), 749-758 (2011).
    • Consiglio, A., & Staino, A. “A stochastic programming model for the optimal issuance of government bonds”. Annals of Operations Research193(1), 159-172 (2012).
    • Valladão, D. M., Veiga, Á, & Veiga, G. “A multistage linear stochastic programming model for optimal corporate debt management”. European Journal of Operational Research237(1), 303-311 (2014).
    • Abdollahi, H. “Multi-Objective Programing for Bank’s Asset-Liability Management: The Case of Iranian Banking Industry”. International Journal of Industrial Engineering & Production Research31(1), 75-85 (2020).
    • Nielsen, S. S., & Poulsen, R. “A two-factor, stochastic programming model of Danish mortgage-backed securities”. Journal of Economic Dynamics and Control28(7), 1267-1289 (2004).
    • Consiglio, A., Cocco, F., & Zenios, S. A. “Scenario optimization asset and liability modelling for individual investors”. Annals of Operations Research152(1), 167 (2007).
    • Pedersen, A. M. B., Weissensteiner, A., & Poulsen, R. “Financial planning for young households”. Annals of Operations Research205(1), 55-76 (2013).
    • Zenios, S. A., & Ziemba, W. T. “Handbook of asset and liability management, vol. 1 Theory and Methodology North-Holland” (2006).
    • Zenios, S. A., & Ziemba, W. T. (Eds.). “Handbook of Asset and Liability Management: Applications and case studies”. Elsevier (2007). 
    • Chambers, D., & Charnes, A. “Inter-temporal analysis and optimization of bank portfolios”. Management Science7(4), 393-410 (1961).
    • Robertson, M. “A Bank Asset Management Model, Applications of Management Science in Banking and Finance”, Gower Press, Epping, Essex, 149-158. (1973).
    • Cohen, K. J., & Hammer, F. S. “Linear programming and optimal bank asset management decisions”. The Journal of Finance22(2), 147-165 (1967).
    • Fielitz, B. D., & Loeffler, T. A. “A linear programming model for commercial bank liquidity management”. Financial Management, 41-50 (1979).
    • Eatman, J. L., & Sealey, C. W. “A spectral analysis of aggregate commercial bank liability management and its relationship to short-run earning asset behavior”. Journal of Financial and Quantitative Analysis12(5), 767-778(1977).
    • Giokas, D., & Vassiloglou, M. “A goal programming model for bank assets and liabilities management”. European Journal of Operational Research50(1), 48-60 (1991).
    • Abdollahi, H. “Multi-Objective Programing for Bank’s Asset-Liability Management: The Case of Iranian Banking Industry”. International Journal of Industrial Engineering & Production Research31(1), 75-85 (2020).
    • Devjak, S., & Bogataj, L. “Optimisation of short term commercial bank loans to corporates in terms of financing operating activities in Slovenia”. Central European Journal of Operations Research15(4), 393-403 (2007).
    • Robinson, R. S. “BANKMOD: An interactive simulation aid for bank financial planning”. Journal of Bank Research4(3), 212-224 (1973).
    • Pyle, D. H. “On the theory of financial intermediation”. The Journal of Finance26(3), 737-747 (1971).
    • Yao, H., Zeng, Y., & Chen, S. “Multi-period mean–variance asset–liability management with uncontrolled cash flow and uncertain time-horizon”. Economic Modelling30, 492-500 (2013).
    • Wei, J., Wong, K. C., Yam, S. C. P., & Yung, S. P. “Markowitz’s mean–variance asset–liability management with regime switching: A time-consistent approach”. Insurance: Mathematics and Economics53(1), 281-291 (2013).
    • Li, D., Shen, Y., & Zeng, Y. “Dynamic derivative-based investment strategy for mean–variance asset–liability management with stochastic volatility”. Insurance: Mathematics and Economics78, 72-86 (2018).
    • Li, X., Wu, X., & Yao, H. “Multi-period asset-liability management with cash flows and probability constraints: A mean-field formulation approach”. Journal of the Operational Research Society71(10), 1563-1580 (2020).
    • Shen, Y., Wei, J., & Zhao, Q. “Mean–variance asset–liability management problem under non-Markovian regime-switching models”. Applied Mathematics & Optimization81(3), 859-897 (2020).
    • Cui, X., Li, X., & Yang, L. “Better than optimal mean–variance portfolio policy in multi-period asset–liability management problem”. Operations Research Letters48(6), 693-696 (2020).
    • Zhu, H. N., Zhang, C. K., & Jin, Z. “Continuous-time mean-variance asset-liability management with stochastic interest rates and inflation risks”. Journal of Industrial & Management Optimization16(2), 813 (2020).
    • Zhang, J., Chen, P., Jin, Z., & Li, S. “Open-loop equilibrium strategy for mean–variance asset–liability management portfolio selection problem with debt ratio”. Journal of Computational and Applied Mathematics380, 112951 (2020).
    • Charnes, A., & Littlechild, S. C. “Intertemporal bank asset choice with stochastic dependence”. NORTHWESTERN UNIV EVANSTON IL TECHNOLOGICAL INST (1968). 
    • Pogue, G. A., & Bussard, R. N. “A linear programming model for short term financial planning under uncertainty” (1971).
    • Haneveld, W. K. K., Streutker, M. H., & Van Der Vlerk, M. H. “An ALM model for pension funds using integrated chance constraints”. Annals of Operations Research177(1), 47-62 (2010).
    • Bradley, S. P., & Crane, D. B. “A dynamic model for bond portfolio management”. Management science19(2), 139-151 (1972).
    • Consigli, G., & Dempster, M. A. “Dynamic stochastic programmingfor asset-liability management”. Annals of Operations Research81, 131-162 (1998).
    • Papi, M., & Sbaraglia, S. “Optimal asset–liability management with constraints: A dynamic programming approach”. Applied Mathematics and Computation173(1), 306-349 (2006).
    • Gülpinar, N., & Pachamanova, D. “A robust optimization approach to asset-liability management under time-varying investment opportunities”. Journal of Banking & Finance37(6), 2031-2041 (2013).
    • Platanakis, E., & Sutcliffe, C. “Asset–liability modelling and pension schemes: the application of robust optimization to USS”. The European Journal of Finance23(4), 324-352 (2017).
    • Cohen, K. J., & Thore, S. “Programming bank portfolios under uncertainty”. Journal of Bank Research1(1), 42-61. (1970).
    • Kusy, M. I., & Ziemba, W. T. “A bank asset and liability management model”. Operations research34(3), 356-376 (1986).
    • Ziemba, W. T., Ziemba, W. T., Mulvey, J. M., Moffatt, H. K., & Mulvey, J. M. (Eds.). “Worldwide asset and liability modeling(Vol. 10)”. Cambridge University Press (1998). 
    • Sodhi, M. S. “LP modeling for asset-liability management: A survey of choices and simplifications”. Operations Research53(2), 181-196 (2005).
    • Dupačová, J., & Polívka, J. Asset-liability management for Czech pension funds using stochastic programming. Annals of Operations Research165(1), 5-28 (2009).
    • Ferstl, R., & Weissensteiner, A. “Asset-liability management under time-varying investment opportunities”. Journal of Banking & Finance35(1), 182-192 (2011).
    • Valladão, D. M., Veiga, Á, & Street, A. “A linear stochastic programming model for optimal leveraged portfolio selection”. Computational Economics51(4), 1021-1032 (2018).
    • De Oliveira, A. D., Filomena, T. P., Perlin, M. S., Lejeune, M., & de Macedo, G. R. “A multistage stochastic programming asset-liability management model: an application to the Brazilian pension fund industry”. Optimization and Engineering18(2), 349-368 (2017).
    • Oguzsoy, C. B., & Gu, S. “Bank asset and liability management under uncertainty”. European Journal of Operational Research102(3), 575-600 (1997).
    • Birge, J. R., & Louveaux, F. V. “A multicut algorithm for two-stage stochastic linear programs”. European Journal of Operational Research34(3), 384-392 (1988).
    • Davari-Ardakani, H., Aminnayeri, M., Seifi, A. “Hedging strategies for multi-period portfolio optimization”. Scientia Iranica, 22(6), 2644-2663 (2015).
    • Tabrizi, B., Torabi, S., Ghaderi, S. “A novel project portfolio selection framework: An application of fuzzy DEMATEL and multi-choice goal programming”. Scientia Iranica, 23(6), 2945-2958 (2016).