Mathematical Review of the Sukuk-Linked Awqaf Model: A Critical Analysis of Notation Consistency and Formula Validity
Abstract
This manuscript provides a critical mathematical review of a Sukuk-Linked Awqaf model with the aim of improving notational consistency, analytical clarity, and economic interpretability. The study focuses on correcting weaknesses arising from inconsistent time indexing, redundant equations, misuse of mathematical symbols, and unclear assumptions regarding asset growth, rental income, construction cost, and revenue sharing. By imposing a consistent growth process for waqaf land value, several artificial discount factors are eliminated and present value expressions are derived directly using standard time value of money principles. Key equalities in the original model are reinterpreted as minimum contractual conditions rather than strict identities to better reflect economic uncertainty. The analysis also introduces explicit decision criteria for all stakeholders - Nadzhir, investors, and state-owned enterprises (SOE) - based on present value comparisons. The revised formulation offers a cleaner and more rigorous mathematical foundation for Sukuk-Linked Awqaf and strengthens its relevance as an instrument of Islamic social finance.
References
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Ang, A., & Timmermann, A. (2012). Regime changes and financial markets. Annual Review of Financial Economics, 4(1), 313–337. https://doi.org/10.1146/annurev-financial-110311-101808
Basher, S. A., & Raboy, D. G. (2018). The misuse of net present value in energy efficiency standards. Renewable and Sustainable Energy Reviews, 96, 218–225. https://doi.org/10.1016/j.rser.2018.07.047
Benninga, S. (2000). Financial modeling (2nd ed.). MIT Press.
Briggs, H., Wonderling, D. E., & Mooney, C. Z. (1997). Pulling cost-effectiveness analysis up by its bootstraps: A non-parametric approach to confidence interval estimation. Health Economics, 6(4), 327–340. https://doi.org/10.1002/(SICI)1099-1050(199707)6:4<327::AID-HEC282>3.0.CO;2-W
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David, A., & Veronesi, P. (2022). A survey of alternative measures of macroeconomic uncertainty: Which measures forecast real variables and explain fluctuations in asset volatilities better? Annual Review of Financial Economics, 14(1), 439–463. https://doi.org/10.1146/annurev-financial-111720-091804
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French, N. (2019). Predicted property investment returns: Risk and growth models. Journal of Property Investment & Finance, 37(6), 580–588. https://doi.org/10.1108/JPIF-07-2019-0096
Hameed, A., & Bashir, M. (2002). Property rights, institutions and economic development: An Islamic perspective. Humanomics, 18(3), 75–91. https://doi.org/10.1108/eb018877
Hamzah, S. R., Bacha, O. I., Mirakhor, A., & Malim, N. A. K. (2018). Empirical evidence of risk shifting in bonds and debt-based sukuk. Journal of Islamic Accounting and Business Research, 9(5), 687–700. https://doi.org/10.1108/JIABR-06-2016-0068
Hasan, R., Ahmad, A. U. F., & Parveen, T. (2019). Sukuk risks: A structured review of theoretical research. Journal of Islamic Accounting and Business Research, 10(1), 35–49. https://doi.org/10.1108/JIABR-06-2015-0026
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Judd, K. L. (1996). Approximation, perturbation, and projection methods in economic analysis. In J. B. Taylor & M. Woodford (Eds.), Handbook of macroeconomics (pp. 509–585). Elsevier.
Kamaruzaman, N. R., & Ishak, M. S. I. (2023). Waqf institutions: A systematic literature review on governance, financial models, and socio-economic impact in Islamic social finance. Advanced International Journal of Business, Entrepreneurship and SMEs, 5(18), 134–151. https://doi.org/10.35631/AIJBES.518014
Klein, P., Weill, L., & Godlewski, C. J. (2018). How sukuk shapes firm performance. The World Economy, 41(3), 699–722. https://doi.org/10.1111/twec.12509
Kuanova, L. A., Sagiyeva, R., & Shirazi, N. S. (2021). Islamic social finance: A literature review and future research directions. Journal of Islamic Accounting and Business Research, 12(5), 707–728. https://doi.org/10.1108/JIABR-11-2020-0356
Lawson, C. (1994). The theory of state-owned enterprises in market economies. Journal of Economic Surveys, 8(3), 283–309. https://doi.org/10.1111/j.1467-6419.1994.tb00104.x
Lim, K.-P., & Brooks, R. (2011). The evolution of stock market efficiency over time: A survey of the empirical literature. Journal of Economic Surveys, 25(1), 69–108. https://doi.org/10.1111/j.1467-6419.2009.00611.x
Mary, M., Mediawati, E., & Adirestuty, F. (2019). The analysis of third-party funds, state sukuk, and corporate sukuk towards financial deepening in Indonesia. Review of Islamic Economics and Finance, 2(2), 53–66. https://doi.org/10.17509/rief.v2i1.22158
Medias, F., Rahman, A. A., Susamto, A. A., & Pambuko, Z. B. (2022). A systematic literature review on the socio-economic roles of waqf: Evidence from Organization of Islamic Cooperation (OIC) countries. Journal of Islamic Accounting and Business Research, 13(1), 177–193. https://doi.org/10.1108/JIABR-01-2021-0028
Mohd Roslen, S. N., Chua, M.-S., & Hj Mohd Ruslan, R. A. (2025). Long-run asymmetric effects of financial risks on Sukuk market development: Empirical evidence from Malaysia. Journal of Islamic Accounting and Business Research, 16(8), 1394–1425. https://doi.org/10.1108/JIABR-08-2022-0200
Nurhanifah, N. V. (2024). Understanding Sukuk market development: An overview of opportunities and challenges. Journal of Waqf and Islamic Economic Philanthropy, 1(2), 1–11. https://doi.org/10.47134/wiep.v1i2.155
Pagourtzi, E., Assimakopoulos, V., Hatzichristos, T., & French, N. (2003). Real estate appraisal: A review of valuation methods. Journal of Property Investment & Finance, 21(4), 383–401. https://doi.org/10.1108/14635780310483656
Qurrata, V. A., Mohd. Shafiai, M. H., Wahid, H., Almaamun, S., & Ismail, A. G. (2025). Institutional economics from Islamic perspective: With special reference to waqf. Sage Open, 15(4). https://doi.org/10.1177/21582440251397178
Rafay, R. S., & Ajmal, M. (2017). Uniform framework for Sukuk al-Ijarah: A proposed model for all madhahib. Journal of Islamic Accounting and Business Research. https://doi.org/10.1108/JIABR-09-2015-0042
Regan, C. M., et al. (2015). Real options analysis for land use management: Methods, application, and implications for policy. Journal of Environmental Management, 161, 144–152. https://doi.org/10.1016/j.jenvman.2015.07.004
Ren, X., Li, J., He, F., & Lucey, B. (2023). Impact of climate policy uncertainty on traditional energy and green markets: Evidence from time-varying Granger tests. Renewable and Sustainable Energy Reviews, 173, 113058. https://doi.org/10.1016/j.rser.2022.113058
Sulaiman, M., & Zakari, M. A. (2019). Financial sustainability of state waqf institutions (SWIs) in Malaysia. Journal of Islamic Accounting and Business Research, 10(2), 236–258. https://doi.org/10.1108/JIABR-05-2016-0054
Umi Masnur Adniyah. (2025). Implementation of the land swap agreement (ruislag) for waqf land for the construction of a toll road. JUSTISI, 11(2), 488–502. https://doi.org/10.33506/js.v11i2.4224
Xie, Q., Parsa, A. R. G., & Redding, B. (2002). The emergence of the urban land market in China: Evolution, structure, constraints and perspectives. Urban Studies, 39(8), 1375–1398. https://doi.org/10.1080/00420980220142682
Zafar, M. B., & Jafar, A. (2025). Waqf over a century: Innovation and tradition in shaping social equity and sustainable development. International Journal of Sociology and Social Policy. https://doi.org/10.1108/IJSSP-12-2024-0625
Zhou, H. (2018). Variance risk premia, asset predictability puzzles, and macroeconomic uncertainty. Annual Review of Financial Economics, 10(1), 481–497. https://doi.org/10.1146/annurev-financial-110217-022737
Adebayo, A. (2025). Conceptualising (corporate) governance in state-owned enterprises: A research agenda. International Journal of Organizational Analysis, 33(10), 4001–4031. https://doi.org/10.1108/IJOA-07-2024-4700
Afief El Ashfahany, D., Astuti, D. P., & Ma’ruf, A. (2023). Sukuk issuance in Indonesia: Orientation, opportunities, and challenges. Mabsya: Jurnal Manajemen Bisnis Syariah, 6(1), 127–148. https://doi.org/10.24090/mabsya.v6i1.8195
Ahmed, H., Hassan, M. K., & Rayfield, B. (2018). When and why firms issue sukuk? Managerial Finance, 44(6), 774–786. https://doi.org/10.1108/MF-06-2017-0207
Alam, N., Salmawati, S., & Zainuddin, Z. (2024). The role of nadzir in resolving waqf land disputes. Golden Ratio of Law and Social Policy Review, 3(2). https://doi.org/10.52970/grlspr.v3i2.329
Alswaidan, M. W., Daynes, A., & Pasgas, P. (2017). Understanding and evaluation of risk in sukuk structures. Journal of Islamic Accounting and Business Research, 8(4). https://doi.org/10.1108/JIABR-05-2015-0021
Ang, A., & Timmermann, A. (2012). Regime changes and financial markets. Annual Review of Financial Economics, 4(1), 313–337. https://doi.org/10.1146/annurev-financial-110311-101808
Basher, S. A., & Raboy, D. G. (2018). The misuse of net present value in energy efficiency standards. Renewable and Sustainable Energy Reviews, 96, 218–225. https://doi.org/10.1016/j.rser.2018.07.047
Benninga, S. (2000). Financial modeling (2nd ed.). MIT Press.
Briggs, H., Wonderling, D. E., & Mooney, C. Z. (1997). Pulling cost-effectiveness analysis up by its bootstraps: A non-parametric approach to confidence interval estimation. Health Economics, 6(4), 327–340. https://doi.org/10.1002/(SICI)1099-1050(199707)6:4<327::AID-HEC282>3.0.CO;2-W
Calvo, G. A. (1978). On the time consistency of optimal policy in a monetary economy. Econometrica, 46(6), 1411–1428. https://doi.org/10.2307/1913836
Cvitanic, J., & Zapatero, F. (2024). Introduction to the economics and mathematics of financial markets. MIT Press.
Czerwinski, A. (2024). Mathematics serving economics: A historical review of mathematical methods in economics. Symmetry, 16(10), 1271. https://doi.org/10.3390/sym16101271
David, A., & Veronesi, P. (2022). A survey of alternative measures of macroeconomic uncertainty: Which measures forecast real variables and explain fluctuations in asset volatilities better? Annual Review of Financial Economics, 14(1), 439–463. https://doi.org/10.1146/annurev-financial-111720-091804
Dirie, K. A., Alam, M. M., & Maamor, S. (2024). Islamic social finance for achieving sustainable development goals: A systematic literature review and future research agenda. International Journal of Ethics and Systems, 40(4), 676–698. https://doi.org/10.1108/IJOES-12-2022-0317
French, N. (2019). Predicted property investment returns: Risk and growth models. Journal of Property Investment & Finance, 37(6), 580–588. https://doi.org/10.1108/JPIF-07-2019-0096
Hameed, A., & Bashir, M. (2002). Property rights, institutions and economic development: An Islamic perspective. Humanomics, 18(3), 75–91. https://doi.org/10.1108/eb018877
Hamzah, S. R., Bacha, O. I., Mirakhor, A., & Malim, N. A. K. (2018). Empirical evidence of risk shifting in bonds and debt-based sukuk. Journal of Islamic Accounting and Business Research, 9(5), 687–700. https://doi.org/10.1108/JIABR-06-2016-0068
Hasan, R., Ahmad, A. U. F., & Parveen, T. (2019). Sukuk risks: A structured review of theoretical research. Journal of Islamic Accounting and Business Research, 10(1), 35–49. https://doi.org/10.1108/JIABR-06-2015-0026
Ismal, R. (2024). Constructing sukuk-linked awqaf (endowment) model. International Journal of Islamic and Middle Eastern Finance and Management, 17(5), 871–882. https://doi.org/10.1108/IMEFM-04-2024-0198
Judd, K. L. (1996). Approximation, perturbation, and projection methods in economic analysis. In J. B. Taylor & M. Woodford (Eds.), Handbook of macroeconomics (pp. 509–585). Elsevier.
Kamaruzaman, N. R., & Ishak, M. S. I. (2023). Waqf institutions: A systematic literature review on governance, financial models, and socio-economic impact in Islamic social finance. Advanced International Journal of Business, Entrepreneurship and SMEs, 5(18), 134–151. https://doi.org/10.35631/AIJBES.518014
Klein, P., Weill, L., & Godlewski, C. J. (2018). How sukuk shapes firm performance. The World Economy, 41(3), 699–722. https://doi.org/10.1111/twec.12509
Kuanova, L. A., Sagiyeva, R., & Shirazi, N. S. (2021). Islamic social finance: A literature review and future research directions. Journal of Islamic Accounting and Business Research, 12(5), 707–728. https://doi.org/10.1108/JIABR-11-2020-0356
Lawson, C. (1994). The theory of state-owned enterprises in market economies. Journal of Economic Surveys, 8(3), 283–309. https://doi.org/10.1111/j.1467-6419.1994.tb00104.x
Lim, K.-P., & Brooks, R. (2011). The evolution of stock market efficiency over time: A survey of the empirical literature. Journal of Economic Surveys, 25(1), 69–108. https://doi.org/10.1111/j.1467-6419.2009.00611.x
Mary, M., Mediawati, E., & Adirestuty, F. (2019). The analysis of third-party funds, state sukuk, and corporate sukuk towards financial deepening in Indonesia. Review of Islamic Economics and Finance, 2(2), 53–66. https://doi.org/10.17509/rief.v2i1.22158
Medias, F., Rahman, A. A., Susamto, A. A., & Pambuko, Z. B. (2022). A systematic literature review on the socio-economic roles of waqf: Evidence from Organization of Islamic Cooperation (OIC) countries. Journal of Islamic Accounting and Business Research, 13(1), 177–193. https://doi.org/10.1108/JIABR-01-2021-0028
Mohd Roslen, S. N., Chua, M.-S., & Hj Mohd Ruslan, R. A. (2025). Long-run asymmetric effects of financial risks on Sukuk market development: Empirical evidence from Malaysia. Journal of Islamic Accounting and Business Research, 16(8), 1394–1425. https://doi.org/10.1108/JIABR-08-2022-0200
Nurhanifah, N. V. (2024). Understanding Sukuk market development: An overview of opportunities and challenges. Journal of Waqf and Islamic Economic Philanthropy, 1(2), 1–11. https://doi.org/10.47134/wiep.v1i2.155
Pagourtzi, E., Assimakopoulos, V., Hatzichristos, T., & French, N. (2003). Real estate appraisal: A review of valuation methods. Journal of Property Investment & Finance, 21(4), 383–401. https://doi.org/10.1108/14635780310483656
Qurrata, V. A., Mohd. Shafiai, M. H., Wahid, H., Almaamun, S., & Ismail, A. G. (2025). Institutional economics from Islamic perspective: With special reference to waqf. Sage Open, 15(4). https://doi.org/10.1177/21582440251397178
Rafay, R. S., & Ajmal, M. (2017). Uniform framework for Sukuk al-Ijarah: A proposed model for all madhahib. Journal of Islamic Accounting and Business Research. https://doi.org/10.1108/JIABR-09-2015-0042
Regan, C. M., et al. (2015). Real options analysis for land use management: Methods, application, and implications for policy. Journal of Environmental Management, 161, 144–152. https://doi.org/10.1016/j.jenvman.2015.07.004
Ren, X., Li, J., He, F., & Lucey, B. (2023). Impact of climate policy uncertainty on traditional energy and green markets: Evidence from time-varying Granger tests. Renewable and Sustainable Energy Reviews, 173, 113058. https://doi.org/10.1016/j.rser.2022.113058
Sulaiman, M., & Zakari, M. A. (2019). Financial sustainability of state waqf institutions (SWIs) in Malaysia. Journal of Islamic Accounting and Business Research, 10(2), 236–258. https://doi.org/10.1108/JIABR-05-2016-0054
Umi Masnur Adniyah. (2025). Implementation of the land swap agreement (ruislag) for waqf land for the construction of a toll road. JUSTISI, 11(2), 488–502. https://doi.org/10.33506/js.v11i2.4224
Xie, Q., Parsa, A. R. G., & Redding, B. (2002). The emergence of the urban land market in China: Evolution, structure, constraints and perspectives. Urban Studies, 39(8), 1375–1398. https://doi.org/10.1080/00420980220142682
Zafar, M. B., & Jafar, A. (2025). Waqf over a century: Innovation and tradition in shaping social equity and sustainable development. International Journal of Sociology and Social Policy. https://doi.org/10.1108/IJSSP-12-2024-0625
Zhou, H. (2018). Variance risk premia, asset predictability puzzles, and macroeconomic uncertainty. Annual Review of Financial Economics, 10(1), 481–497. https://doi.org/10.1146/annurev-financial-110217-022737
Published
2026-06-30
How to Cite
PRATAMA, Jovian Dian.
Mathematical Review of the Sukuk-Linked Awqaf Model: A Critical Analysis of Notation Consistency and Formula Validity.
Theoretical and Practical Research in Economic Fields, [S.l.], v. 17, n. 2, p. 340 - 355, june 2026.
ISSN 2068-7710.
Available at: <https://journals.aserspublishing.eu/tpref/article/view/9511>. Date accessed: 02 july 2026.
doi: https://doi.org/10.14505/tpref.v17.2(38).04.
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Articles
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