Establishing a stochastic model for optimal decision making incorporating a random sum of discounted random variables
*Constantinos T. ArtikisCorresponding authorctartikis@gmail.comDepartment of TourismFaculty of Economic SciencesIonian UniversityCorfu, 49132, Greece0000-0003-2987-4898View full profile → , Panagiotis T. Artikisptartikis@gmail.comDepartment of Accounting & FinanceSchool of Management, Economic & Social SciencesUniversity of West AtticaEgaleo, Athens, 12244, Greece0000-0002-8301-3485View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 06 May 2024
- Published Online:
- 03 Apr 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1882
- Pages:
- 831–850
Abstract
Keywords
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References
[1] M. Ahsanullah, BG. Kibria, and M. Shakil, ‘Sum, Product and Ratio for the Normal Random Variables’, Normal and Student´s t Distributions and Their Applications, pp. 63-79, (2014). doi: https://doi.org/10.2991/978-94-6239-061-4_4.
[2] A. Aleškevičienė, R. Leipus, and J. Šiaulys, ‘Tail behavior of random sums under consistent variation with applications to the compound renewal risk model’, Extremes, Vo. 11, pp. 261-279, (2008) doi: https://doi.org/10.1007/s10687-008-0057-3.
[3] I. Al Kattan, A. Al Nunu , and K. Saleh, ‘A stochastic model for improving information security in supply chain systems’, International Journal of Information Systems and Supply Chain Management (IJISSCM), Vol. 2, No.3, pp. 35-49, (2009) doi:10.4018/jisscm.2009070103.
[4] M.C. Andrade, P.T. Urgilés, and M.A. Estrella, ‘Information and communication technologies in the development of stochastic models applied to the health sector’, Medicina, Vol. 80, pp. 31-38, (2020), PMID: 32044739 .
[5] R. Annavajjala, A. Chockalingam, and SK. Mohammed, ‘On a ratio of functions of exponential random variables and some applications’, IEEE Transactions on Communications, Vol. 58, pp. 3091-3097, (2010), doi: 10.1109/TCOMM.2010.091710.100038.
[6] T.P. Artikis and A.G. Malliaris, ‘Discounting certain random sums’, Scandinavian Actuarial Journal, Vol.1, pp. 34-38, (1990), doi: https://doi.org/10.1080/03461238.1990.10413871.
[7] T. Artikis, D. Jerwood, and A. Voudouri, ‘Analytical and simulation techniques for discounting binomial random sums’, Mathematical and computer modelling, Vol. 16, pp. 53-58, (1992), doi: https://doi.org/10.1016/0895-7177(92)90045-M.
[8] P.T. Artikis, ‘Incorporating a discrete renewal random sum in computational intelligence and cindynics’, Multimedia Services in Intelligent Environments: Software Development Challenges and Solutions, pp.173-186, (2010), doi: https://doi.org/10.1007/978-3-642-13355-8_11.
[9] P.T. Artikis and C.T. Artikis, ‘Stochastic models for risk control programs of organizations’, Kybernetes, Vol. 39 No. 4, pp. 570-577, (2010), doi: https://doi.org/10.1108/03684921011036790.
[10] C.T. Artikis, and P.T Artikis, ‘Formulation and incorporation of a stochastic model for supporting optimal decision making in global risk governance’, Journal of Information and Optimization Sciences, Vol. 42., pp. 1-9, (2021) doi: https://doi.org/10.1080/02522667.2020.1857904.
[11] C.T. Artikis and P.T. Artikis, ‘Discounting for proactive decision making in systemics’, International Journal of Applied Systemic Studies, Vol. 10, No.4, pp.343-352, (2023) doi: https://doi.org/10.1504/IJASS.2023.135729.
[12] P.T. Artikis and C.T. Artikis, ‘Proactive decision making by incorporation of discrete random sums’, Intelligent Decision Technologies, Vol.17, No. 4, pp.119-1206, (2023), doi:10.3233/IDT-230268.
[13] S.H. Begg, R.B. Bratvold and J.M. Campbell, ‘Improving investment decisions using a stochastic integrated asset model’ In SPE Annual Technical Conference and Exhibition, SPE-71414, (2001), doi: https://doi.org/10.2118/71414-MS.
[14] O. Berman and E. Kim, ‘Stochastic models for inventory management at service facilities’, Stochastic Models, Vol. 15, No.4, pp.695-718, (1999), doi: https://doi.org/10.1080/15326349908807558.
[15] P. Bhattacharya, S. Paul and K.S. Choudhury, ‘Different Types of Epidemic Models and their Characteristic Behaviour by using Matlab’, Journal of Interdisciplinary Mathematics, 18(5), pp. 569–592, (2015), https://doi.org/10.1080/09720502.2014.914280
[16] J. P. N. Bishwal, ‘Sequential Monte Carlo methods for stochastic volatility models: a review’, Journal of Interdisciplinary Mathematics, Vol. 13, pp. 619–635, (2010). https://doi.org/10.1080/09720502.2010.10700723
[17] E. Borgonovo and L. Peccati, ‘Sensitivity analysis in decision making: a consistent approach’, Advances in decision making under risk and uncertainty. Springer Berlin Heidelberg, pp. 65-89, (2008), available at: https://link.springer.com/content/pdf/10.1007/978-3-540-68437-4_5.pdf
[18] CL. Chang, JÁ. Jiménez-Martín, E. Maasoumi and T. Pérez-Amaral T., ‘A stochastic dominance approach to financial risk management strategies’, Journal of Econometrics, Vol.187 No.2, pp.472-485, (2015) doi: https://doi.org/10.1016/j.jeconom.2015.02.032.
[19] J. P. C. Chuang, W. S. Chou, and P. Julianne, ‘Inventory models with stochastic ramp type demand’, Journal of Interdisciplinary Mathematics, Vol. 19(1), pp. 55–64, (2016), https://doi.org/10.1080/09720502.2015.1084775
[20] G. D’Amico, F. Petroni and F. Prattico, ‘Economic performance indicators of wind energy based on wind speed stochastic modeling’, Applied Energy, Vol. 154, pp. 290-297, (2015), doi: https://doi.org/10.1016/j.apenergy.2015.04.124.
[21] E.S.S De Cursi and R. Sampaio, Uncertainty quantification and stochastic modeling with matlab, Elsevier, (2015), doi: https://doi.org/10.1016/C2014-0-04713-2.
[22] R. A. de Freitas, E. P. Vogel, A. L. Korzenowski, and L. A. O. Rocha, ‘Stochastic model to aid decision making on investments in renewable energy generation: Portfolio diffusion and investor risk aversion’, Renewable energy, Vol. 162, pp. 1161-1176, (2020), doi: https://doi.org/10.1016/j.renene.2020.08.012.
[23] A. Diederich, ‘Dynamic stochastic models for decision making under time constraints’, Journal of Mathematical Psychology, Vol. 41, No. 3, pp. 260-274, (1997), doi: https://doi.org/10.1006/jmps.1997.1167.
[24] E. Di Lorenzo, M. Sibillo and G. Tessitore, ‘A stochastic model for financial evaluation: applications to actuarial contracts’, Applied Stochastic Models in Business and Industry, Vol. 15, No. 4, pp. 269-275, (1999), doi: https://doi.org/10.1002/(SICI)1526-4025(199910/12)15:4%3C269::AID-ASMB392%3E3.0.CO;2-F.
[25] E. Domínguez, B. Pérez, ÁL .Rubio and M.A. Zapata, ‘A taxonomy for key performance indicators management’, Computer Standards & Interface, Vol. 64, pp. 24-40, (2019), doi: https://doi.org/10.1016/j.csi.2018.12.001.
[26] C.H. Fouche, J. Mukuddem-Petersen and M.A. Petersen, ‘Continuous-time stochastic modelling of capital adequacy ratios for banks’, Applied Stochastic Models in Business and Industry, Vol. 22, No.1, pp. 41-71, (2006), doi: https://doi.org/10.1002/asmb.609.
[27] E. Fregonara, R. Giordano, D.G. Ferrando and S. Pattono, ‘Economic-environmental indicators to support investment decisions: A focus on the buildings’ end-of-life stage’, Buildings, Vol. 7, No. 3, p. 65, (2017), doi: https://doi.org/10.3390/buildings7030065.
[28] S. French, ‘Modelling, making inferences and making decisions: the roles of sensitivity analysis’, Top, Vol. 11, pp. 229-251, (2003), doi: https://doi.org/10.1007/BF02579043.
[29] M. Goh, J.Y. Lim and F. Meng, ‘A stochastic model for risk management in global supply chain networks’, European Journal of Operational Research, Vol. 182, No. 1, pp. 164-173, (2007), doi: https://doi.org/10.1016/j.ejor.2006.08.028.
[30] R.W. Grubbström and Z. Wang, ‘A stochastic model of multi-level/multi-stage capacity-constrained production–inventory systems’, International journal of production economics, Vol.81, pp. 483-494, (2003), doi: https://doi.org/10.1016/S0925-5273(02)00358-4.
[31] C.H. Hesse, ‘A general procedure for stochastic modelling of systems consisting of a large number of interacting components’, Applied stochastic models and data analysis, Vol. 13(3-4), pp. 249-258, (1997), doi: https://doi.org/10.1002/(SICI)1099-0747(199709/12)13:3/4%3C249::AID-ASM319%3E3.0.CO;2-N
[32] D.V. Hinkley, ‘On the ratio of two correlated normal random variables’, Biometrika, Vol. 56, No. 3, pp. 635-639, (1969), doi: https://doi.org/10.1093/biomet/56.3.635.
[33] K. Høyland, E. Ranberg . and S.W. Wallace, ‘Developing and Implementing a Stochastic Decision-Support Model Within an Organizational Context: Part II—The Organization’, Journal of Risk Finance, Vol. 5 No. 2, pp. 58-63, (2004), doi: https://doi.org/10.1108/eb022987.
[34] V. Kaarnioja, F.Y. Kuo and I.H. Sloan, ‘Uncertainty quantification using periodic random variables’, SIAM Journal on Numerical Analysis, Vol. 58, No. 2, pp. 1068-1091, (2020), doi: https://doi.org/10.1137/19M1262796.
[35] M. Khodabakhshi . and M. Ahmadi, ‘An approach to cost-benefit analysis by competitive advantages with stochastic data’, Journal of Modelling in Management, Vol. 17 No. 1, pp. 297-308, (2022), doi: https://doi.org/10.1108/JM2-07-2020-0185.
[36] C. Klüppelberg and T. Mikosch, “Large deviations of heavy-tailed random sums with applications in insurance and finance”, Journal of Applied Probability, Vol. 34, No. 2, pp. 293-308, (1997), doi: https://doi.org/10.2307/3215371.
[37] H. Ko and S. Lee, ‘Fourier transform and regularity of characteristic functions’, Proceedings of the American Mathematical Society, Vol. 145, No. 3, pp. 1097-1107, (2017), doi: https://doi.org/10.1090/proc/13435.
[38] R. Korn, Optimal portfolios: stochastic models for optimal investment and risk management in continuous time, World scientific, (1997), Handle: RePEc:wsi:wsbook:3548.
[39] P. Kumar, R. Shankar and S.S. Yadav, ‘Flexibility in global supply chain: modeling the enablers’, Journal of Modelling in Management, Vol. 3 No. 3, pp. 277-297, (2008), doi: https://doi.org/10.1108/17465660810920609.
[40] S.A. Ladoucette and J.J. Teugels, ‘Limit distributions for the ratio of the random sum of squares to the square of the random sum with applications to risk measures’, Publications de l’Institut Mathematique, Vol. 80, No. 94, pp. 219-240, (2006), doi: https://doi.org/10.2298/PIM0694219L.
[41] L. Le Cam, ‘On the distribution of sums of independent random variables”, In Bernoulli 1713, Bayes 1763, Laplace 1813: Anniversary Volume. Proceedings of an International Research Seminar Statistical Laboratory University of California, Berkeley 1963, pp. 179-202, Springer Berlin Heidelberg (1965), doi: https://doi.org/10.1007/978-3-642-49749-0_10.
[42] X. Z. Liao, L. H. Peng, L. X. Wu, M. W. Tian, and S. R. Yan, ‘Research n the optimization of modern portfolio model based on optimal investment weight’, Journal of Interdisciplinary Mathematics, Vol. 21(5), pp. 1157–1162, (2018), https://doi.org/10.1080/09720502.2018.1494313
[43] R. Lin, J.S. Lin, K. Chen and P.C. Julian, “Note on inventory model with net present value”, Journal of Interdisciplinary Mathematics, Vol. 10(4), pp. 587–592, (2007), https://doi.org/10.1080/09720502.2007.10700518
[44] G. Marsden, C. Kelly and C. Snell, ‘Selecting indicators for strategic performance management’, Transportation research record, Vol. 1956, No. 1, pp. 21-29, (2006), doi: https://doi.org/10.1177/0361198106195600103.
[45] S. Nadarajah and S. Kotz, ‘On the product and ratio of Gamma and Weibull random variables’, Econometric Theory, Vol. 22, No. 2, pp. 338-344, (2006), doi: https://doi.org/10.1017/S0266466606060154.
[46] B.L. Nelson, Stochastic modeling: analysis & simulation, Courier Corporation, (2010), ISBN (Print): 978-0070462137.
[47] M. Pinsky and S. Karlin, An introduction to stochastic modeling. Academic press, BL. (2010), ISBN (Print): 9780123814166.
[48] A. .N. Podkorytov and M. Van Minh, ‘On the inversion formula of the Fourier transform of the characteristic function of several variables’, Journal of Mathematical Sciences, Vol. 120, No. 2, pp. 1191-1194, (2004), doi: https://doi.org/10.1023/B:JOTH.0000014846.04894.
[49] C. Powell , Y. Lawryshyn and T. Bender, ‘Using stochastic models to determine financial indicators and technical objectives for organic solar cells’, Solar energy materials and solar cells. Vol.107, pp. 236-247, (2012) doi: https://doi.org/10.1016/j.solmat.2012.06.038.
[50] D. Prajapati, S. Mondal and D. Kundu, ‘Optimal decision-theoretic sampling plan for two exponential distributions under joint censoring scheme’, Applied Stochastic Models in Business and Industry, Vol. 37, No. 3, pp. 560-576, (2021), doi: https://doi.org/10.1002/asmb.2595.
[51] G.D. Rubin and B.N. Patel, ‘Financial forecasting and stochastic modeling: predicting the impact of business decisions’, Radiology, Vol. 283, No. 2, pp. 342-358, (2017), doi: https://doi.org/10.1148/radiol.2017161800
[52] N. Savelli and G.P. Clemente, ‘A Risk-Theory Model to Assess the Capital Requirement for Mortality and Longevity Risk’, Journal of Interdisciplinary Mathematics, Vol. 16, pp. 397–429, (2017), https://doi.org/10.1080/09720502.2013.849943
[53] S. Sharma and A.J. Obaid, A. J. ‘Mathematical modelling, analysis and design of fuzzy logic controller for the control of ventilation systems using MATLAB fuzzy logic toolbox’, Journal of Interdisciplinary Mathematics, Vol. 23, pp. 843–849, (2020) https://doi.org/10.1080/09720502.2020.1727611
[54] S.S. Shin, K.S. Lee and H.G. Cho, ‘An objective method of risk assessment based on stochastic modelling’, Journal of Korean Society for Quality Management, Vol. 41, No. 3, pp. 465, (2013), doi: https://doi.org/10.7469/JKSQM.2013.41.3.465.
[55] J.S. Song, ‘The effect of leadtime uncertainty in a simple stochastic inventory model’, Management Science, Vol. 40, No. 5, pp. 603-613, (1994), doi: https://doi.org/10.1287/mnsc.40.5.603.
[56] C.S. Tapiero, Applied stochastic models and control for finance and insurance., Springer Science & Business Media, (2012), doi: https://doi.org/10.1007/978-1-4615-5823-1.
[57] S. Vanduffel, T. Hoedemakers and J. Dhaene, ‘Comparing approximations for risk measures of sums of nonindependent lognormal random variables’, North American Actuarial Journal, Vol. 9, No. 4, pp. 71-82, (2005), doi: https://doi.org/10.1080/10920277.2005.10596226.
[58] A. Voudouri and E. Ntziachristos, ‘A binomial random sum of present value models in investment analysis’, SPOUDAI-Journal of Economics and Business, Vol. 47, pp. 15-20, (1997), doi: https://spoudai.unipi.gr/index.php/spoudai/article/viewFile/1069/1148.
[59] T. Vrouwenvelder, ‘Stochastic modelling of extreme action events in structural engineering’, Probabilistic Engineering Mechanics, Vol. 15, No. 1, pp.109-117, (2000), doi: https://doi.org/10.1016/S0266-8920(99)00014-4.
[60] U. Wagner and A. Taudes, ‘Stochastic models of consumer behaviour’, European Journal of Operational Research, Vol. 29, No. 1, pp. 1-23, (1987), doi: https://doi.org/10.1016/0377-2217(87)90189-5.
[61] S. Wang and W. Wang, ‘Precise large deviations for sums of random variables with consistently varying tails in multi-risk models’, Journal of Applied Probability, Vol. 44, No. 4, pp. 889-900, (2007), doi: https://doi.org/10.1239/jap/1197908812.
[62] Y. Yakoubov, M. Teeger and D.B. Duval, ‘A stochastic investment model for asset and liability management’, In Proceedings of the 9th International AFIR Colloquium, pp. 237-66, (1999), available at: https://www.actuaries.org/AFIR/Colloquia/Tokyo/Yaboubov_Teeger_Duval.pdf.
[63] Y. Yang and Y. Zhao, “Modified PROMETHEEII for venture capital investment selection decision-making towards SMEs”, Journal of Interdisciplinary Mathematics, Vol. 21, pp. 1017–1029, (2018). https://doi.org/10.1080/09720502.2018.1456824.
[64] Q. Zhao and Q. Li, ‘Supply chain optimization decision based on mixed component commonality under stochastic constraints’, Journal of Interdisciplinary Mathematics, Vol. 21(4), pp. 941–948, (2018). https://doi.org/10.1080/09720502.2018.1481587.
[65] L. Zhu, “Supply chain inventory model for perishable items under delayed payment” Journal of Interdisciplinary Mathematics, Vol. 21, pp. 849–857, (2018), https://doi.org/10.1080/09720502.2018.1475063.




