A model for adaptive risk aversion preferences in portfolio optimization and prospect theory

Document Type : Original Article

Authors
Roohollah Mehralizadeh shiadehi 1
Hossein Didehkhani 1
Ali Khozain 2
Arash Naderian 3
1 Department of Financial Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul. Iran
2 Department of Accounting, Aliabad Katoul branch, Islamic Azad University, Aliabad Katoul, Iran
3 Department of Accounting, Aliabad Katoul branch, Islamic Azad University, Aliabad Katoul, Iran.
10.30495/jik.2025.23601
Abstract
In this research, we will present a model of adaptive risk aversion by reference point in prospect theory. We funded many theoretical and researches are shown risk aversion is dependent on wealth. We used the out coming wealth from a portfolio optimization determine as the investor's reference point. Compatibility of the reference point with the wealth of portfolio performance at the end of the investment period is a measure to determine new risk aversion. After proposing an adaptive risk aversion measure, the model was implemented for 35 shares of the Tehran Stock Exchange market plus a risk-free asset during 7 investment periods, and finally, by solving the model and applying the genetic algorithm, the adaptive risk aversion was calculated.
Keywords
Prospect Theory
Adaptive Risk Aversion
Portfolio Optimization
Reference Point in Prospect Theory
  1. ابراهیمیان, کامل, عباسی, ابراهیم, عالم تبریز, & محمدزاده. (2021). پیش‌ بینی‌ روند‌ روزانه‌ قیمت‌ سهام‌ با‌ استفاده‌ از‌ متن‌ کاوی‌ احساسات‌ کاربران‌ شبکه‌ اجتماعی‌ و‌ داده‌ کاوی‌ نماگرهای‌ تکنیکال.دانش سرمایه‌گذاری, 10(40), 451-469.‎
  2. ابراهیمی سرو علیا, م., سلیمی, م., & قوچی فرد, ح. (1399). اثر زیان گریزی نزدیک بینانه(MLA) سرمایه‌گذاران بر سرمایه‌گذاری در سهام در بورس اوراق بهادار تهران. فصلنامه علمی مطالعات تجربی حسابداری مالی.
  3. ابراهیمی, س., باباخانی , م., متقی دستنایی , س., & جبارزاده , آ. (1390). اثر ریسک گریزی فرد در انتخاب پویای سبد مالی بهینه. پژوهشنامه اقتصادی.
  4. ابراهیمی, س., باباخانی, م., متقی دستنایی, س., & جبارزاده, آ. (1388). اثر ریسک‌گریزی فرد در انتخاب پویای سبدمالی بهینه. پژوهشنامه اقتصادی.
  5. شیری قهی, ا., دیده خانی, ح., خلیلی دامغانی, ک., & سعیدی, پ. (1396). مطالعه تطبیقی مدل بهینه‌سازی پرتفوی چند دوره ای چندهدفه در محیط اعتبار فازی با معیارهای متفاوت ریسک. مدیریت اوراق بهادار.
  6. شیری قهی, ا., دیده خانی, ح., خلیلی دامغانی, ک., & سعیدی, پ. (1397). طراحی مدل بهینه‌سازی پرتفوی چند دوره ای میانگین - ارزش در معرض خطر میانگین در محیط اعتبار فازی. مجله مهندسی مالی, 131-151.
  7. کفاش پنجه شاهی, م., & برزیده, ف. (1391). تأثیر عملکرد گذشته سرمایه‌گذاران بر قیمت سهام براساس نظریه چشم‌انداز. دانش سرمایه‌گذاری.
  8. میرعباسی, ی., نیکومرام , ه., سعیدی , ع., & حق شناس, ف. (1397). بررسی کارایی بهینه‌سازی پرتفوی مبتنی بر ریسک نامطلوب و پتانسیل مطلوب و متغیرهای روانشناختی. فصلنامه مهندسی مالی.

 

 

 

  1. Besnainou, I. B., & Portait, R. (1998). Dynamic Asset Allocation in a Mean-Variance Framework. Management Science.
  2. Björk, T., Murgoci, A., & Zhou, X. (2014). MEAN–VARIANCE PORTFOLIO OPTIMIZATION WITH STATE-DEPENDENT RISK AVERSION. Mathematical Finance.
  3. Blake, D., Wright , D., & Zhang, Y. (2013). Target-driven investing: optimal investment strategies in defined contribution pension plans under loss aversion. Econ Dynam Control.
  4. Chabakauri, B. s. (2010). Dynamic mean-variance asset allocation. Rev Financ Stud, 2970–3016.
  5. Çepni, O., Demirer, R., Gupta, R., & Pierdzioch, C. (2020). Time-varying risk aversion and the predictability of bond premia. Finance Research Letters, 34, 101241.
  6. Celikyurt, U., & Özekici, S. (2007). Multiperiod portfolio optimization models in stochastic markets using the mean–variance approach. European Journal of Operational Research, 179(1), 186-202. Chen, P., Yang, H., & Yin, G. (2008). Markowitz’s mean-variance asset-liability management with regime switching: A continuous-time model. Insurance: Mathematics and Economics.
  7. Cui , x., Li, d., Wang, s., & Zhu, S. (2012). Better than dynamic meanvariance: time inconsistency and free cash flow stream. Math Financ.
  8. Dai, Z., & Chang, X. (2021). Forecasting stock market volatility: Can the risk aversion measure exert an important role? The North American Journal of Economics and Finance, 58, 101510
  9. Dantzig, G., & Infanger, G. (1993). Multi-stage stochastic linear programs for portfolio optimization. Ann Oper Res.
  10. Díaz, A., & Esparcia, C. (2021). Dynamic optimal portfolio choice under time-varying risk aversion. International Economics, 166, 1-22.
  11. Dong He, X., & Zhou, X. (2011). Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment. Management Science, 315-331.
  12. Fabozzi, F. j., & Markowitz , H. m. (2012). Mean-Variance Model for Portfolio Selection. Encyclopedia of Financial Models.
  13. Fotros, M. H., Miri, I., & Miri, A. (2020). Comparison of Portfolio Optimization for Investors at Different Levels of Investors' Risk Aversion in Tehran Stock Exchange with Meta-Heuristic Algorithms. Advances in Mathematical Finance and Applications, 5(1), 1-10.
  14. Fu, C., Lari-Lavassani , a., & li, x. (2010). Dynamic meanvariance portfolio selection with borrowing constraint. Eur J Oper Res.
  15. Gao, j., Li , d., Cui, x., & Wang, s. (2015). Time cardinality constrained mean-variance dynamic portfolio selection and market timing: A stochastic control approach. Automatica.
  16. Georgescu , i. (2012). Possibility theory and the risk.
  17. Green, r., & Burton, H. (1992). When will mean-variance efficient portfolios be well diversified? The J Financ.
  18. Guo, s., Yu, l., Li , x., & Kar, S. (2016). Fuzzy multi-period portfolio selection with different investment horizons. Eur J Oper Res.
  19. hu, y., jin, h., & zhou, x. (2012). Time inconsistent stochastic liner quadratic control. siam j control optim.
  20. Hu, Y., Jin, H., & Zhou, X. (2017). Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium. SIAM Journal on Control and Optimization.
  21. Huang, X. (2012). Mean-variance models for portfolio selection subject to experts’ estimations. Expert Syst Appl.
  22. Kahneman, D., & Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. The Econometric Society.
  23. Kamdem, j., Deffo, c., & Fono , L. (2012). Moments and semi-moments for fuzzy portfolio selection. Insur Math Econ.
  24. Khalili-Damghani , k., Sadi-Nezhad , s., & Tavana , m. (2013). Solving multiperiod project selection problems with fuzzy goal programming based on TOPSIS and a fuzzy preference relation. Inform Sci.
  25. Li, D., & Lung , W. N. (2001). Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation. Mathematical Finance.
  26. Liu, B., & Liu, Y.-K. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems.
  27. Murgoci , B., & Zhou , X. (2014). Mean-variance portfolio optimization with statedependent risk aversion. Math Financ, 1–24.
  28. Pedrycz, W. (2014). Allocation of information granularity in optimization and decision-making models: towards building the foundations of granular computing. Eur J Oper Res.
  29. Rieger, M. o., wang, m., & hens, t. (2011). Prospect theory around the world. NHH Brage.
  30. Rudloff , b., Street, a., & Vallado, D. (2014). Allocation of information granularity in optimization and decision-making models: towards building the foundations of granular computing. Eur J Oper Res.
  31. Statman, M., & Shefrin, H. (1985). Explaining investor preference for cash dividends. Journal of financial economics.
  32. Strotz, R. (1955). Myopia and Inconsistency in Dynamic Utility Maximization. The Review of Economic Studies.
  33. Werner, K., & Zank, H. (2017). A revealed reference point for prospect theory. Economic Theory.
  34. Wu, H., & chen, h. (2015). Nash equilibrium strategy for a multi-period mean–variance portfolio selection problem with regime switching. Economic Modelling, 79-90.
  35. Zhou, J., Li, X., Kar, S., Zhang , G., & Yu , H. (2017). Time consistent fuzzy multi-period rolling portfolio optimization with adaptive risk aversion factor. Journal of Ambient Intelligence and Humanized Computing.
  36. Zhou, J., Li, X., & Pedrycz, W. (2016). Mean-Semi-Entropy Models of Fuzzy Portfolio Selection. IEEE Transactions on Fuzzy Systems.