Abstract
The possibilistic mean – variance (MV) model enables the practitioners to model the imprecise probability and integrate their subjective judgements into the portfolio selection problem. Thus, it is a considerable alternative of the Markowitz’s traditional MV model. In this study, we analyze this model mathematically under the assumption that the possibility distributions of asset returns are given with the triangular fuzzy numbers. Within this scope, the portfolios which maximize the utility or performance are derived analytically. Furthermore, we illustrate the structure of its efficient frontier with examples.
Keywords
Portfolio selection possibility theory triangular fuzzy numbers mean -variance model efficient frontier linear programming
References
- Markowitz, H., Portfolio selection, The Journal of Finance, 7, 1, 77-91, (1952).
- Goldfarb, D. ve Iyengar, G., Robust portfolio selection problems, Mathematics of Operations Research, 28, 1, 1-38, (2003).
- Breuer, T., Providing against the worst: risk capital for worst case scenarios, Managerial Finance, 32, 9, 716–730, (2006).
- Garlappi, L., Uppal, R. ve Wang, T., Portfolio selection with parameter and model uncertainty: A multi-prior approach, The Review of Financial Studies, 20, 1, 41-81, (2006).
- Tütüncü, R. H. ve Koenig, M., Robust asset allocation, Annals of Operations Research, 132, 1-4, 157-187, (2004).
- Huang, D., Zhu, S., Fabozzi, F. J. ve Fukushima, M., Portfolio selection under distributional uncertainty: a relative robust CVaR approach, European Journal of Operational Research, 203, 1, 185-194, (2010).
- Bhattacharyya, R., Kar, S. ve Majumder, D. D., Fuzzy mean–variance–skewness portfolio selection models by interval analysis, Computers & Mathematics with Applications, 61, 1, 126-137, (2011).
- Duran, A. ve Bommarito, M. J., A profitable trading and risk management strategy despite transaction costs, Quantitative Finance, 11, 6, 829-848, (2011).
- Jorion, P., Bayes-Stein estimation for portfolio analysis, The Journal of Financial and Quantitative Analysis, 21, 3, 279-292, (1986).
- Carlsson, C., Fullér, R. ve Majlender, P., A possibilistic approach to selecting portfolios with highest utility score, Fuzzy Sets and Systems, 131, 1, 13-21, (2002).
- Taş, O., Kahraman, C. ve Güran, C. B., A Scenario Based Linear Fuzzy Approach in Portfolio Selection Problem: Application in the Istanbul Stock Exchange, Journal of Multiple-Valued Logic & Soft Computing, 26, 3-5, 269-294, (2016).
- Zhang, W. G., Zhang, X. L. ve Xiao, W. L., Portfolio selection under possibilistic mean–variance utility and a SMO algorithm, European Journal of Operational Research, 197, 2, 693-700, (2009).
- Dubois, D., Possibility theory and statistical reasoning, Computational Statistics & Data Analysis, 51, 1, 47-69, (2006).
- Klir, G. ve Yuan, B., Fuzzy sets and fuzzy logic, Prentice Hall, (1995).
- Zimmermann, H. J., Fuzzy set theory and its applications, Springer, (2001).
- Roman-Flores, H., Barros, L. C. ve Bassanezi, R. C., A note on Zadeh's extensions, Fuzzy Sets and Systems, 117, 3, 327-331, (2001).
- Carlsson, C. ve Fuller, R., On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems, 122, 315-326, (2001).
- Deb, K., Multi-objective optimization using evolutionary algorithms, John Wiley & Sons, (2001).
- Bajalinov, E. B., Linear-fractional programming theory, methods, applications and software, Springer, (2013).
- Bykadorov, I. A., On quasiconvexity in fractional programming in Komlosi, S., Rapcsak, T. ve Schaible, S., Generalized Convexity, Springer, (1994).
- Biswas, A., Verma, S., ve Ojha, D. B., Optimality and Convexity Theorems for Linear Fractional Programming Problem, International Journal of Computational and Applied Mathematics, 12, 3, 911-916, (2017).
Abstract
Olabilirlik ortalama – varyans (OV) modeli, kesin olmayan olasılığın modellenebilmesine ve kişisel yargıların ve beklentilerin portföy seçimi problemine entegre edilebilmesine imkan verir. Bu nedenle Markovitz’in geleneksel OV modelinin dikkate değer bir alternatifidir. Bu çalışmada varlık getirilerinin olabilirlik dağılımlarının üçgensel bulanık sayılar ile verildiği varsayımı altında bu modelin matematiksel analizi yapılmıştır. Bu kapsamda performansı ya da faydayı maksimum yapan portföyler analitik olarak elde edilmiştir. Ayrıca bu modelin verdiği etkin sınırın yapısı örnekler ile açıklanmıştır.
Keywords
Portföy seçimi olabilirlik teorisi üçgensel bulanık sayılar ortalama – varyans modeli etkin sınır lineer programlama
References
- Markowitz, H., Portfolio selection, The Journal of Finance, 7, 1, 77-91, (1952).
- Goldfarb, D. ve Iyengar, G., Robust portfolio selection problems, Mathematics of Operations Research, 28, 1, 1-38, (2003).
- Breuer, T., Providing against the worst: risk capital for worst case scenarios, Managerial Finance, 32, 9, 716–730, (2006).
- Garlappi, L., Uppal, R. ve Wang, T., Portfolio selection with parameter and model uncertainty: A multi-prior approach, The Review of Financial Studies, 20, 1, 41-81, (2006).
- Tütüncü, R. H. ve Koenig, M., Robust asset allocation, Annals of Operations Research, 132, 1-4, 157-187, (2004).
- Huang, D., Zhu, S., Fabozzi, F. J. ve Fukushima, M., Portfolio selection under distributional uncertainty: a relative robust CVaR approach, European Journal of Operational Research, 203, 1, 185-194, (2010).
- Bhattacharyya, R., Kar, S. ve Majumder, D. D., Fuzzy mean–variance–skewness portfolio selection models by interval analysis, Computers & Mathematics with Applications, 61, 1, 126-137, (2011).
- Duran, A. ve Bommarito, M. J., A profitable trading and risk management strategy despite transaction costs, Quantitative Finance, 11, 6, 829-848, (2011).
- Jorion, P., Bayes-Stein estimation for portfolio analysis, The Journal of Financial and Quantitative Analysis, 21, 3, 279-292, (1986).
- Carlsson, C., Fullér, R. ve Majlender, P., A possibilistic approach to selecting portfolios with highest utility score, Fuzzy Sets and Systems, 131, 1, 13-21, (2002).
- Taş, O., Kahraman, C. ve Güran, C. B., A Scenario Based Linear Fuzzy Approach in Portfolio Selection Problem: Application in the Istanbul Stock Exchange, Journal of Multiple-Valued Logic & Soft Computing, 26, 3-5, 269-294, (2016).
- Zhang, W. G., Zhang, X. L. ve Xiao, W. L., Portfolio selection under possibilistic mean–variance utility and a SMO algorithm, European Journal of Operational Research, 197, 2, 693-700, (2009).
- Dubois, D., Possibility theory and statistical reasoning, Computational Statistics & Data Analysis, 51, 1, 47-69, (2006).
- Klir, G. ve Yuan, B., Fuzzy sets and fuzzy logic, Prentice Hall, (1995).
- Zimmermann, H. J., Fuzzy set theory and its applications, Springer, (2001).
- Roman-Flores, H., Barros, L. C. ve Bassanezi, R. C., A note on Zadeh's extensions, Fuzzy Sets and Systems, 117, 3, 327-331, (2001).
- Carlsson, C. ve Fuller, R., On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems, 122, 315-326, (2001).
- Deb, K., Multi-objective optimization using evolutionary algorithms, John Wiley & Sons, (2001).
- Bajalinov, E. B., Linear-fractional programming theory, methods, applications and software, Springer, (2013).
- Bykadorov, I. A., On quasiconvexity in fractional programming in Komlosi, S., Rapcsak, T. ve Schaible, S., Generalized Convexity, Springer, (1994).
- Biswas, A., Verma, S., ve Ojha, D. B., Optimality and Convexity Theorems for Linear Fractional Programming Problem, International Journal of Computational and Applied Mathematics, 12, 3, 911-916, (2017).
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | January 10, 2020 |
| Submission Date | July 26, 2019 |
| Published in Issue | Year 2020 Volume: 22 Issue: 1 |