Article
Full entry |
PDF
(1.2 MB)
Feedback
PDF
(1.2 MB)
Feedback
Keywords:
multistage risk premium; utility function; portfolio optimization; multistage stochastic programming
multistage risk premium; utility function; portfolio optimization; multistage stochastic programming
Summary:
This paper deals with a multistage stochastic programming portfolio selection problem with a new type of risk premium constraints. These risk premiums are constructed on the multistage scenario tree. Two ways of the construction are introduced and compared. The risk premiums are incorporated in the multistage stochastic programming portfolio selection problem. The problem maximizes the multivariate (multiperiod) utility function under condition that the multistage risk premiums are smaller than a prescribed level. The problem does not assume any separability of the multiperiod utility function. The performance of the suggested models is demonstrated for several kinds of multiperiod utility functions and several formulations of the multistage risk premium constraints. In all cases, including the risk premium constraints avoids the riskier positions.
References:
[1] Ambarish, R., Kallberg, J. G.: Multivariate risk premiums. Theory Decision 22 (1987), 77-96. DOI 10.1007/bf00125658 | MR 0874520
[2] Branda, M., Kopa, M.: Dea models equivalent to general n-th order stochastic dominance efficiency tests. Oper. Res. Lett.44 (2016), 285-289. DOI 10.1016/j.orl.2016.02.007 | MR 3466671
[3] Duncan, G. T.: A matrix measure of multivariate local risk aversion. Econometrica 45 (1977), 895-903. DOI 10.2307/1912680 | MR 0496493 | Zbl 0367.90017
[4] Dupačová, J., Kopa, M.: Robustness of optimal portfolios under risk and stochastic dominance constraints. Europ. J. Oper. Res. 234 (2014), 2, 434-441. DOI 10.1016/j.ejor.2013.06.018 | MR 3144732
[5] Dupačová, J., Hurt, J., Štěpán, J.: Stochastic Modeling in Economics and Finance. Kluwer, 2002. MR 2008457
[6] Høyland, K., Kaut, M., Wallace, S. W.: A heuristic for moment-matching scenario generation. Comput. Optim. Appl. 24 (2003), 2-3, 169-185. DOI 10.1023/a:1021853807313 | MR 1969151 | Zbl 1094.90579
[7] French, K. R.: 6 portfolios formed on size and book-to-market (2 $\times$ 3).
[8] Kihlstrom, R. E., Mirman, L. J.: Risk aversion with many commodities. J. Econom. Theory 8 (1974), 361-388. DOI 10.1016/0022-0531(74)90091-x | MR 0496471
[9] Kopa, M., Moriggia, V., Vitali, S.: Individual optimal pension allocation under stochastic dominance constraints. Ann. Oper. Res. 260 (2018), 1-2, 255-291. DOI 10.1007/s10479-016-2387-x | MR 3741562
[10] Post, T., Kopa, M.: Portfolio choice based on third-degree stochastic dominance. Management Sci. 63 (2017), 10, 3381-3392. DOI 10.1287/mnsc.2016.2506
[11] Post, T., Fang, Y., Kopa, M.: Linear tests for decreasing absolute risk aversion stochastic dominance. Management Sci. 61 (2015), 7, 1615-1629. DOI 10.1287/mnsc.2014.1960
[12] Pratt, J. W.: Risk aversion in the small and the large. Econometrica 32 (1064), 122-136. DOI 10.2307/1913738
[13] Richard, S. F.: Multivariate risk aversion, utility dependence and separable utility functions. Management Sci. 21 (1975), 12-21. DOI 10.1287/mnsc.22.1.12 | MR 0436907
[14] Rockafellar, R. T., Uryasev, S.: Conditional value-at-risk for general loss distributions. J. Banking Finance 26 (2002), 1443-1471. DOI 10.1016/s0378-4266(02)00271-6
[15] Shapiro, A., Dentcheva, D., Ruszczynski, A.: Lectures on Stochastic Programming. SIAM, Philadelphia 2009. DOI 10.1137/1.9780898718751 | MR 2562798
[16] Šmíd, M., Kopa, M.: Dynamic model of market with uninformed market maker. Kybernetika 53 (2017), 5, 922-958. DOI 10.14736/kyb-2017-5-0922
[17] Vitali, S., Moriggia, V., Kopa, M.: Optimal pension fund composition for an italian private pension plan sponsor. Comput. Management Sci. 14 (2017), 1, 135-160. DOI 10.1137/1.9780898718751 | MR 3599603
Search
Partner of
