Dynamic portfolio optimization with risk management and strategy constraints
Kybernetika, Tome 50 (2014) no. 6, pp. 1032-1048
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We investigate the problem of power utility maximization considering risk management and strategy constraints. The aim of this paper is to obtain admissible dynamic portfolio strategies. In case the floor is guaranteed with probability one, we provide two admissible solutions, the option based portfolio insurance in the constrained model, and the alternative method and show that none of the solutions dominate the other. In case the floor is guaranteed partially, we provide one admissible solution, the portfolio insurance with spreads.
We investigate the problem of power utility maximization considering risk management and strategy constraints. The aim of this paper is to obtain admissible dynamic portfolio strategies. In case the floor is guaranteed with probability one, we provide two admissible solutions, the option based portfolio insurance in the constrained model, and the alternative method and show that none of the solutions dominate the other. In case the floor is guaranteed partially, we provide one admissible solution, the portfolio insurance with spreads.
DOI : 10.14736/kyb-2014-6-1032
Classification : 49L20, 60J65, 91G10, 91G20
Keywords: power utility maximization; risk management; convex constraints
@article{10_14736_kyb_2014_6_1032,
     author = {Krommerov\'a, Csilla and Melicher\v{c}{\'\i}k, Igor},
     title = {Dynamic portfolio optimization with risk management and strategy constraints},
     journal = {Kybernetika},
     pages = {1032--1048},
     year = {2014},
     volume = {50},
     number = {6},
     doi = {10.14736/kyb-2014-6-1032},
     mrnumber = {3301784},
     zbl = {06416872},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-6-1032/}
}
TY  - JOUR
AU  - Krommerová, Csilla
AU  - Melicherčík, Igor
TI  - Dynamic portfolio optimization with risk management and strategy constraints
JO  - Kybernetika
PY  - 2014
SP  - 1032
EP  - 1048
VL  - 50
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-6-1032/
DO  - 10.14736/kyb-2014-6-1032
LA  - en
ID  - 10_14736_kyb_2014_6_1032
ER  - 
%0 Journal Article
%A Krommerová, Csilla
%A Melicherčík, Igor
%T Dynamic portfolio optimization with risk management and strategy constraints
%J Kybernetika
%D 2014
%P 1032-1048
%V 50
%N 6
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-6-1032/
%R 10.14736/kyb-2014-6-1032
%G en
%F 10_14736_kyb_2014_6_1032
Krommerová, Csilla; Melicherčík, Igor. Dynamic portfolio optimization with risk management and strategy constraints. Kybernetika, Tome 50 (2014) no. 6, pp. 1032-1048. doi: 10.14736/kyb-2014-6-1032

[1] Basak, S., Shapiro, A.: Value-at-Risk based risk management: optimal policies and asset prices. Rev. Financ. Stud. 14 (2001), 371-405. | DOI

[2] Baxter, M., Rennie, A.: Financial Calculus. Cambridge University Press, Cambridge 1996. | Zbl

[3] Bertrand, P., Prigent, J.-L.: Portfolio insurance strategies: Obpi versus Cppi. University of CERGY Working Paper No. 2001-30; GREQAM Working Paper (December 2001), available at SSRN: http://ssrn.com/abstract=299688

[4] Hakansson, N. H.: Optimal investment and consumption strategies under risk for a class of utility functions. Econometrica 38 (1970), 5, 587-607. | DOI | Zbl

[5] Leland, H. E., Rubinstein, M.: The evolution of portfolio insurance. In: The Evolution of Portfolio Insurance (D. L. Lushin, ed.), Wiley Sons, New York 1976.

[6] Leland, H. E., Rubinstein, M.: Replicating options with positions in stock and cash. Financ. Anal. J. 37 (1981), 4, 63-71. | DOI

[7] Krommerová, Cs.: Expected utility maximization with risk management and strategy constraints. In: Zborník z prvého česko-slovenského workshopu mladých ekonómov (2012), electronic document, pp. 1-21.

[8] Mehra, R., Prescott, E.: The equity premium: a puzzle. J. Monetary Economics 15 (1985), 145-161. | DOI

[9] Merton, R. C.: Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Econom. Statist. 51 (1969), 3, 247-257. | DOI

[10] Nutz, M.: Power utility maximization in constrained exponential Lévy models. Math. Finance 22 (2012), 4, 690-709. | DOI | MR | Zbl

[11] Nutz, M.: The Bellman equation for power utility maximization with semimartingales. Ann. Appl. Probab. 22 (2012), 1, 363-406. | DOI | MR | Zbl

[12] Perold, A., Sharpe, W. F.: Dynamic strategies for asset allocation. Financ. Anal. J. 44 (1988), 1, 16-27. | DOI

[13] Prigent, J.-L.: Portfolio Optimization and Performance Analysis. Chapman and Hall/CRC Financial Mathematics Series, Boca Raton 2007. | MR | Zbl

[14] Samuelson, P. A.: Lifetime porfolio selection by dynamic stochastic programming. Rev. Econom. Statist. 51 (1969), 3, 239-246. | DOI

Cité par Sources :