Previous |  Up |  Next

Article

Keywords:
power utility maximization; risk management; convex constraints
Summary:
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.
References:
[1] Basak, S., Shapiro, A.: Value-at-Risk based risk management: optimal policies and asset prices. Rev. Financ. Stud. 14 (2001), 371-405. DOI 10.1093/rfs/14.2.371
[2] Baxter, M., Rennie, A.: Financial Calculus. Cambridge University Press, Cambridge 1996. Zbl 0858.62094
[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 10.2307/1912196 | Zbl 0205.48902
[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 10.2469/faj.v37.n4.63
[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 10.1016/0304-3932(85)90061-3
[9] Merton, R. C.: Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Econom. Statist. 51 (1969), 3, 247-257. DOI 10.2307/1926560
[10] Nutz, M.: Power utility maximization in constrained exponential Lévy models. Math. Finance 22 (2012), 4, 690-709. DOI 10.1111/j.1467-9965.2011.00480.x | MR 2968281 | Zbl 1272.91102
[11] Nutz, M.: The Bellman equation for power utility maximization with semimartingales. Ann. Appl. Probab. 22 (2012), 1, 363-406. DOI 10.1214/11-AAP776 | MR 2932550 | Zbl 1239.91165
[12] Perold, A., Sharpe, W. F.: Dynamic strategies for asset allocation. Financ. Anal. J. 44 (1988), 1, 16-27. DOI 10.2469/faj.v44.n1.16
[13] Prigent, J.-L.: Portfolio Optimization and Performance Analysis. Chapman and Hall/CRC Financial Mathematics Series, Boca Raton 2007. MR 2317120 | Zbl 1188.91003
[14] Samuelson, P. A.: Lifetime porfolio selection by dynamic stochastic programming. Rev. Econom. Statist. 51 (1969), 3, 239-246. DOI 10.2307/1926559
Partner of
EuDML logo