Kybernetika 50 no. 6, 1032-1048, 2014

Dynamic portfolio optimization with risk management and strategy constraints

Csilla Krommerová and Igor MelicherčíkDOI: 10.14736/kyb-2014-6-1032

Abstract:

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.

Keywords:

power utility maximization, risk management, convex constraints

Classification:

49L20, 60J65, 91G10, 91G20

paper.pdf

References:

  1. S. Basak and A. Shapiro: Value-at-Risk based risk management: optimal policies and asset prices. Rev. Financ. Stud. 14 (2001), 371-405.   CrossRef
  2. M. Baxter and A. Rennie: Financial Calculus. Cambridge University Press, Cambridge 1996.   CrossRef
  3. P. Bertrand and J.-L. Prigent: Portfolio insurance strategies: Obpi versus Cppi. University of CERGY Working Paper No. 2001-30; GREQAM Working Paper (December 2001), available at SSRN: \url{http://ssrn.com/abstract=299688}.   CrossRef
  4. N. H. Hakansson: Optimal investment and consumption strategies under risk for a class of utility functions. Econometrica 38 (1970), 5, 587-607.   CrossRef
  5. H. E. Leland and M. Rubinstein: The evolution of portfolio insurance. In: The Evolution of Portfolio Insurance (D. L. Lushin, ed.), Wiley Sons, New York 1976.   CrossRef
  6. H. E. Leland and M. Rubinstein: Replicating options with positions in stock and cash. Financ. Anal. J. 37 (1981), 4, 63-71.   CrossRef
  7. Cs. Krommerová: Expected utility maximization with risk management and strategy constraints. In: Zborník z prvého česko-slovenského workshopu mladých ekonómov (2012), electronic document, pp. 1-21.   CrossRef
  8. R. Mehra and E. Prescott: The equity premium: a puzzle. J. Monetary Economics 15 (1985), 145-161.   CrossRef
  9. R. C. Merton: Lifetime portfolio selection under uncertainty: the continuous-time case. Rev. Econom. Statist. 51 (1969), 3, 247-257.   CrossRef
  10. M. Nutz: Power utility maximization in constrained exponential Lévy models. Math. Finance 22 (2012), 4, 690-709.   CrossRef
  11. M. Nutz: The Bellman equation for power utility maximization with semimartingales. Ann. Appl. Probab. 22 (2012), 1, 363-406.   CrossRef
  12. A. Perold and W. F. Sharpe: Dynamic strategies for asset allocation. Financ. Anal. J. 44 (1988), 1, 16-27.   CrossRef
  13. J.-L. Prigent: Portfolio Optimization and Performance Analysis. Chapman and Hall/CRC Financial Mathematics Series, Boca Raton 2007.   CrossRef
  14. P. A. Samuelson: Lifetime porfolio selection by dynamic stochastic programming. Rev. Econom. Statist. 51 (1969), 3, 239-246.   CrossRef