Abstract
A variant of the mean-variance problem is studied where the conditional variances of the gain in the last periods are minimized by a backward iteration.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
E.J. Elton and M.J. GruberFinance as a Dynamic ProcessEnglewood cliffs: Prentice Hall, 1975.
R.C. Dalang, A. Morton and W. WillingerEquivalent martingale measures and no-arbitrage in stochastic securities market modelsStochastics and Stochastic Reports 29 (1990), 185–201,.
P. GranditsThe p-optimal martingale measure and its asymptotic relation with the minimal-entropy martingale measure“Bernoulli 5 (1999), 225–248.
R.R. Grauer and N.H. HakanssonOn the use of mean-variance and quadratic approximations in implementing dynamic investment policiesManag. sci.39 (1993), 856–871.
W. Härdle and C.M. HafnerDiscrete time option pricing with flexible volatility estimationFinance Stochast.4 (2000), 189–208.
J. Jacod and A. N. ShiryaevLocal martingales and the fundamental asset pricing theorems in the discrete-time caseFinance Stochast. 3 (1998), 259–273.
D. Lamberton, H. Pham and M. SchweizerLocal risk-minimization under transaction costs Math. Oper. Res. 23 (1998), 585–612.
C. MaA discrete-time intertemporal asset pricing modelMathematical Finance 8 (1998), 249–275.
H.M. MarkowitzPortfolio selection J. of Fin.7 (1952), 77–91.
J.MossinOptimal multiperiod portfolio policies J. of Bus., 41(1068), 215–229.
S.R. PliskaIntroduction to Mathematical FinanceBlackwell publisher, Malden, USA, Oxford, UK, 1997.
L.C.G. RogersEquivalent martingale measures and no-arbitrageStochastics and Stochastic Reports 51 (1994), 41–49.
P.A. SamuelsonLifetime portfolio selection by dynamic stochastic programmingRev. Econ. Stat.51 (1969), 239–246.
M. SchälOn quadratic cost criteria for option hedgingMath. Oper. Res. 19 (1994), 121–131.
M. SchälMartingale measures and hedging for discrete-time financial marketsMath. Oper. Res. 24 (1999), 509–528.
M. SchälPortfolio optimization and martingale measuresMathematical Finance 10 (2000), 289–304.
M. SchälPrice systems constructed by optimal dynamic portfoliosMath. Meth. Oper. Res. 51 (2000), 375–397.
M. SchälMarkov decision theory in finance and dynamic options. Tobe published in Shwartz A, Feinberg E (eds.) Markov decision processes, (2000) Kluwer.
M. SchweizerApproximating random variables by stochastic integralsAnn. Probab. 22 (1994), 1536–1575.
M. SchweizerVariance-optimal hedging in discrete timeMath. Oper. Res. 20 (1995), 1–32.
M. SchweizerApproximation pricing and the variance-optimal martingale measureAnn. Probability24 (1996), 206–236.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Basel AG
About this paper
Cite this paper
Schäl, M. (2001). Local optimality in the multi-dimensional multi-period mean-variance portfolio problem. In: Kohlmann, M., Tang, S. (eds) Mathematical Finance. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8291-0_29
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8291-0_29
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9506-4
Online ISBN: 978-3-0348-8291-0
eBook Packages: Springer Book Archive