nach oben

Erschienen in:

2019 | OriginalPaper | Buchkapitel

10. Optimal Investment

verfasst von : Ernst Eberlein, Jan Kallsen

Erschienen in: Mathematical Finance

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

As an investor in a securities market you have to decide how to arrange your portfolio. In this chapter we consider the natural situation that you want to maximise your profits. It is not entirely obvious how to formalise this goal because the payoff of investments is typically random.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Markets, Strategies, Arbitrage

Nächstes Kapitel Arbitrage-Based Valuation and Hedging of Derivatives

Nur mit Berechtigung zugänglich

I. Bajeux-Besnainou, R. Portait, Dynamic asset allocation in a mean-variance framework. Manag. Sci. 44(11), S79–S95 (1998)MATHCrossRef

13.

S. Basak, G. Chabakauri, Dynamic mean-variance asset allocation. Rev. Financ. Stud. 23(8), 2970–3016 (2010)CrossRef

21.

F. Bellini, M. Frittelli, On the existence of minimax martingale measures. Math. Finance 12(1), 1–21 (2002)MathSciNetMATHCrossRef

22.

G. Benedetti, L. Campi, J. Kallsen, J. Muhle-Karbe, On the existence of shadow prices. Finance Stochast. 17(4), 801–818 (2013)MathSciNetMATHCrossRef

24.

S. Biagini, M. Frittelli, A unified framework for utility maximization problems: an Orlicz space approach. Ann. Appl. Probab. 18(3), 929–966 (2008)MathSciNetMATHCrossRef

27.

J.-M. Bismut, Growth and optimal intertemporal allocation of risks. J. Econom. Theory 10(2), 239–257 (1975)MathSciNetMATHCrossRef

29.

T. Björk, Arbitrage Theory in Continuous Time, 3rd edn. (Oxford Univ. Press, Oxford, 2009)MATH

35.

T. Björk, A. Murgoci, X. Zhou, Mean-variance portfolio optimization with state-dependent risk aversion. Math. Finance 24(1), 1–24 (2014)MathSciNetMATHCrossRef

55.

A. Černý, J. Kallsen, On the structure of general mean-variance hedging strategies. Ann. Probab. 35(4), 1479–1531 (2007)MathSciNetMATHCrossRef

65.

J. Cvitanić, I. Karatzas, Hedging and portfolio optimization under transaction costs: a martingale approach. Math. Finance 6(2), 133–165 (1996)MathSciNetMATHCrossRef

66.

C. Czichowsky, Time-consistent mean-variance portfolio selection in discrete and continuous time. Finance Stochast. 17(2), 227–271 (2013)MathSciNetMATHCrossRef

67.

C. Czichowsky, W. Schachermayer, Duality theory for portfolio optimisation under transaction costs. Ann. Appl. Probab. 26(3), 1888–1941 (2016)MathSciNetMATHCrossRef

68.

C. Czichowsky, J. Muhle-Karbe, W. Schachermayer, Transaction costs, shadow prices, and duality in discrete time. SIAM J. Financial Math. 5(1), 258–277 (2014)MathSciNetMATHCrossRef

98.

R. Elliott, Stochastic Calculus and Applications (Springer, New York, 1982)MATH

125.

T. Goll, J. Kallsen, Optimal portfolios for logarithmic utility. Stoch. Process. Appl. 89(1), 31–48 (2000)MathSciNetMATHCrossRef

126.

T. Goll, J. Kallsen, A complete explicit solution to the log-optimal portfolio problem. Ann. Appl. Probab. 13(2), 774–799 (2003)MathSciNetMATHCrossRef

127.

T. Goll, L. Rüschendorf, Minimax and minimal distance martingale measures and their relationship to portfolio optimization. Finance Stochast. 5(4), 557–581 (2001)MathSciNetMATHCrossRef

136.

H. He, N. Pearson, Consumption and portfolio policies with incomplete markets and short-sale constraints: the finite-dimensional case. Math. Finance 1(3), 1–10 (1991)MathSciNetMATHCrossRef

137.

H. He, N. Pearson, Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case. J. Econom. Theory 54(2), 259–304 (1991)MathSciNetMATHCrossRef

146.

Y. Hu, P. Imkeller, M. Müller, Utility maximization in incomplete markets. Ann. Appl. Probab. 15(3), 1691–1712 (2005)MathSciNetMATHCrossRef

148.

F. Hubalek, J. Kallsen, L. Krawczyk, Variance-optimal hedging for processes with stationary independent increments. Ann. Appl. Probab. 16(2), 853–885 (2006)MathSciNetMATHCrossRef

153.

J. Jacod, P. Protter, Probability Essentials, 2nd edn. (Springer, Berlin, 2004)MATHCrossRef

154.

J. Jacod, A. Shiryaev, Limit Theorems for Stochastic Processes, 2nd edn. (Springer, Berlin, 2003)MATHCrossRef

161.

E. Jouini, H. Kallal, Martingales and arbitrage in securities markets with transaction costs. J. Econom. Theory 66(1), 178–197 (1995)MathSciNetMATHCrossRef

162.

D. Kahneman, Thinking, Fast and Slow (Farrar, Straus and Giroux, New York, 2011)

163.

J. Kallsen, Semimartingale Modelling in Finance. PhD thesis, University of Freiburg, 1998

164.

J. Kallsen, A utility maximization approach to hedging in incomplete markets. Math. Methods Oper. Res. 50(2), 321–338 (1999)MathSciNetMATHCrossRef

165.

J. Kallsen, Optimal portfolios for exponential Lévy processes. Math. Methods Oper. Res. 51(3), 357–374 (2000)MathSciNetCrossRef

167.

J. Kallsen, Utility-based derivative pricing in incomplete markets, in Mathematical Finance—Bachelier Congress 2000, ed. by H. Geman, D. Madan, S. Pliska, T. Vorst (Springer, Berlin, 2002), pp. 313–338CrossRef

173.

J. Kallsen, J. Muhle-Karbe, On using shadow prices in portfolio optimization with transaction costs. Ann. Appl. Probab. 20(4), 1341–1358 (2010)MathSciNetMATHCrossRef

174.

J. Kallsen, J. Muhle-Karbe. Utility maximization in models with conditionally independent increments. Ann. Appl. Probab. 20(6), 2162–2177 (2010)MathSciNetMATHCrossRef

175.

J. Kallsen, J. Muhle-Karbe, Existence of shadow prices in finite probability spaces. Math. Methods Oper. Res. 73(2), 251–262 (2011)MathSciNetMATHCrossRef

176.

J. Kallsen, J. Muhle-Karbe, Option pricing and hedging with small transaction costs. Math. Finance 25(4), 702–723 (2015)MathSciNetMATHCrossRef

177.

J. Kallsen, J. Muhle-Karbe, The general structure of optimal investment and consumption with small transaction costs. Math. Finance 27(3), 659–703 (2017)MathSciNetMATHCrossRef

180.

J. Kallsen, T. Rheinländer, Asymptotic utility-based pricing and hedging for exponential utility. Stat. Decis. 28(1), 17–36 (2011)MathSciNetMATH

187.

I. Karatzas, S. Shreve, Methods of Mathematical Finance (Springer, Berlin, 1998)MATHCrossRef

188.

I. Karatzas, G. Žitković, Optimal consumption from investment and random endowment in incomplete semimartingale markets. Ann. Probab. 31(4), 1821–1858 (2003)MathSciNetMATHCrossRef

189.

I. Karatzas, J. Lehoczky, S. Shreve, G. Xu, Martingale and duality methods for utility maximization in an incomplete market. SIAM J. Control Optim. 29(3), 702–730 (1991)MathSciNetMATHCrossRef

197.

D. Kramkov, W. Schachermayer, The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9(3), 904–950 (1999)MathSciNetMATHCrossRef

205.

J. Laurent, H. Pham, Dynamic programming and mean-variance hedging. Finance Stochast. 3(1), 83–110 (1999)MathSciNetMATHCrossRef

208.

M. Loewenstein, On optimal portfolio trading strategies for an investor facing transactions costs in a continuous trading market. J. Math. Econom. 33(2), 209–228 (2000)MathSciNetMATHCrossRef

213.

H. Markowitz, Portfolio selection. J. Finance 7(1), 77–91 (1952)

214.

R. Martin, Optimal trading under proportional transaction costs. Risk, 54–59 (2014)

215.

R. Martin, T. Schöneborn, Mean reversion pays, but costs. arXiv preprint arXiv:1103.4934 (2011)

217.

R. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case. Rev. Econ. Stat. 51(3), 247–257 (1969)CrossRef

218.

R. Merton, Optimum consumption and portfolio rules in a continuous-time model. J. Econom. Theory 3(4), 373–413 (1971)MathSciNetMATHCrossRef

222.

J. Mossin, Optimal multiperiod portfolio policies. J. Bus. 41(2), 215–229 (1968)CrossRef

225.

M. Nutz, Power utility maximization in constrained exponential Lévy models. Math. Finance 22(4), 690–709 (2012)MathSciNetMATHCrossRef

226.

B. Øksendal, Stochastic Differential Equations, 6th edn. (Springer, Berlin, 2003)MATHCrossRef

227.

B. Øksendal, A. Sulem, Applied Stochastic Control of Jump Diffusions, 2nd edn. (Springer, Berlin, 2007)MATHCrossRef

234.

H. Pham, Continuous-Time Stochastic Control and Optimization with Financial Applications (Springer, Berlin, 2009)MATHCrossRef

235.

H. Pham, T. Rheinländer, M. Schweizer, Mean-variance hedging for continuous processes: new proofs and examples. Finance Stochast. 2(2), 173–198 (1998)MathSciNetMATHCrossRef

236.

E. Platen, D. Heath , A Benchmark Approach to Quantitative Finance (Springer, Berlin, 2006)MATHCrossRef

243.

T. Rheinländer, G. Steiger, Utility indifference hedging with exponential additive processes. Asia-Pac. Financ. Mark. 17(2), 151–169 (2010)MATHCrossRef

244.

H. Richardson, A minimum variance result in continuous trading portfolio optimization. Manag. Sci. 35(9), 1045–1055 (1989)MathSciNetMATHCrossRef

248.

C. Rogers, The relaxed investor and parameter uncertainty. Finance Stochast. 5(2), 131–154 (2001)MathSciNetMATHCrossRef

250.

C. Rogers, Optimal Investment (Springer, Heidelberg, 2013)MATHCrossRef

253.

R. Rouge, N. El Karoui, Pricing via utility maximization and entropy. Math. Finance 10(2), 259–276 (2000)MathSciNetMATHCrossRef

258.

P. Samuelson, Lifetime portfolio selection by dynamic stochastic programming. Rev. Econ. Stat. 51, 239–246 (1969)CrossRef

260.

W. Schachermayer, M. Sîrbu, E. Taflin, In which financial markets do mutual fund theorems hold true? Finance Stochast. 13(1), 49–77 (2009)MathSciNetMATHCrossRef

266.

M. Schweizer, Risk-minimality and orthogonality of martingales. Stochastics Stochastics Rep. 30(2), 123–131 (1990)MathSciNetMATHCrossRef

267.

M. Schweizer, Option hedging for semimartingales. Stoch. Process. Appl. 37(2), 339–363 (1991)MathSciNetMATHCrossRef

268.

M. Schweizer, Approximating random variables by stochastic integrals. Ann. Probab. 22(3), 1536–1575 (1994)MathSciNetMATHCrossRef

269.

M. Schweizer, Approximation pricing and the variance-optimal martingale measure. Ann. Probab. 24(1), 206–236 (1996)MathSciNetMATHCrossRef

273.

R. Shiller, Online data—Robert Shiller. url: http://www.econ.yale.edu/\~shiller/data.htm. Accessed: 1 May 2018

287.

N. Touzi, Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE (Springer, New York, 2013)MATHCrossRef

290.

J. von Neumann, O. Morgenstern, Theory of Games and Economic Behavior, 2nd edn. (Princeton Univ. Press, Princeton, 1947)MATH

Titel: Optimal Investment
verfasst von: Ernst Eberlein
Jan Kallsen
Verlag: Springer International Publishing
Buch: Mathematical Finance
Print ISBN: 978-3-030-26105-4

Electronic ISBN: 978-3-030-26106-1

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-26106-1_10