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UTILITY MAXIMIZATION IN AFFINE STOCHASTIC VOLATILITY MODELS

JAN KALLSEN

Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Westring 383, 24118 Kiel, Germany

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and

JOHANNES MUHLE-KARBE

Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria

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https://doi.org/10.1142/S0219024910005851Cited by:37 (Source: Crossref)

Abstract

We consider the classical problem of maximizing expected utility from terminal wealth. With the help of a martingale criterion explicit solutions are derived for power utility in a number of affine stochastic volatility models.

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References

O. Barndorff-Nielsen and N. Shephard, Journal of the Royal Statistical Society, Series B 63, 167 (2001). Crossref, Google Scholar
F. Bellini and M. Frittelli, Mathematical Finance 12, 1 (2002). Crossref, Web of Science, Google Scholar
F. Benth, K. Karlsen and K. Reikvam, Finance & Stochastics 5, 275 (2001). Crossref, Google Scholar
F. Benth, K. Karlsen and K. Reikvam, Mathematical Finance 13, 215 (2003). Crossref, Web of Science, Google Scholar
I. Bronstein, K. Semendjajew, G. Musiol and M. Mühlig, Taschenbuch der Mathematik, expanded edition (Harri Deutsch, Thun, 2001) . Google Scholar
P. Carret al., Mathematical Finance 13, 345 (2003). Crossref, Web of Science, Google Scholar
A. Černý and J. Kallsen, The Annals of Probability 35, 1479 (2007). Crossref, Web of Science, Google Scholar
R. Cont and P. Tankov , Financial Modelling with Jump Processes ( Chapman & Hall/CRC , Boca Raton , 2004 ) . Google Scholar
D. Filipović, Stochastic Processes and their Applications 115, 639 (2005). Crossref, Web of Science, Google Scholar
N. Framstad, B. Øksendal and A. Sulem, Optimal consumption and portfolio in a jump diffusion market, Technical Report 5, Norges handelshø yskole. Institutt for foretaksø konomi (1999) . Google Scholar
T. Goll and J. Kallsen, Stochastic Processes and their Applications 89, 31 (2000). Crossref, Web of Science, Google Scholar
T. Goll and J. Kallsen, The Annals of Applied Probability 13, 774 (2003). Web of Science, Google Scholar
T. Goll and L. Rüschendorf, Finance & Stochastics 5, 557 (2001). Crossref, Google Scholar
S. Heston, The Review of Financial Studies 6, 327 (1993). Crossref, Web of Science, Google Scholar
D. Hobson, Mathematical Finance 14, 537 (2004). Crossref, Web of Science, Google Scholar
T. Hurd, Statistics & Decisions 22, 225 (2004). Crossref, Google Scholar
J. Jacod and A. Shiryaev , Limit Theorems for Stochastic Processes , 2nd edn. ( Springer , Berlin , 2003 ) . Crossref, Google Scholar
J. Kallsen, Mathematical Methods of Operations Research 51, 357 (2000). Crossref, Web of Science, Google Scholar
J. Kallsen, Utility-based derivative pricing in incomplete markets, Mathematical Finance — Bachelier Congress 2000, eds. H. Gemanet al. (Springer, Berlin, 2002) pp. 313–338. Google Scholar
J. Kallsen, Theory of Probability and Its Applications 48, 152 (2004). Crossref, Web of Science, Google Scholar
J. Kallsen, From Stochastic Calculus to Mathematical Finance, eds. Yu. Kabanov, R. Liptser and J. Stoyanov (Springer, Berlin, 2006) pp. 343–368. Crossref, Google Scholar
J. Kallsen and C. Kühn, Finance & Stochastics 8, 261 (2004). Crossref, Web of Science, Google Scholar
J. Kallsen and J. Muhle-Karbe, Stochastic Processes and Their Applications 120, 163 (2010). Crossref, Web of Science, Google Scholar
I. Karatzas and S. Shreve , Methods of Mathematical Finance ( Springer , Berlin , 1998 ) . Crossref, Google Scholar
R. Korn , Optimal Portfolios: Stochastic Models for Optimal Investment and Risk Management in Continuous Time ( World Scientific , Singapore , 1997 ) . Crossref, Google Scholar
R. Korn and H. Kraft, Mathematical Finance 14, 403 (2004). Crossref, Web of Science, Google Scholar
H. Kraft, Quantitative Finance 5, 303 (2005). Crossref, Web of Science, Google Scholar
D. Kramkov and W. Schachermayer, The Annals of Applied Probability 9, 904 (1999). Web of Science, Google Scholar
D. Kramkov and M. Sîrbu, The Annals of Applied Probability 16, 2140 (2006). Crossref, Web of Science, Google Scholar
D. Kramkov and M. Sîrbu, Stochastic Processes and their Applications 117, 1606 (2007). Crossref, Web of Science, Google Scholar
J. Liu, The Review of Financial Studies 20, 1 (2007). Crossref, Web of Science, Google Scholar
J. Muhle-Karbe, On Utility-Based Investment, Pricing and Hedging in Incomplete Markets. Ph.D. dissertation (TU München), München, 2009 . Google Scholar
K. Sato , Lévy Processes and Infinitely Divisible Distributions ( Cambridge University Press , Cambridge , 1999 ) . Google Scholar