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Explicit solutions of some utility maximization problems in incomplete markets

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  • Tehranchi, Michael

Abstract

In this note we prove Hölder-type inequalities for products of certain functionals of correlated Brownian motions. These estimates are applied to the study of optimal portfolio choice in incomplete markets when the investor's utility is of the form U(X,Y)=g(X)h(Y), where X is the investor's wealth and Y is a random factor not perfectly correlated with the market. Explicit solutions are found when g is the exponential, power, or logarithmic utility function.

Suggested Citation

  • Tehranchi, Michael, 2004. "Explicit solutions of some utility maximization problems in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 109-125, November.
    • Handle: RePEc:eee:spapps:v:114:y:2004:i:1:p:109-125
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    References listed on IDEAS

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    1. David Hobson, 2004. "STOCHASTIC VOLATILITY MODELS, CORRELATION, AND THE q‐OPTIMAL MEASURE," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 537-556, October.
    2. (**), Hui Wang & Jaksa Cvitanic & (*), Walter Schachermayer, 2001. "Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 5(2), pages 259-272.
    3. Thaleia Zariphopoulou, 2001. "A solution approach to valuation with unhedgeable risks," Finance and Stochastics, Springer, vol. 5(1), pages 61-82.
    4. Jaksa Cvitanić & Walter Schachermayer & Hui Wang, 2017. "Erratum to: Utility maximization in incomplete markets with random endowment," Finance and Stochastics, Springer, vol. 21(3), pages 867-872, July.
    5. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    6. Marek Musiela & Thaleia Zariphopoulou, 2004. "An example of indifference prices under exponential preferences," Finance and Stochastics, Springer, vol. 8(2), pages 229-239, May.
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    Cited by:

    1. Oleksii Mostovyi, 2017. "Optimal consumption of multiple goods in incomplete markets," Papers 1705.02291, arXiv.org, revised Jan 2018.
    2. Bernard, C. & De Gennaro Aquino, L. & Vanduffel, S., 2023. "Optimal multivariate financial decision making," European Journal of Operational Research, Elsevier, vol. 307(1), pages 468-483.
    3. Pilar Iglesias & Jaime San Martín & Soledad Torres & Frederi Viens, 2011. "Option pricing under a Gamma-modulated diffusion process," Annals of Finance, Springer, vol. 7(2), pages 199-219, May.
    4. Vicky Henderson & Gechun Liang, 2014. "Pseudo linear pricing rule for utility indifference valuation," Finance and Stochastics, Springer, vol. 18(3), pages 593-615, July.
    5. Lena Schutte, 2017. "Retirement Wealth under Fixed Limits: The Optimal Strategy for Exponential Utility," Papers 1712.00463, arXiv.org.
    6. Ethem Çanakoğlu & Süleyman Özekici, 2009. "Portfolio selection in stochastic markets with exponential utility functions," Annals of Operations Research, Springer, vol. 166(1), pages 281-297, February.
    7. Jean-Pierre Fouque & Ruimeng Hu, 2017. "Optimal Portfolio under Fractional Stochastic Environment," Papers 1703.06969, arXiv.org, revised Dec 2017.
    8. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2015. "The pricing of contingent claims and optimal positions in asymptotically complete markets," Papers 1509.06210, arXiv.org, revised Sep 2016.
    9. Jean-Pierre Fouque & Ruimeng Hu, 2018. "Portfolio Optimization under Fast Mean-reverting and Rough Fractional Stochastic Environment," Papers 1804.03002, arXiv.org, revised Jan 2019.
    10. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2021. "Optimal investment, derivative demand, and arbitrage under price impact," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 3-35, January.
    11. Rohini Kumar & Hussein Nasralah, 2016. "Asymptotic approximation of optimal portfolio for small time horizons," Papers 1611.09300, arXiv.org, revised Feb 2018.
    12. Jean-Pierre Fouque & Ruimeng Hu, 2017. "Optimal Portfolio under Fast Mean-reverting Fractional Stochastic Environment," Papers 1706.03139, arXiv.org, revised Feb 2018.
    13. Vicky Henderson & Gechun Liang, 2011. "A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk," Papers 1111.3856, arXiv.org, revised Sep 2015.
    14. Michail Anthropelos & Scott Robertson & Konstantinos Spiliopoulos, 2018. "Optimal Investment, Demand and Arbitrage under Price Impact," Papers 1804.09151, arXiv.org, revised Dec 2018.
    15. Monoyios, Michael, 2007. "The minimal entropy measure and an Esscher transform in an incomplete market model," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1070-1076, June.
    16. Laurence Carassus & Massinissa Ferhoune, 2024. "Efficient Approximations for Utility-Based Pricing," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-38, June.
    17. Benjamin James Duthie, 2019. "Portfolio optimisation under rough Heston models," Papers 1909.02972, arXiv.org.
    18. Rubtsov, Alexey & Xu, Wei & Šević, Aleksandar & Šević, Željko, 2021. "Price of climate risk hedging under uncertainty," Technological Forecasting and Social Change, Elsevier, vol. 165(C).

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