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Optimal Investment and Consumption for Multidimensional Spread Financial Markets with Logarithmic Utility

Author

Listed:
  • Sahar Albosaily

    (Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il P.O. Box 2440, Saudi Arabia)

  • Serguei Pergamenchtchikov

    (Laboratoire de Mathématiques Raphael Salem, UMR 6085 CNRS-Université de Rouen, F76801 Saint-Étienne-du-Rouvray, France
    International Laboratory of Statistics of Stochastic Processes and Quantitative Finance, Tomsk State University, 634050 Tomsk, Russia)

Abstract

We consider a spread financial market defined by the multidimensional Ornstein–Uhlenbeck (OU) process. We study the optimal consumption/investment problem for logarithmic utility functions using a stochastic dynamical programming method. We show a special verification theorem for this case. We find the solution to the Hamilton–Jacobi–Bellman (HJB) equation in explicit form and as a consequence we construct optimal financial strategies. Moreover, we study the constructed strategies with numerical simulations.

Suggested Citation

  • Sahar Albosaily & Serguei Pergamenchtchikov, 2021. "Optimal Investment and Consumption for Multidimensional Spread Financial Markets with Logarithmic Utility," Stats, MDPI, vol. 4(4), pages 1-15, November.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:4:p:58-1026:d:690503
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    References listed on IDEAS

    as
    1. Belkacem Berdjane & Serguei Pergamenshchikov, 2013. "Optimal consumption and investment for markets with random coefficients," Finance and Stochastics, Springer, vol. 17(2), pages 419-446, April.
    2. Christopher Krauss, 2017. "Statistical Arbitrage Pairs Trading Strategies: Review And Outlook," Journal of Economic Surveys, Wiley Blackwell, vol. 31(2), pages 513-545, April.
    3. Paul Berhanu Girma & Albert S. Paulson, 1999. "Risk arbitrage opportunities in petroleum futures spreads," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(8), pages 931-955, December.
    4. Holger Kraft & Thomas Seiferling & Frank Thomas Seifried, 2017. "Optimal consumption and investment with Epstein–Zin recursive utility," Finance and Stochastics, Springer, vol. 21(1), pages 187-226, January.
    5. João Frois Caldeira & Gulherme Valle Moura, 2013. "Selection of a Portfolio of Pairs Based on Cointegration: A Statistical Arbitrage Strategy," Brazilian Review of Finance, Brazilian Society of Finance, vol. 11(1), pages 49-80.
    6. Zebedee, Allan A. & Kasch-Haroutounian, Maria, 2009. "A closer look at co-movements among stock returns," Journal of Economics and Business, Elsevier, vol. 61(4), pages 279-294, July.
    7. Margaret A. Monroe & Richard A. Cohn, 1986. "The relative efficiency of the gold and treasury bill futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 6(3), pages 477-493, September.
    8. Jun Liu & Allan Timmermann, 2013. "Optimal Convergence Trade Strategies," The Review of Financial Studies, Society for Financial Studies, vol. 26(4), pages 1048-1086.
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    Cited by:

    1. Yaacov Kopeliovich & Michael Pokojovy & Julia Bernatska, 2024. "On Merton's Optimal Portfolio Problem with Sporadic Bankruptcy for Isoelastic Utility," Papers 2403.15923, arXiv.org, revised Nov 2024.

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