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Closed‐Form Solutions For Optimal Portfolio Selection With Stochastic Interest Rate And Investment Constraints

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  • Jér^me Detemple
  • Marcel Rindisbacher

Abstract

We examine the portfolio choice problem of an investor with constant relative risk aversion in a financial market with partially hedgeable interest rate risk. The individual shadow price of the portfolio constraint is characterized as the solution of a new backward equation involving Malliavin derivatives. A generalization of this equation is studied and solved in explicit form. This result, applied to our financial model, yields closed‐form solutions for the shadow price and the optimal portfolio. The effects of parameters such as risk aversion, interest rate volatility, investment horizon, and tightness of the constraint are examined. Applications of our method to a monetary economy with inflation risk and to an international setting with currency risk are also provided.

Suggested Citation

  • Jér^me Detemple & Marcel Rindisbacher, 2005. "Closed‐Form Solutions For Optimal Portfolio Selection With Stochastic Interest Rate And Investment Constraints," Mathematical Finance, Wiley Blackwell, vol. 15(4), pages 539-568, October.
  • Handle: RePEc:bla:mathfi:v:15:y:2005:i:4:p:539-568
    DOI: 10.1111/j.1467-9965.2005.00250.x
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Georgy Chabakauri, 2012. "Asset Pricing with Heterogeneous Investors and Portfolio Constraints," FMG Discussion Papers dp707, Financial Markets Group.
    2. Romain Deguest & Lionel Martellini & Vincent Milhau, 2018. "A Reinterpretation of the Optimal Demand for Risky Assets in Fund Separation Theorems," Management Science, INFORMS, vol. 64(9), pages 4333-4347, September.
    3. Hubar, Sylwia & Koulovatianos, Christos & Li, Jian, 2020. "The role of labor-income risk in household risk-taking," European Economic Review, Elsevier, vol. 129(C).
    4. Jérôme Detemple, 2014. "Portfolio Selection: A Review," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 1-21, April.
    5. Castañeda, Pablo & Reus, Lorenzo, 2019. "Suboptimal investment behavior and welfare costs: A simulation based approach," Finance Research Letters, Elsevier, vol. 30(C), pages 170-180.
    6. Shen, Yang & Siu, Tak Kuen, 2012. "Asset allocation under stochastic interest rate with regime switching," Economic Modelling, Elsevier, vol. 29(4), pages 1126-1136.
    7. Thijs Kamma & Antoon Pelsser, 2019. "Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading Constraints," Papers 1906.12317, arXiv.org, revised Oct 2019.
    8. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    9. Chen, Binbin & Huang, Shih-Feng & Pan, Guangming, 2015. "High dimensional mean–variance optimization through factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 140-159.
    10. Chenxu Li & Olivier Scaillet & Yiwen Shen, 2020. "Wealth Effect on Portfolio Allocation in Incomplete Markets," Papers 2004.10096, arXiv.org, revised Aug 2021.
    11. Chenxu Li & O. Scaillet & Yiwen Shen, 2020. "Decomposition of Optimal Dynamic Portfolio Choice with Wealth-Dependent Utilities in Incomplete Markets," Swiss Finance Institute Research Paper Series 20-22, Swiss Finance Institute.
    12. Yacin Jerbi, 2016. "Early exercise premium method for pricing American options under the J-model," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 2(1), pages 1-26, December.
    13. Haluk Yener & Fuat Can Beylunioglu, 2017. "Outperforming A Stochastic Benchmark Under Borrowing And Rectangular Constraints," Working Papers 1701, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    14. Chabakauri, Georgy, 2010. "Asset pricing with heterogeneous investors and portfolio constraints," LSE Research Online Documents on Economics 43142, London School of Economics and Political Science, LSE Library.
    15. Rytchkov, Oleg, 2016. "Time-Varying Margin Requirements and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 51(2), pages 655-683, April.
    16. Chabakauri, Georgy, 2012. "Asset pricing with heterogeneous investors and portfolio constraints," LSE Research Online Documents on Economics 119046, London School of Economics and Political Science, LSE Library.
    17. Kristoffer Lindensjo, 2016. "An explicit formula for optimal portfolios in complete Wiener driven markets: a functional It\^o calculus approach," Papers 1610.05018, arXiv.org, revised Dec 2017.
    18. Georgy Chabakauri, 2012. "Asset Pricing with Heterogeneous Investors and Portfolio Constraints," 2012 Meeting Papers 636, Society for Economic Dynamics.
    19. Szymon Peszat & Dariusz Zawisza, 2020. "The investor problem based on the HJM model," Papers 2010.13915, arXiv.org, revised Dec 2021.
    20. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    21. Castaneda, Pablo & Rudolph, Heinz P., 2011. "Upgrading investment regulations in second pillar pension systems : a proposal for Colombia," Policy Research Working Paper Series 5775, The World Bank.
    22. Marine Carrasco & N'Golo Koné, 2023. "Test for Trading Costs Effect in a Portfolio Selection Problem with Recursive Utility," CIRANO Working Papers 2023s-03, CIRANO.

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