IDEAS home Printed from https://ideas.repec.org/a/wly/jnddns/v2016y2016i1n9606497.html

Optimal Investment‐Consumption Strategy under Inflation in a Markovian Regime‐Switching Market

Author

Listed:
  • Huiling Wu

Abstract

This paper studies an investment‐consumption problem under inflation. The consumption price level, the prices of the available assets, and the coefficient of the power utility are assumed to be sensitive to the states of underlying economy modulated by a continuous‐time Markovian chain. The definition of admissible strategies and the verification theory corresponding to this stochastic control problem are presented. The analytical expression of the optimal investment strategy is derived. The existence, boundedness, and feasibility of the optimal consumption are proven. Finally, we analyze in detail by mathematical and numerical analysis how the risk aversion, the correlation coefficient between the inflation and the stock price, the inflation parameters, and the coefficient of utility affect the optimal investment and consumption strategy.

Suggested Citation

  • Huiling Wu, 2016. "Optimal Investment‐Consumption Strategy under Inflation in a Markovian Regime‐Switching Market," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:9606497
    DOI: 10.1155/2016/9606497
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2016/9606497
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2016/9606497?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Munk, Claus & Sorensen, Carsten, 2004. "Optimal consumption and investment strategies with stochastic interest rates," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1987-2013, August.
    2. Paolo Battocchio & Francesco Menoncin, 2002. "Optimal Portfolio Strategies with Stochastic Wage Income and Inflation: The Case of a Defined Contribution Pension Plan," CeRP Working Papers 19, Center for Research on Pensions and Welfare Policies, Turin (Italy).
    3. U. Çakmak & S. Özekici, 2006. "Portfolio optimization in stochastic markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 151-168, February.
    4. Hyeng Keun Koo, 1998. "Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 49-65, January.
    5. Francesco, MENONCIN, 2003. "Optimal Real Consumption and Asset Allocation for a HARA Investor with Labour Income," LIDAM Discussion Papers IRES 2003015, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    6. Zeng, Yan & Wu, Huiling & Lai, Yongzeng, 2013. "Optimal investment and consumption strategies with state-dependent utility functions and uncertain time-horizon," Economic Modelling, Elsevier, vol. 33(C), pages 462-470.
    7. Carl Chiarella & Chih-Ying Hsiao & Willi Semmler, 2007. "Intertemporal Investment Strategies Under Inflation Risk," Research Paper Series 192, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, June.
    9. Zhongfei Li & Ken Seng Tan & Hailiang Yang, 2008. "Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(1), pages 47-64.
    10. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    11. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
    12. Munk, Claus, 2000. "Optimal consumption/investment policies with undiversifiable income risk and liquidity constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(9), pages 1315-1343, August.
    13. Han, Nan-wei & Hung, Mao-wei, 2012. "Optimal asset allocation for DC pension plans under inflation," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 172-181.
    14. Pliska, Stanley R. & Ye, Jinchun, 2007. "Optimal life insurance purchase and consumption/investment under uncertain lifetime," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1307-1319, May.
    15. Cheung, Ka Chun & Yang, Hailiang, 2004. "Asset Allocation with Regime-Switching: Discrete-Time Case," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 99-111, May.
    16. Kwak, Minsuk & Shin, Yong Hyun & Choi, U Jin, 2011. "Optimal investment and consumption decision of a family with life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 176-188, March.
    17. de Jong, Frank, 2008. "Pension fund investments and the valuation of liabilities under conditional indexation," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 1-13, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huiling Wu, 2016. "Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-17, July.
    2. Zeng, Yan & Wu, Huiling & Lai, Yongzeng, 2013. "Optimal investment and consumption strategies with state-dependent utility functions and uncertain time-horizon," Economic Modelling, Elsevier, vol. 33(C), pages 462-470.
    3. Munk, Claus & Sørensen, Carsten, 2010. "Dynamic asset allocation with stochastic income and interest rates," Journal of Financial Economics, Elsevier, vol. 96(3), pages 433-462, June.
    4. Lin, Zhenmei & Lai, Chong & Li, Rui, 2025. "Optimal consumption and portfolio selection for retirees under inflation and pension default risk," The North American Journal of Economics and Finance, Elsevier, vol. 79(C).
    5. Cai, Jun & Ge, Chenliang, 2012. "Multi-objective private wealth allocation without subportfolios," Economic Modelling, Elsevier, vol. 29(3), pages 900-907.
    6. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2016, January-A.
    7. Wei-Ting Pan, 2016. "The Impact of Mandatory Savings on Life Cycle Consumption and Portfolio Choice," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 32, July-Dece.
    8. John H. Cochrane, 2014. "A Mean-Variance Benchmark for Intertemporal Portfolio Theory," Journal of Finance, American Finance Association, vol. 69(1), pages 1-49, February.
    9. Liang, Zongxia & Zhao, Xiaoyang, 2016. "Optimal mean–variance efficiency of a family with life insurance under inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 164-178.
    10. Zhiping Chen & Liyuan Wang & Ping Chen & Haixiang Yao, 2019. "Continuous-Time Mean–Variance Optimization For Defined Contribution Pension Funds With Regime-Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-33, September.
    11. Larsen, Linda Sandris & Munk, Claus, 2012. "The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts," Journal of Economic Dynamics and Control, Elsevier, vol. 36(2), pages 266-293.
    12. Kwak, Minsuk & Lim, Byung Hwa, 2014. "Optimal portfolio selection with life insurance under inflation risk," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 59-71.
    13. Lin, Wen-chang & Lu, Jin-ray, 2012. "Risky asset allocation and consumption rule in the presence of background risk and insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 150-158.
    14. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    15. Guambe, Calisto & Kufakunesu, Rodwell, 2015. "A note on optimal investment–consumption–insurance in a Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 30-36.
    16. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Leibniz Institute for Financial Research SAFE.
    17. Zhou, Y., 2014. "Essays on habit formation and inflation hedging," Other publications TiSEM 4886da12-1b84-4fd9-aa07-3, Tilburg University, School of Economics and Management.
    18. Björn Bick & Holger Kraft & Claus Munk, 2013. "Solving Constrained Consumption-Investment Problems by Simulation of Artificial Market Strategies," Management Science, INFORMS, vol. 59(2), pages 485-503, June.
    19. Alderborn, Joakim, 2024. "A life insurance model with asymmetric time preferences," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 17-31.
    20. Yang Wang & Jianwei Lin & Dandan Chen & Jizhou Zhang, 2023. "Optimal Investment–Consumption–Insurance Problem of a Family with Stochastic Income under the Exponential O-U Model," Mathematics, MDPI, vol. 11(19), pages 1-19, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:9606497. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3059 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.