IDEAS home Printed from https://ideas.repec.org/a/taf/applec/v42y2010i30p3831-3838.html
   My bibliography  Save this article

Stochastic optimization applied to self-financing portfolio: does bequest matter?

Author

Listed:
  • Saziye Gaziog-super-˜lu
  • Azize Bastıyalı-Hayfavi

Abstract

The article studies stochastic optimization of an intertemporal consumption model to allocate financial assets between risky and risk-free assets. We use a stochastic optimization technique, in which utility is maximized subject to a self-financing portfolio constraint. The papers in literature have estimated the errors of Euler equations using data from financial markets. It has been shown that it is sufficient to test the first order Euler equation implied by the model. However, they all assume a constant consumption-wealth ratio that constrains the boundary conditions, hence influencing the coefficient of the risk premium. The main contribution of our article is that we drop the assumption of a constant consumption-wealth ratio. We have an analytical solution using a utility maximization model with a stochastic self-financing portfolio. We introduce a terminal condition of wealth with and without bequests. We also simulate the stochastic optimization with a self-financing portfolio, distinguishing risk neutral investors (γ-low) from high risk averse investors (γ-high). We show that the model with bequest has a higher level of wealth and a smoother decline of consumption over time than the model with no bequest at the end of the period. The model with no bequest has the same level of consumption and a sharp fall at the end of the period. Risk averse agents with high return assets have a higher amount of wealth than risk-neutral agents with lower return assets.

Suggested Citation

  • Saziye Gaziog-super-˜lu & Azize Bastıyalı-Hayfavi, 2010. "Stochastic optimization applied to self-financing portfolio: does bequest matter?," Applied Economics, Taylor & Francis Journals, vol. 42(30), pages 3831-3838.
  • Handle: RePEc:taf:applec:v:42:y:2010:i:30:p:3831-3838
    DOI: 10.1080/00036840802112364
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/00036840802112364
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/00036840802112364?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    2. 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.
    3. Martin Lettau & Sydney Ludvigson, 2009. "Euler Equation Errors," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(2), pages 255-283, April.
    4. John Y. Campbell & John Cochrane, 1999. "Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 107(2), pages 205-251, April.
    5. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Jun Liu, 2005. "An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 131-164.
    7. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    8. Bakshi, Gurdip S & Chen, Zhiwu, 1996. "The Spirit of Capitalism and Stock-Market Prices," American Economic Review, American Economic Association, vol. 86(1), pages 133-157, March.
    9. Selden, Larry, 1978. "A New Representation of Preferences over "Certain A Uncertain" Consumption Pairs: The "Ordinal Certainty Equivalent" Hypothesis," Econometrica, Econometric Society, vol. 46(5), pages 1045-1060, September.
    10. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
    11. Kocherlakota, Narayana R, 1990. "Disentangling the Coefficient of Relative Risk Aversion from the Elasticity of Intertemporal Substitution: An Irrelevance Result," Journal of Finance, American Finance Association, vol. 45(1), pages 175-190, March.
    12. Martin Lettau, 2000. "Cross-variable restrictions in Euler equations and risk premia," Applied Economics Letters, Taylor & Francis Journals, vol. 7(2), pages 99-101.
    13. Christopher D. Carroll, 1997. "Buffer-Stock Saving and the Life Cycle/Permanent Income Hypothesis," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(1), pages 1-55.
    14. Hubbard, R. Glenn & Skinner, Jonathan & Zeldes, Stephen P., 1994. "The importance of precautionary motives in explaining individual and aggregate saving," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 40(1), pages 59-125, June.
    15. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
    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. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    2. Ludvigson, Sydney C., 2013. "Advances in Consumption-Based Asset Pricing: Empirical Tests," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 799-906, Elsevier.
    3. Sydney Ludvigson, 2008. "The Research Agenda: Sydney Ludvigson on Empirical Evaluation of Economic Theories of Risk Premia," EconomicDynamics Newsletter, Review of Economic Dynamics, vol. 9(2), April.
    4. Falato, Antonio, 2009. "Happiness maintenance and asset prices," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1247-1262, June.
    5. Kabderian Dreyer, Johannes & Sharma, Vivek & Smith, William, 2023. "Warm-glow investment and the underperformance of green stocks," International Review of Economics & Finance, Elsevier, vol. 83(C), pages 546-570.
    6. Kevin X.D. Huang & Zheng Liu & John Qi Zhu, 2015. "Temptation and Self‐Control: Some Evidence and Applications," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 47(4), pages 581-615, June.
    7. van Binsbergen, Jules H. & Fernández-Villaverde, Jesús & Koijen, Ralph S.J. & Rubio-Ramírez, Juan, 2012. "The term structure of interest rates in a DSGE model with recursive preferences," Journal of Monetary Economics, Elsevier, vol. 59(7), pages 634-648.
    8. Thomas Q. Pedersen, 2008. "Intertemporal Asset Allocation with Habit Formation in Preferences: An Approximate Analytical Solution," CREATES Research Papers 2008-60, Department of Economics and Business Economics, Aarhus University.
    9. Aase, Knut K., 2014. "Recursive utility and jump-diffusions," Discussion Papers 2014/9, Norwegian School of Economics, Department of Business and Management Science.
    10. Garcia, Rene & Renault, Eric & Semenov, Andrei, 2006. "Disentangling risk aversion and intertemporal substitution through a reference level," Finance Research Letters, Elsevier, vol. 3(3), pages 181-193, September.
    11. Orazio P. Attanasio & Guglielmo Weber, 2010. "Consumption and Saving: Models of Intertemporal Allocation and Their Implications for Public Policy," Journal of Economic Literature, American Economic Association, vol. 48(3), pages 693-751, September.
    12. Smith, William T., 1999. "Risk, the Spirit of Capitalism and Growth: The Implications of a Preference for Capital," Journal of Macroeconomics, Elsevier, vol. 21(2), pages 241-262, April.
    13. Rojo-Suárez, Javier & Alonso-Conde, Ana B. & Lago-Balsalobre, Rubén, 2024. "Industry bubbles and unexpected consumption shocks: A cross-sectional explanation of stock returns under recursive preferences," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 1156-1169.
    14. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    15. Beeler, Jason & Campbell, John Y., 2012. "The Long-Run Risks Model and Aggregate Asset Prices: An Empirical Assessment," Critical Finance Review, now publishers, vol. 1(1), pages 141-182, January.
    16. Stefan Nagel, 2013. "Empirical Cross-Sectional Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 167-199, November.
    17. Stuart Hyde & Mohamed Sherif, 2004. "Don't break the habit: structural stability tests of consumption models in the UK," Money Macro and Finance (MMF) Research Group Conference 2003 49, Money Macro and Finance Research Group.
    18. Kihlstrom, Richard, 2009. "Risk aversion and the elasticity of substitution in general dynamic portfolio theory: Consistent planning by forward looking, expected utility maximizing investors," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 634-663, September.
    19. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
    20. Roussanov, Nikolai, 2014. "Composition of wealth, conditioning information, and the cross-section of stock returns," Journal of Financial Economics, Elsevier, vol. 111(2), pages 352-380.

    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:taf:applec:v:42:y:2010:i:30:p:3831-3838. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAEC20 .

    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.