IDEAS home Printed from https://ideas.repec.org/p/ecm/wc2000/1146.html
   My bibliography  Save this paper

Optimal Consumption and Investment with Levy Processes

Author

Listed:
  • Jose Fajardo Barbachan

    (Catholic University of Brasilia)

Abstract

This paper study the intertemporal consumption and investment problem in a continuous time setting when the secutity prices follow a Geometric Levy Process. Using stochastic calculus for semimartingals we obtain sufficient conditions for the existence of optimal consump- tion and investment policies.

Suggested Citation

  • Jose Fajardo Barbachan, 2000. "Optimal Consumption and Investment with Levy Processes," Econometric Society World Congress 2000 Contributed Papers 1146, Econometric Society.
    • Handle: RePEc:ecm:wc2000:1146
    as

    Download full text from publisher

    File URL: http://fmwww.bc.edu/RePEc/es2000/1146.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Philip H. Dybvig, Chi-fu Huang, 1988. "Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 377-401.
    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. Fajardo, Jose Santiago, 2006. "Equivalent Martingale Measures and Lévy Processes," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 60(4), February.
    4. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    5. Jakša Cvitanić & Ioannis Karatzas, 1996. "Hedging And Portfolio Optimization Under Transaction Costs: A Martingale Approach12," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165, April.
    6. Svensson, Lars E. O. & Werner, Ingrid M., 1993. "Nontraded assets in incomplete markets : Pricing and portfolio choice," European Economic Review, Elsevier, vol. 37(5), pages 1149-1168, June.
    7. Barbachan, José Santiago Fajardo, 2003. "Optimal Consumption and Investment with Lévy Processes," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 57(4), October.
    8. Kristin Reikvam & Fred Espen Benth & Kenneth Hvistendahl Karlsen, 2001. "Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach," Finance and Stochastics, Springer, vol. 5(3), pages 275-303.
    9. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    10. He, Hua & Pages, Henri F, 1993. "Labor Income, Borrowing Constraints, and Equilibrium Asset Prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(4), pages 663-696, October.
    11. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    12. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    13. Barbachan, José Fajardo, 2000. "Optimal Consumption and Investment with Hyperbolic Lévy Motion," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 20(1), May.
    14. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    15. Tina Hviid Rydberg, 1999. "Generalized Hyperbolic Diffusion Processes with Applications in Finance," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 183-201, April.
    16. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    17. Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
    18. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fajardo, José & Corcuera, José Manuel & Menouken Pamen, Olivier, 2016. "On the optimal investment," MPRA Paper 71901, University Library of Munich, Germany.
    2. Barbachan, José Santiago Fajardo, 2003. "Optimal Consumption and Investment with Lévy Processes," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 57(4), October.

    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. Barbachan, José Fajardo, 2000. "Optimal Consumption and Investment with Hyperbolic Lévy Motion," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 20(1), May.
    2. Schwartz, Eduardo S & Tebaldi, Claudio, 2004. "Illiquid Assets and Optimal Portfolio Choice," University of California at Los Angeles, Anderson Graduate School of Management qt7q65t12x, Anderson Graduate School of Management, UCLA.
    3. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    4. repec:dau:papers:123456789/5374 is not listed on IDEAS
    5. Wahid Faidi & Hanen Mezghanni & Mohamed Mnif, 2019. "Expected Utility Maximization Problem Under State Constraints and Model Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1123-1152, December.
    6. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    7. 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.
    8. Jessica A. Wachter, 2010. "Asset Allocation," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 175-206, December.
    9. Schroder, Mark & Skiadas, Costis, 2005. "Lifetime consumption-portfolio choice under trading constraints, recursive preferences, and nontradeable income," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 1-30, January.
    10. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    11. Chen, An & Vellekoop, Michel, 2017. "Optimal investment and consumption when allowing terminal debt," European Journal of Operational Research, Elsevier, vol. 258(1), pages 385-397.
    12. Masahiko Egami & Hideki Iwaki, 2007. "An optimal life insurance policy in the investment-consumption problem in an incomplete market," Papers 0801.0195, arXiv.org, revised May 2011.
    13. Mnif, Mohammed & Pham, Huyên, 2001. "Stochastic optimization under constraints," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 149-180, May.
    14. 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.
    15. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    16. Letendre, Marc-Andre & Smith, Gregor W., 2001. "Precautionary saving and portfolio allocation: DP by GMM," Journal of Monetary Economics, Elsevier, vol. 48(1), pages 197-215, August.
    17. Christoph Belak & An Chen & Carla Mereu & Robert Stelzer, 2014. "Optimal investment with time-varying stochastic endowments," Papers 1406.6245, arXiv.org, revised Feb 2022.
    18. Roche, Hervé & Tompaidis, Stathis & Yang, Chunyu, 2013. "Why does junior put all his eggs in one basket? A potential rational explanation for holding concentrated portfolios," Journal of Financial Economics, Elsevier, vol. 109(3), pages 775-796.
    19. Gerrard, Russell & Kyriakou, Ioannis & Nielsen, Jens Perch & Vodička, Peter, 2023. "On optimal constrained investment strategies for long-term savers in stochastic environments and probability hedging," European Journal of Operational Research, Elsevier, vol. 307(2), pages 948-962.
    20. 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.
    21. Peter Praetz & Michael Naphtali & John Nolan, 1975. "A Test of the Efficient Market Theory Using Filter Tests on Stock Prices," The Economic Record, The Economic Society of Australia, vol. 51(1), pages 66-72, March.

    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:ecm:wc2000:1146. 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: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    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.