IDEAS home Printed from https://ideas.repec.org/p/col/000092/020658.html
   My bibliography  Save this paper

Optimal investment with insurable background risk and nonlinear portfolio allocation frictions

Author

Listed:
  • Ramírez, H
  • Serrano, R

Abstract

We study investment and insurance demand decisions for an agent in a theoretical continuoustime expected utility maximization model that combines risky assets with an (exogenous) insurable background risk. This risk takes the form of a jump-diffusion process with negative jumps in the return rate of the (self-financed) wealth. The main distinctive feature of our model is that the agent’s decision on portfolio choice and insurance demand causes nonlinear friction in the dynamics of the wealth process. We use the dynamic programming approach to find optimality conditions under which the agent assumes the insurable risk entirely, or partially, or purchases total insurance against it. In particular, we consider differential and piece-wise linear portfolio allocation frictions, with differential borrowing and lending rates as our most emblematic example. Finally, we present a mutual-fund separation result and illustrate our results with several numerical examples when the adverse jump risk has Beta distribution.

Suggested Citation

  • Ramírez, H & Serrano, R, 2023. "Optimal investment with insurable background risk and nonlinear portfolio allocation frictions," Documentos de Trabajo 20658, Universidad del Rosario.
    • Handle: RePEc:col:000092:020658
    as

    Download full text from publisher

    File URL: https://repository.urosario.edu.co/server/api/core/bitstreams/306a7c27-d9c9-4238-82f6-4f1d65ebb200/content
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
    2. Roche, Herve, 2003. "Stochastic growth: a duality approach," Journal of Economic Theory, Elsevier, vol. 113(1), pages 131-143, November.
    3. Eeckhoudt, Louis & Gollier, Christian & Schlesinger, Harris, 1996. "Changes in Background Risk and Risk-Taking Behavior," Econometrica, Econometric Society, vol. 64(3), pages 683-689, May.
    4. Franke, Guenter & Schlesinger, Harris & Stapleton, Richard C., 2011. "Risk taking with additive and multiplicative background risks," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1547-1568, July.
    5. Guenter Franke & Harris Schlesinger & Richard C. Stapleton, 2018. "Risk†Taking†Neutral Background Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(2), pages 335-353, June.
    6. Domenico Cuoco & Hong Liu, 2000. "A Martingale Characterization of Consumption Choices and Hedging Costs with Margin Requirements," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 355-385, July.
    7. Patrick Bolton & Neng Wang & Jinqiang Yang, 2019. "Optimal Contracting, Corporate Finance, and Valuation with Inalienable Human Capital," Journal of Finance, American Finance Association, vol. 74(3), pages 1363-1429, June.
    8. Nguyen-Thanh Long, 2004. "Investment optimization under constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 175-201, October.
    9. Perera, Ryle S., 2010. "Optimal consumption, investment and insurance with insurable risk for an investor in a Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 479-484, June.
    10. Moore, Kristen S. & Young, Virginia R., 2006. "Optimal insurance in a continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 47-68, August.
    11. 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.
    12. Cuoco, Domenico & Cvitanic, Jaksa, 1998. "Optimal consumption choices for a 'large' investor," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 401-436, March.
    13. Mohamed Mnif, 2013. "Optimal Risk Control Under Marked Point Processes Shocks: A Dynamic Programming Duality Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(07), pages 1-45.
    14. I. Klein & L. C. G. Rogers, 2007. "Duality In Optimal Investment And Consumption Problems With Market Frictions," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 225-247, April.
    15. Gollier, Christian & Pratt, John W, 1996. "Risk Vulnerability and the Tempering Effect of Background Risk," Econometrica, Econometric Society, vol. 64(5), pages 1109-1123, September.
    16. Harrison Hong & Neng Wang & Jinqiang Yang, 2020. "Mitigating Disaster Risks in the Age of Climate Change," NBER Working Papers 27066, National Bureau of Economic Research, Inc.
    17. Heaton, John & Lucas, Deborah, 2000. "Portfolio Choice in the Presence of Background Risk," Economic Journal, Royal Economic Society, vol. 110(460), pages 1-26, January.
    18. George Allayannis & Jane Ihrig & James P. Weston, 2001. "Exchange-Rate Hedging: Financial versus Operational Strategies," American Economic Review, American Economic Association, vol. 91(2), pages 391-395, May.
    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. Guo, Xu & Wong, Wing-Keung & Zhu, Lixing, 2013. "An analysis of portfolio selection with multiplicative background risk," MPRA Paper 51331, University Library of Munich, Germany.
    2. Huang, Hung-Hsi & Wang, Ching-Ping, 2013. "Portfolio selection and portfolio frontier with background risk," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 177-196.
    3. Dionne, Georges & Li, Jingyuan, 2014. "Comparative Ross risk aversion in the presence of mean dependent risks," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 128-135.
    4. Moawia Alghalith & Xu Guo & Wing-Keung Wong & Lixing Zhu, 2016. "A General Optimal Investment Model In The Presence Of Background Risk," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-8, March.
    5. Li, Jingyuan & Liu, Dongri & Wang, Jianli, 2016. "Risk aversion with two risks: A theoretical extension," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 100-105.
    6. Gollier Christian & Schlee Edward E, 2006. "Increased Risk-Bearing with Background Risk," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-31, March.
    7. James Huang & Richard Stapleton, 2017. "Higher-order risk vulnerability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 387-406, February.
    8. Aragón, Fernando M. & Molina, Oswaldo & Outes-León, Ingo W., 2020. "Property rights and risk aversion: Evidence from a titling program," World Development, Elsevier, vol. 134(C).
    9. Baptista, Alexandre M., 2008. "Optimal delegated portfolio management with background risk," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 977-985, June.
    10. Lisa Cameron & Manisha Shah, 2015. "Risk-Taking Behavior in the Wake of Natural Disasters," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 484-515.
    11. Heinzel, Christoph, 2023. "Comparing utility derivative premia under additive and multiplicative risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 23-40.
    12. Henry Chiu, W., 2020. "Financial risk taking in the presence of correlated non-financial background risk," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 167-179.
    13. Fernando M. Aragon & Oswaldo Molina & Ingo W. Outes-Leon, 2017. "Can public policies change risk preferences? The effect of property titling on risk aversion," Discussion Papers dp17-09, Department of Economics, Simon Fraser University.
    14. Eichner, Thomas & Wagener, Andreas, 2012. "Tempering effects of (dependent) background risks: A mean-variance analysis of portfolio selection," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 422-430.
    15. Martín Egozcue & Jiang Wu & Ričardas Zitikis, 2017. "Optimal two-stage pricing strategies from the seller’s perspective under the uncertainty of buyer’s decisions," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-25, December.
    16. Hallegatte,Stephane & Bangalore,Mook & Jouanjean,Marie Agnes, 2016. "Higher losses and slower development in the absence of disaster risk management investments," Policy Research Working Paper Series 7632, The World Bank.
    17. Chen, Xuanjuan & Sun, Zhenzhen & Yao, Tong & Yu, Tong, 2020. "Does operating risk affect portfolio risk? Evidence from insurers' securities holding," Journal of Corporate Finance, Elsevier, vol. 62(C).
    18. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2010. "An analysis of portfolio selection with background risk," Journal of Banking & Finance, Elsevier, vol. 34(12), pages 3055-3060, December.
    19. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.
    20. 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.

    More about this item

    Keywords

    Portfolio allocation; Insurance demand; CRRA utility; Background risk; Jump-diffusions; Dynamic programming; Differential rates; Fund separation Theorem;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:col:000092:020658. 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: Facultad de Economía (email available below). General contact details of provider: https://edirc.repec.org/data/ferosco.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.