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Optimal investment with insurable background risk and nonlinear portfolio allocation frictions

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  • 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
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    1. Lin, Xiaoji & Wang, Chong & Wang, Neng & Yang, Jinqiang, 2018. "Investment, Tobin’s q, and interest rates," Journal of Financial Economics, Elsevier, vol. 130(3), pages 620-640.
    2. Back, Kerry, 2010. "Asset Pricing and Portfolio Choice Theory," OUP Catalogue, Oxford University Press, number 9780195380613.
    3. Ilia Tsetlin & Robert L. Winkler, 2005. "Risky Choices and Correlated Background Risk," Management Science, INFORMS, vol. 51(9), pages 1336-1345, September.
    4. Roche, Herve, 2003. "Stochastic growth: a duality approach," Journal of Economic Theory, Elsevier, vol. 113(1), pages 131-143, November.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Robert S. Pindyck & Neng Wang, 2013. "The Economic and Policy Consequences of Catastrophes," American Economic Journal: Economic Policy, American Economic Association, vol. 5(4), pages 306-339, November.
    10. 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.
    11. Harrison Hong & Neng Wang & Jinqiang Yang, 2023. "Mitigating Disaster Risks in the Age of Climate Change," Econometrica, Econometric Society, vol. 91(5), pages 1763-1802, September.
    12. 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.
    13. Günter Franke & Harris Schlesinger & Richard C. Stapleton, 2006. "Multiplicative Background Risk," Management Science, INFORMS, vol. 52(1), pages 146-153, January.
    14. 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.
    15. 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.
    16. 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.
    17. Sergio Rebelo & Neng Wang & Jinqiang Yang, 2022. "Rare Disasters, Financial Development, and Sovereign Debt," Journal of Finance, American Finance Association, vol. 77(5), pages 2719-2764, October.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
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    Keywords

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

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