Optimal investment with insurable background risk and nonlinear portfolio allocation frictions

We study investment and insurance demand decisions for an agent in a theoretical continuous-time 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 o...

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Autores:
Tipo de recurso:
Fecha de publicación:
2023
Institución:
Universidad del Rosario
Repositorio:
Repositorio EdocUR - U. Rosario
Idioma:
eng
OAI Identifier:
oai:repository.urosario.edu.co:10336/38218
Acceso en línea:
https://doi.org/10.48713/10336_38218
https://repository.urosario.edu.co/handle/10336/38218
Palabra clave:
Portfolio allocation
Insurance demand
CRRA utility
Background risk
Jump-diffusions
Dynamic programming
Differential rates
Fund separation Theorem
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License
http://creativecommons.org/licenses/by-nc-sa/4.0/
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oai_identifier_str oai:repository.urosario.edu.co:10336/38218
network_acronym_str EDOCUR2
network_name_str Repositorio EdocUR - U. Rosario
repository_id_str
dc.title.none.fl_str_mv Optimal investment with insurable background risk and nonlinear portfolio allocation frictions
title Optimal investment with insurable background risk and nonlinear portfolio allocation frictions
spellingShingle Optimal investment with insurable background risk and nonlinear portfolio allocation frictions
Portfolio allocation
Insurance demand
CRRA utility
Background risk
Jump-diffusions
Dynamic programming
Differential rates
Fund separation Theorem
title_short Optimal investment with insurable background risk and nonlinear portfolio allocation frictions
title_full Optimal investment with insurable background risk and nonlinear portfolio allocation frictions
title_fullStr Optimal investment with insurable background risk and nonlinear portfolio allocation frictions
title_full_unstemmed Optimal investment with insurable background risk and nonlinear portfolio allocation frictions
title_sort Optimal investment with insurable background risk and nonlinear portfolio allocation frictions
dc.subject.none.fl_str_mv Portfolio allocation
Insurance demand
CRRA utility
Background risk
Jump-diffusions
Dynamic programming
Differential rates
Fund separation Theorem
topic Portfolio allocation
Insurance demand
CRRA utility
Background risk
Jump-diffusions
Dynamic programming
Differential rates
Fund separation Theorem
description We study investment and insurance demand decisions for an agent in a theoretical continuous-time 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.
publishDate 2023
dc.date.none.fl_str_mv 2023-03-09
2023-03-13T12:41:24Z
dc.type.none.fl_str_mv info:eu-repo/semantics/workingPaper
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_8042
dc.identifier.none.fl_str_mv https://doi.org/10.48713/10336_38218
https://repository.urosario.edu.co/handle/10336/38218
url https://doi.org/10.48713/10336_38218
https://repository.urosario.edu.co/handle/10336/38218
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://ideas.repec.org/p/col/000092/020658.html
https://ideas.repec.org/p/col/000092/020658.html
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
http://purl.org/coar/access_right/c_abf2
dc.format.none.fl_str_mv 26 pp
application/pdf
dc.publisher.none.fl_str_mv Universidad del Rosario
Facultad de Economía
publisher.none.fl_str_mv Universidad del Rosario
Facultad de Economía
dc.source.none.fl_str_mv George Allayannis, Jane Ihrig, and James P Weston. Exchange-rate hedging: Financial versus operational strategies. American Economic Review, 91(2):391–395, 2001
Tomasz R Bielecki and Marek Rutkowski. Valuation and hedging of contracts with funding costs and collateralization. SIAM Journal on Financial Mathematics, 6(1):594–655, 2015.
Patrick Bolton, Neng Wang, and Jinqiang Yang. Optimal contracting, corporate finance, and valuation with inalienable human capital. The Journal of Finance, 74(3):1363–1429, 2019.
Eric Briys. Insurance and consumption: The continuous time case. The Journal of Risk and Insurance, 53(4):718–723, 1986.
Domenico Cuoco and Jakˇsa Cvitani ́c. Optimal consumption choices for a ‘large’ investor. Journal of Economic Dynamics and Control, 22(3):401–436, 1998.
Domenico Cuoco and Hong Liu. A martingale characterization of consumption choices and hedging costs with margin requirements. Math. Finance, 10(3):355–385, 2000.
Louis Eeckhoudt, Christian Gollier, and Harris Schlesinger. Changes in background risk and risk taking behavior. Econometrica: Journal of the Econometric Society, pages 683–689, 1996.
Louis Eeckhoudt, Christian Gollier, and Harris Schlesinger. Economic and financial decisions under risk. Princeton University Press, 2011.
Guenter Franke, Harris Schlesinger, and Richard C Stapleton. Risk taking with additive and multiplicative background risks. Journal of Economic Theory, 146(4):1547–1568, 2011.
Guenter Franke, Harris Schlesinger, and Richard C Stapleton. Risk-taking-neutral background risks. Journal of Risk and Insurance, 85(2):335–353, 2018.
Louis Eeckhoudt, Christian Gollier, and Harris Schlesinger. Economic and financial decisions under risk. Princeton University Press, 2011. Guenter Franke, Harris Schlesinger, and Richard C Stapleton. Risk taking with additive and multiplicative background risks. Journal of Economic Theory, 146(4):1547–1568, 2011. Guenter Franke, Harris Schlesinger, and Richard C Stapleton. Risk-taking-neutral background risks. Journal of Risk and Insurance, 85(2):335–353, 2018. G ̈unter Franke, Harris Schlesinger, and Richard C Stapleton. Multiplicative background risk. Management Science, 52(1):146–153, 2006.
instname:Universidad del Rosario
reponame:Repositorio Institucional EdocUR
instname_str Universidad del Rosario
institution Universidad del Rosario
reponame_str Repositorio Institucional EdocUR
collection Repositorio Institucional EdocUR
repository.name.fl_str_mv
repository.mail.fl_str_mv
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spelling Optimal investment with insurable background risk and nonlinear portfolio allocation frictionsPortfolio allocationInsurance demandCRRA utilityBackground riskJump-diffusionsDynamic programmingDifferential ratesFund separation TheoremWe study investment and insurance demand decisions for an agent in a theoretical continuous-time 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.Universidad del RosarioFacultad de Economía2023-03-092023-03-13T12:41:24Zinfo:eu-repo/semantics/workingPaperhttp://purl.org/coar/version/c_b1a7d7d4d402bccehttp://purl.org/coar/resource_type/c_804226 ppapplication/pdfhttps://doi.org/10.48713/10336_38218 https://repository.urosario.edu.co/handle/10336/38218George Allayannis, Jane Ihrig, and James P Weston. Exchange-rate hedging: Financial versus operational strategies. American Economic Review, 91(2):391–395, 2001Tomasz R Bielecki and Marek Rutkowski. Valuation and hedging of contracts with funding costs and collateralization. SIAM Journal on Financial Mathematics, 6(1):594–655, 2015.Patrick Bolton, Neng Wang, and Jinqiang Yang. Optimal contracting, corporate finance, and valuation with inalienable human capital. The Journal of Finance, 74(3):1363–1429, 2019.Eric Briys. Insurance and consumption: The continuous time case. The Journal of Risk and Insurance, 53(4):718–723, 1986.Domenico Cuoco and Jakˇsa Cvitani ́c. Optimal consumption choices for a ‘large’ investor. Journal of Economic Dynamics and Control, 22(3):401–436, 1998.Domenico Cuoco and Hong Liu. A martingale characterization of consumption choices and hedging costs with margin requirements. Math. Finance, 10(3):355–385, 2000.Louis Eeckhoudt, Christian Gollier, and Harris Schlesinger. Changes in background risk and risk taking behavior. Econometrica: Journal of the Econometric Society, pages 683–689, 1996.Louis Eeckhoudt, Christian Gollier, and Harris Schlesinger. Economic and financial decisions under risk. Princeton University Press, 2011.Guenter Franke, Harris Schlesinger, and Richard C Stapleton. Risk taking with additive and multiplicative background risks. Journal of Economic Theory, 146(4):1547–1568, 2011.Guenter Franke, Harris Schlesinger, and Richard C Stapleton. Risk-taking-neutral background risks. Journal of Risk and Insurance, 85(2):335–353, 2018.Louis Eeckhoudt, Christian Gollier, and Harris Schlesinger. Economic and financial decisions under risk. Princeton University Press, 2011. Guenter Franke, Harris Schlesinger, and Richard C Stapleton. Risk taking with additive and multiplicative background risks. Journal of Economic Theory, 146(4):1547–1568, 2011. Guenter Franke, Harris Schlesinger, and Richard C Stapleton. Risk-taking-neutral background risks. Journal of Risk and Insurance, 85(2):335–353, 2018. G ̈unter Franke, Harris Schlesinger, and Richard C Stapleton. Multiplicative background risk. Management Science, 52(1):146–153, 2006.instname:Universidad del Rosarioreponame:Repositorio Institucional EdocURenghttps://ideas.repec.org/p/col/000092/020658.htmlhttps://ideas.repec.org/p/col/000092/020658.htmlhttp://creativecommons.org/licenses/by-nc-sa/4.0/http://purl.org/coar/access_right/c_abf2Ramírez, HSerrano Perdomo, Rafael Antoniooai:repository.urosario.edu.co:10336/382182023-06-14T09:04:38Z

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