[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v70y2016icp89-104.html
   My bibliography  Save this article

Exponential utility maximization for an insurer with time-inconsistent preferences

Author

Listed:
  • Zhao, Qian
  • Wang, Rongming
  • Wei, Jiaqin
Abstract
This paper studies the optimal consumption–investment–reinsurance problem for an insurer with a general discount function and exponential utility function in a non-Markovian model. The appreciation rate and volatility of the stock, the premium rate and volatility of the risk process of the insurer are assumed to be adapted stochastic processes, while the interest rate is assumed to be deterministic. The object is to maximize the utility of intertemporal consumption and terminal wealth. By the method of multi-person differential game, we show that the time-consistent equilibrium strategy and the corresponding equilibrium value function can be characterized by the unique solutions of a BSDE and an integral equation. Under appropriate conditions, we show that this integral equation admits a unique solution. Furthermore, we compare the time-consistent equilibrium strategies with the optimal strategy for exponential discount function, and with the strategies for naive insurers in two special cases.

Suggested Citation

  • Zhao, Qian & Wang, Rongming & Wei, Jiaqin, 2016. "Exponential utility maximization for an insurer with time-inconsistent preferences," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 89-104.
    • Handle: RePEc:eee:insuma:v:70:y:2016:i:c:p:89-104
    DOI: 10.1016/j.insmatheco.2016.06.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668716301147
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2016.06.003?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. Wang, Zengwu & Xia, Jianming & Zhang, Lihong, 2007. "Optimal investment for an insurer: The martingale approach," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 322-334, March.
    2. R. A. Pollak, 1968. "Consistent Planning," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 201-208.
    3. Méder, Zsombor Z. & Flesch, János & Peeters, Ronald, 2017. "Naiveté and sophistication in dynamic inconsistency," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 40-54.
    4. Marie-Amélie Morlais, 2009. "Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem," Finance and Stochastics, Springer, vol. 13(1), pages 121-150, January.
    5. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
    6. Steven M. Goldman, 1980. "Consistent Plans," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 533-537.
    7. 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.
    8. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    9. Marín-Solano, Jesús & Navas, Jorge, 2010. "Consumption and portfolio rules for time-inconsistent investors," European Journal of Operational Research, Elsevier, vol. 201(3), pages 860-872, March.
    10. repec:dau:papers:123456789/11473 is not listed on IDEAS
    11. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 573-597.
    12. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    13. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    14. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    15. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    16. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 391-401.
    17. Peng, Xingchun & Wei, Linxiao & Hu, Yijun, 2014. "Optimal investment, consumption and proportional reinsurance for an insurer with option type payoff," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 78-86.
    18. Peng, Xingchun & Chen, Fenge & Hu, Yijun, 2014. "Optimal investment, consumption and proportional reinsurance under model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 222-234.
    19. Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
    20. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    21. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    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. Farkhondeh Rouz, O. & Shahmorad, S. & Ahmadian, D., 2024. "Double weakly singular kernels in stochastic Volterra integral equations with application to the rough Heston model," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    2. Yushi Hamaguchi, 2019. "Time-inconsistent consumption-investment problems in incomplete markets under general discount functions," Papers 1912.01281, arXiv.org, revised Mar 2021.
    3. Chen Shou & Xiang Shengpeng & He Hongbo, 2019. "Do Time Preferences Matter in Intertemporal Consumption and Portfolio Decisions?," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(2), pages 1-13, June.

    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. Zhao, Qian & Shen, Yang & Wei, Jiaqin, 2014. "Consumption–investment strategies with non-exponential discounting and logarithmic utility," European Journal of Operational Research, Elsevier, vol. 238(3), pages 824-835.
    2. Alia, Ishak & Chighoub, Farid & Sohail, Ayesha, 2016. "A characterization of equilibrium strategies in continuous-time mean–variance problems for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 212-223.
    3. Drouhin, Nicolas, 2020. "Non-stationary additive utility and time consistency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 1-14.
    4. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.
    5. Ivar Ekeland & Traian A. Pirvu, 2007. "Investment and Consumption without Commitment," Papers 0708.0588, arXiv.org.
    6. Li, Yongwu & Li, Zhongfei, 2013. "Optimal time-consistent investment and reinsurance strategies for mean–variance insurers with state dependent risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 86-97.
    7. Takeo Hori & Koichi Futagami, 2019. "A Non‐unitary Discount Rate Model," Economica, London School of Economics and Political Science, vol. 86(341), pages 139-165, January.
    8. Ivar Ekeland & Traian A Pirvu, 2008. "On a Non-Standard Stochastic Control Problem," Papers 0806.4026, arXiv.org.
    9. Efe A Ok & Yusufcan Masatlioglu, 2003. "A General Theory of Time Preferences," Levine's Bibliography 234936000000000089, UCLA Department of Economics.
    10. Faralla, Valeria & Novarese, Marco & Ardizzone, Antonella, 2017. "Framing Effects in Intertemporal Choice: A Nudge Experiment," MPRA Paper 82086, University Library of Munich, Germany.
    11. Bart Cockx & Corinna Ghirelli & Bruno Van der Linden, 2013. "Monitoring Job Search Effort with Hyperbolic Time Preferences and Non-Compliance: A Welfare Analysis," CESifo Working Paper Series 4187, CESifo.
    12. Bernergård, Axel, 2011. "Folk Theorems for Present-Biased Players," SSE/EFI Working Paper Series in Economics and Finance 736, Stockholm School of Economics.
    13. Marín-Solano, Jesús & Navas, Jorge, 2010. "Consumption and portfolio rules for time-inconsistent investors," European Journal of Operational Research, Elsevier, vol. 201(3), pages 860-872, March.
    14. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    15. Xue Dong He & Xun Yu Zhou, 2021. "Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation," Papers 2105.01829, arXiv.org.
    16. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.
    17. Kan, Kamhon, 2007. "Cigarette smoking and self-control," Journal of Health Economics, Elsevier, vol. 26(1), pages 61-81, January.
    18. Ryoji Ohdoi & Koichi Futagami & Takeo Hori, 2015. "Welfare and Tax Policies in a Neoclassical Growth Model with Non-unitary Discounting," Discussion Papers in Economics and Business 15-14, Osaka University, Graduate School of Economics.
    19. Zhao, Hui & Rong, Ximin, 2012. "Portfolio selection problem with multiple risky assets under the constant elasticity of variance model," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 179-190.
    20. Tyson, Christopher J., 2008. "Management of a capital stock by Strotz's naive planner," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2214-2239, July.

    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:eee:insuma:v:70:y:2016:i:c:p:89-104. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.