IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1005.3956.html
   My bibliography  Save this paper

Smooth Value Functions for a Class of Nonsmooth Utility Maximization Problems

Author

Listed:
  • Baojun Bian
  • Sheng Miao
  • Harry Zheng

Abstract

In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is continuous on the closure of its domain. The key idea is to work on the dual control problem and the dual HJB equation. We construct a smooth, strictly convex solution to the dual HJB equation and show that its conjugate function is a smooth, strictly concave solution to the primal HJB equation satisfying the terminal and boundary conditions.

Suggested Citation

  • Baojun Bian & Sheng Miao & Harry Zheng, 2010. "Smooth Value Functions for a Class of Nonsmooth Utility Maximization Problems," Papers 1005.3956, arXiv.org.
  • Handle: RePEc:arx:papers:1005.3956
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1005.3956
    File Function: Latest version
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Escobar-Anel, Marcos & Havrylenko, Yevhen & Kschonnek, Michel & Zagst, Rudi, 2022. "Decrease of capital guarantees in life insurance products: Can reinsurance stop it?," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 14-40.

    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:arx:papers:1005.3956. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.