Optimal Constrained Investment in the Cramer-Lundberg model
AbstractWe consider an insurance company whose surplus is represented by the classical Cramer-Lundberg process. The company can invest its surplus in a risk free asset and in a risky asset, governed by the Black-Scholes equation. There is a constraint that the insurance company can only invest in the risky asset at a limited leveraging level; more precisely, when purchasing, the ratio of the investment amount in the risky asset to the surplus level is no more than a; and when shortselling, the proportion of the proceeds from the short-selling to the surplus level is no more than b. The objective is to find an optimal investment policy that minimizes the probability of ruin. The minimal ruin probability as a function of the initial surplus is characterized by a classical solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation. We study the optimal control policy and its properties. The interrelation between the parameters of the model plays a crucial role in the qualitative behavior of the optimal policy. E.g., for some ratios between a and b, quite unusual and at first ostensibly counterintuitive policies may appear, like short-selling a stock with a higher rate of return to earn lower interest, or borrowing at a higher rate to invest in a stock with lower rate of return. This is in sharp contrast with the unrestricted case, first studied in Hipp and Plum (2000), or with the case of no shortselling and no borrowing studied in Azcue and Muler (2009).
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1112.4007.
Date of creation: Dec 2011
Date of revision:
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-03 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hipp, Christian & Plum, Michael, 2000. "Optimal investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 215-228, October.
- Azcue, Pablo & Muler, Nora, 2009. "Optimal investment strategy to minimize the ruin probability of an insurance company under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 26-34, February.
- Anna Frolova & Serguei Pergamenshchikov & Yuri Kabanov, 2002. "In the insurance business risky investments are dangerous," Finance and Stochastics, Springer, vol. 6(2), pages 227-235.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.