Optimal risk control for a large corporation in the presence of returns on investments

Bjarne Højgaard and Michael Taksar
Additional contact information
Bjarne Højgaard: Department of Mathematical Sciences, Aalborg University, Fredrik Bajers VEJ 7G, 9220 Aalborg Øst, Denmark
Michael Taksar: Department of Appl. Math. and Stat., SUNY - Stony Brook , New York, USA Manuscript

Finance and Stochastics, 2001, vol. 5, issue 4, 527-547

Abstract: This paper represents a model for the financial valuation of a firm which has control on the dividend payment stream and its risk, as well as potential profit by choosing different business activities among those available to it. Furthermore the company invests its free reserve in an asset, which may or may not contain an element of risk. The company chooses a dividend payment policy and we associate the value of the company with the expected present value of the net dividend distributions (under the optimal policy). One of the examples could be a large corporation such as an insurance company, whose liquid assets in the absence of control and investments fluctuate as a Brownian motion with a constant positive drift and a constant diffusion coefficient. We interpret the diffusion coefficient as risk exposure, while drift is understood as potential profit. At each moment of time, there is an option to reduce risk exposure, simultaneously reducing the potential profit, like using proportional reinsurance with another carrier for an insurance company. The company invests its reserve in a financial asset, whose price evolve as a geometric Brownian motion, with mean rate $r>0$ and diffusion constant $\sigma_P\geq 0$. Thus $\sigma_P=0$ corresponds to investments in a riskless bank account. The objective is to find a policy, consisting of risk control and dividend payment scheme, which maximizes the expected total discounted dividends paid out until the time of bankruptcy. We apply the theory of controlled diffusions to solve the problem. We show that if the discount rate c is less than r, the optimal return function is infinite. If $r=c$ the return function is finite for all $x

Keywords: Dividend pay-out; proportional reinsurance; diffusion models; stochastic control theory; HJB equation; singular control (search for similar items in EconPapers)
JEL-codes: C61 G22 (search for similar items in EconPapers)
Date: 2001-10-04
Note: received: October 1999; final version received: January 2001
References: Add references at CitEc
Citations: View citations in EconPapers (23)

Downloads: (external link)
http://link.springer.de/link/service/journals/00780/papers/1005004/10050527.pdf (application/pdf)
Access to the full text of the articles in this series is restricted

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:5:y:2001:i:4:p:527-547

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().