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Applied
Math Seminar
Quarter 2001
3:15 - 4:15 p.m.
Sloan Mathematics Corner
Building 380, Room 380-C
Friday, November 2, 2001
Xin Guo
Mathematical Sciences Department
IBM T J Watson Research Center
To hire or not to hire
Abstract:
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The recent economic situation has changed the perspective
of many dotcoms. What optimal hiring strategy should a dotcom adopt to
maximize its profit and survival?
We consider a risk management problem for a company with the following
parameters: a constant liability payment rate, return/risk proportional
to the size of the business unit, and an internal competition factor between
different units. The goal is to maximize the expected present value of
the total dividend distributions, via controls of the size of the business
unit and the dividend payoff.
We derive explicit solutions and optimal policies via a delicate analysis
of the corresponding Hamilton-Jacobian-Bellman equations. Our analytical
results shows considerable consistency with common business hunch; for
example, it shows that under the optimal strategy, a company with debt
will go bankrupt in finite time with probability one while the survival
chances improve for a company free of debt. We will also discuss some
relevant applications in the re-insurance business.
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