SFB 303 Discussion Paper No. B - 455
Author: Taksar, Michael I.
Title: Optimal Risk/Dividend Distribution Control Models.
Applications to Insurance
Abstract: The current paper presents a short survey of stochastic
models of risk control and dividend optimization techniques for
a financial corporation. While being close to consumption / investment
of Mathematical Finance, dividend optimization models possess special
which do not allow them to be treated as a particular case
of consumption/investment models.
In a typical model of this sort, in the absence of control,
the reserve (surplus) process, which represents the liquid
assets of the company, is governed by a Brownian motion with
constant drift and diffusion coefficient.
This is a limiting case of the classical Cramer-Lundberg model in
which the reserve is a compound Poisson process, amended by
a linear term, representing a constant influx of the insurance premiums.
Risk control action corresponds to
reinsuring part of the claims the cedent is required
to pay simultaneously diverting part of the premiums to a reinsurance
This translates into controlling the drift and the diffusion coefficient
of the approximating process. The dividend distribution policy consists
of choosing the times and the amounts of dividends to be paid put to
shareholders. Mathematically, the cumulative dividend process
is described by an increasing functional which may or may not be
with respect to time.
The objective in the models presented here is maximization of the
We will discuss models with different types of conditions imposed upon
a company and different types of reinsurances available, such as
noncheap, proportional in a presence of
a constant debt liability, excess-of-loss.
We will show that in most cases the optimal dividend distribution
scheme is of a barrier type, while the risk control policy depends
substantially on the nature of reinsurance available.
Keywords: Stochastic Control, Optimization; Reinsurance
JEL-Classification-Number: G22; G31
Creation-Date: August 1999
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