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Risk Analysis in Finance and Insurance (E-book)
Financial and insurance markets always operate under various types of uncertainties
that can affect the financial position of companies and individuals.
In financial and insurance theories, these uncertainties are usually referred to
as risks. Given certain states of the market, and the economy in general, one
can talk about risk exposure. It is expected that individuals, companies, and
public establishments that aim to accumulate wealth should examine their
risk exposure. The process of risk management consists of a sequence of corresponding
actions over a period of time that are designed to mitigate the level
of risk exposure. Some of the main principles and ingredients of risk management
are qualitative identification of risk, estimation of possible losses,
choosing the appropriate strategies for avoiding losses and for shifting the risk
to other parts of the financial system, including analysis of the involved costs,
and using feedback for developing adequate controls.
The first six chapters of this book are devoted to the financial market
risks. We aim to give an elementary and yet comprehensive introduction to
the main ideas, methods, and stochastic models of financial mathematics. The
probabilistic approach appears to be one of the most efficient ways of modeling
uncertainties in financial markets. Risks (or uncertainties of financial
market operations) are described in terms of statistically stable stochastic experiments,
and therefore estimation of risks is reduced to the construction
of financial forecasts adapted to these experiments. Using conditional expectations,
one can quantitatively describe these forecasts given the observable
market prices and events. Thus, it can be possible to construct dynamic hedging
strategies and those for optimal investment. The foundations and key
concepts of the modern methodology of quantitative financial analysis are the
main focus of Chapters 1–6.
Insurance against possible financial losses is one of the key ingredients of
risk management. However, the insurance business is an integral part of the
financial system. Chapters 7–8 focus on the problems of managing insurance
risks. Multiple intrinsic connections between insurance risks and financial risks
are also considered.
Our treatment of insurance risk management demonstrates that methods
of risk evaluation and management in insurance and finance are interrelated
and can be treated using a single integrated approach. Estimations of future
payments and their corresponding risks are key operational tasks of financial
and insurance companies. Management of these risks requires an accurate
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viii Introduction
evaluation of the present values of future payments, and therefore the adequate
modeling of (financial and insurance) risk processes. Stochastic analysis is one
of the most powerful tools for such modeling, and it is the fundamental basis
of our presentation.
Finally, we note that probabilistic methods were used in finance and insurance
since the early 1950s. They were developed extensively over the past
decades, especially after the seminal papers by F. Black and M. Scholes and
R. C. Merton, published in 1973.
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