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Worst-case portfolios with risk processes (Paperback)
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Worst-case portfolios with risk processes (Paperback)
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The problem of optimizing investments in the presence of random
risk is of real concern for insurance companies. Like ordinary
investors, they have a set of risky and non-risky assets as a
choice to invest into. But their wealth depends not only on how
they allocate the money, but also on the occurring claims that they
have to pay for. These claims arrive randomly, and therefore the
risk that they represent is not hedgeable. This work explores the
investment strategies which take this risk into account. Chapter 1
introduces the model (a diffusion process) for the available
assets. Chapter 2 formulates and presents solutions of various
optimization problems for the investor, among which maximizing
exponential utility of the final wealth and minimizing probability
of ruin. It will be shown that the mentioned problems both result
in the constant investment independent of the level of wealth of
the company. Chapter 3 covers the extension of the model with a
possibility of a crash modelled as a fall of the stock prices which
get highly correlated at the moment of the crash. The optimal
strategy for minimizing exponential utility of final wealth will
turn to be the one which is indifferent between occurrence of the
highest crash possible and its non-occurrence at all.
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