Publication: Good deal measurement in asset pricing: Actuarial and financial implications
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2016-09-12
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Abstract
We will integrate in a single optimization problem a risk measure
beyond the variance and either arbitrage free real market quotations or financial pricing
rules generated by an arbitrage free stochastic pricing model. A sequence of investment
strategies such that the couple (risk; price) diverges to (-∞, -∞) will be called
good deal. We will see that good deals often exist in practice, and the paper main
objective will be to measure the good deal size. The provided good deal measures will
equal an optimal ratio between both risk and price, and there will exist alternative
interpretations of these measures. They will also provide the minimum relative (per
dollar) price modification that prevents the good deal existence. Moreover, they will
be a crucial instrument to detect those securities or marketed claims which are over
or under-priced. Many classical actuarial and financial optimization problems may
generate wrong solutions if the used market quotations or stochastic pricing models
do not prevent the good deal existence. This fact will be illustrated in the paper,
and it will be pointed out how the provided good deal measurement may be useful to
overcome this caveat. Numerical experiments will be yielded as well.
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Risk measure, Compatibility between prices and risks, Good deal size measurement, Actuarial and financial implications