Good deal measurement in asset pricing: Actuarial and financial implications

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.