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Stochastic Finance, 4th Edition by Alexander Schied, Hans Föllmer

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11Dynamic risk measures

In this chapter we return to the quantification of financial risk in terms of monetary risk measures. As we saw in Chapter 4, a monetary risk measure specifies the capital which is needed in order to make a given financial position acceptable. In our present dynamic setting, the capital requirement at a given time will depend on the available information and will thus become a random variable. In Section 11.1 we introduce the notion of a conditional monetary risk measure. In the convex case we prove a conditional version of the robust representation theorem which involves the conditional expected losses under various models Q and a conditional penalization of these models.

As time varies, both the capital requirement and ...

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