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### The Natural Domain For Law Invariant Risk Functionals

**Optimization**

Speaker: | Alois Pichler, University of Trondheim & University of Vienna |

Location: | 3106 MSB |

Start time: | Fri, Feb 14 2014, 11:00AM |

This talk addresses the objective function in stochastic optimization, which is often the expectation or a risk measure (i.e., a risk functional). While the expectation is nicely defined on L1 , the natural domain of a risk functional is not so immediate. We introduce a new Banach space, which is generated by the risk functional itself and which naturally constitutes the domain. The risk functional is continuous with respect to the norm of the new space. Typically, the new space is strictly larger than an associated Lp space. In addition the dual of this space is investigated, and its properties are elaborated.