A quantitative spatial Risk Measure for Extreme Events

The environmental or climatic change events are often represented by the spatial data, as well as in extreme case. So, taking into account the spatial features of these events is essential for any risk to be assessed. Most of the previous proposed spatial risk measures considered the dispersion of the loss function as the severity amount of the risk. This is because no spatial information can be provided by the expectation of this loss of function. In the present paper, we moved forward in developing the quantitative risk measures by proposing one combination between the spatial features and severity amount at the same time. Asymptotic behavior and its axiomatic properties have been well studied for this proposed spatial risk measure. A simulation study has been carried out to verify the theoretical results.