q-fin updates on arXiv.org
Fri, 13 Mar 2020 06:01:48 GMT language
The inf-convolution of risk measures is directly related to risk sharing and
general equilibrium, and it has attracted considerable attention in
mathematical finance and insurance problems. However, the theory is restricted
to finite (or at most countable in rare cases) sets of risk measures. In this
study, we extend the inf-convolution of risk measures in its convex-combination
form to an arbitrary (not necessarily finite or even countable) set of
alternatives. The intuitive principle of this approach is to regard a
probability measure as a generalization of convex weights in the finite case.
Subsequently, we extensively generalize known properties and results to this
framework. Specifically, we investigate the preservation of properties, dual
representations, optimal allocations, and self-convolution.