Risk measures and optimal reinsurance: finding a connection via BSDEs

The aim of this talk is to connect utiility maximization problems and the optimization of dynamic
risk measures, which are usually considered as two different branches or approaches to financial
problems.
A reinsurance contract allows an insurance company to transfer part of the risk to another company,
namely the reinsurer, in order to reduce the future losses, which are usually modeled as a marked
point process. Finding the optimal reinsurance agreement translates into a stochastic control
problem for the insurer. Recently, some authors showed that the optimal value process for the utility
maximization problem can be characterized as the solution of a BSDE with jumps. In
other works, it is proved that some BSDEs induce dynamic risk measures, which can be financially
interpreted as a default time and an associated mark. In this talk we aim to explore the properties of
the risk measure induced by the optimal reinsurance policy under dierent risk models with jumps.
The talk is based on a work in progress with Fulvia Confortola (Politecnico of Milan).