Risk measures and optimal reinsurance: finding a connection via BSDEs

Brachetta Matteo, Politecnico of Mialn
Confortola Fulvia, Politecnico of Milan
Sgarra Carlo, University of Bari

A reinsurance contract allows an insurance company to transfer part of the risk to another company, the reinsurer, in order to reduce the future losses, which are usually modeled as a marked point process (see [1]). 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, see e.g. [2]. In [3] the authors 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 different risk models with jumps. References [1] H. Schmidli, Risk Theory, Springer International Publishing, 2018. [2] M. Brachetta,C. Ceci A BSDE-based approach for the optimal reinsurance problem under partial information, Insurance: Mathematics and Economics, 95(2020), 1 - 16. [3] A. Calvia, E. Rosazza Gianin Risk Measures and Progressive Enlargement of Filtration: A BSDE Approach, SIAM Journal on Financial Mathematics, 11(2020), 815 - 848.

Area: CS6 - Stochastic optimal control, BSDEs, and applications (Fulvia Confortola and Alessandro Calvia)

Keywords: Backward Stochastic Differential Equations, Stochastic Control, Finance

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