The Institute for Statistics and Mathematics is pleased to invite you to the next research seminar, taking place on campus:

Claudia Ceci (Department of Methods and Models for Economics, Territory and Finance; University of Rome “La Sapienza”)
A BSDE-Based Optimal Reinsurance in a Model With Jump Clusters
Friday, June 21, 2024, 10:30 am, Building D4, Room D4.0.127

Abstract:
We investigate the optimal reinsurance problem in a risk model with jump clustering features for general reinsurance contracts and premiums. This modeling framework is inspired by the concept initially proposed in [3], combining Hawkes and Cox processes with shot noise intensity models. Specifically, these processes describe self-exciting and externally excited jumps in the claim arrival intensity, respectively. The insurer aims to maximize the expected exponential utility of terminal wealth. We discuss the problem under both full and partial information. In the complete information framework, we compare two different methodologies: the classical stochastic control approach based on the Hamilton-Jacobi-Bellman (HJB) equation and a backward stochastic differential equation (BSDE) approach. Differently from the classical HJB-approach, the BSDE method enables us to solve the problem without imposing any requirements for regularity on the associated value function. Furthermore, we investigate the problem when the insurance company has restricted information about the claim arrival intensity. Using nonlinear filtering techniques, we reduce the partially observable problem into an equivalent problem under full information which is solved by applying a BSDE-approach. Note that due the infinite dimensionality of the filter process, the HJB-method cannot be applied. Finally, we discuss optimal strategies and provide explicit results in some relevant cases. The talk is based on the papers [1] and [2].

We aim to stream all on-campus talks via Zoom. A direct link to the stream will be posted on our website.

For further information and the seminar schedule, please see:
www.wu.ac.at/en/statmath/research/resseminar