Project CEMAPRE internal
| Title | Ruin and dividend problems in the primal and dual risk models, for application in actuarial science and finance (Continuation) |
| Participants | Renata Alcoforado, Alana Azevedo de Macedo, Agnieszka Bergel, Rui M.R. Cardoso, Mercè Clarammunt, Alfredo Egídio dos Reis (Principal Investigator), Abraham Hernández-Pacheco, Maité Marmol, Alexandra Moura, Eugenio Rodriguez Martinez |
| Summary | We consider the Carmér-Lundberg risk model for insurance application, or Primal Model, and the Dual Risk Model with applications to Finance. We first have worked both models together enhancing its connections [see Afonso et al. (2013)], starting first with the compound Poisson model. Later, we generalised for other sort of renewal models, Erlang and Phase-type [see Rodriguez-M. et al. (2015) and Bergel et al. (2017)]. Also see Bayraktar & Egami (2008)] and Bergel and Egidio dos Reis (2016). We refer to our 2018 Ruin Theory project. In 2019 we continued working in the scope of the phase-type renewal models and started developing by introducing claim dependence [see Li et al. (2017)], both in the claim counts as well as for severities. Still in the claim independent case, basing on the dual model approach we worked on several ruin and dividend measures, completed the evaluation of the probability of getting a dividend, and the distribution of a single dividend. We worked on future dividend expectations following the lines given by Afonso et al. (2013). We also worked on the number of gains down to ruin and to reach a given upper target. We completed this topic by working a special type of "Gerber-Shiu (2005) transform", adapted to the dual model. We worked a penalty function under randomised observations, random observations follow a Poisson process, and gain arrivals are more general renewal arrivals. For next project periods we will be extending this study for other renewal random observations. Besides, introduce claim dependence to our models, work in the primal model where we can consider the study of the duration of a negative surplus, as well as Parisian ruin, ruin probability approach for optimisation of pension fund investments. Also, we will be working in cyber risk behaviour and measuring. |