## Project CEMAPRE internal

Title | Ruin and dividend problems in the primal and dual risk models, for application in actuarial science and nance. Continuation. |

Participants | Lourdes B. Afonso, Renata Alcoforado, Alana Azevedo de Macedo, Agnieszka Bergel, Rui M.R. Cardoso, Alfredo Egídio dos Reis (Principal Investigator), Gracinda R. Geuerreiro, Eugenio Rodriguez Martinez |

Summary | In Risk Theory for insurance application, the calculation of ruin probabilities for an insurance portfolio is essential both for risk assessment and premium calculation. Classical Ruin Theory has focused on the Carmér-Lundberg risk model, or Primal Model. Related to this, the Dual Risk Model was developed more recently, with applications to Finance. We have managed to work together the two models, enhancing its connections [see Afonso et al. (2013)]. We started first with the compound Poisson model, later we generalised for some other sort of renewal models, Erlang and Phase-type [see Rodriguez-M. et al. (2015) and Bergel et al. (2016)]. The Primal Model was developed for applications the insurance business and the Dual Model for some sorts of finance problems, an example is modeling the capital of an economic activity involved in research and development [e.g. see Bayraktar & Egami (2008)]. See also Bergel and Egidio dos Reis (2016). This work is a 2-3 year project. We refer to our 2017 Ruin Theory project. In 2018 we will continue and complete with the phase-type renewal models and develop claim dependence [see Li et al. (2017)]. In the dual approach we complete the evaluation of the probability of getting a dividend, and the distribution of a single dividend. We keep working on dividend strategies, such as the maximisation of the expected discounted future dividends. For all this we follow the lines given by Afonso et al. (2011). Also, we intend to work on the "Gerber-Shiu (2005) type" transforms adapted to the dual model, in the primal model we consider the study of the duration of a negative surplus and consider Parisian ruin. |