## Project CEMAPRE internal

Title | Developments in ruin theory, the primal and dual risk models, ruin probabilities and dividend strategies for application in actuarial science and finance. Continuation. |

Participants | Renata Alcoforado, Agnieszka Bergel, Rui M.R. Cardoso, Alfredo Egídio dos Reis (Principal Investigator), Mónica Martinho, Eugenio Rodriguez Martinez |

Summary | In Risk Theory with application in the insurance business, the calculation of ruin probabilities for an insurance portfolio is essential both for risk assessment and premium calculation. Classical Ruin Theory has focused in the developments based on the Carmér-Lundberg risk model, we will call it the Primal Model. The so called Dual Risk Model has applications in Finance. We have managed to work together the two models, enhancing its connections [see Afonso et al. (2013)]. We worked both models taking advantage of their particular existing findings. We started first with the compound Poisson model, later we generalized 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 the insurance business and the Dual Model was targeted for applications in finance problems such as 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 2016 Ruin Theory project. In 2016 we targeted the generalisation to Phase-type models. We will continue in 2017 and intend to introduce claim dependence. We evaluated ruin probabilities for the process free of dividends barrier, then we set an upper and reflecting dividend barrier and dealt with different types of problems. Hence, we set the presence of two barriers: the reflecting and dividend barrier and the absorbing ruin barrier. Now, we want to evaluate the probability of getting a dividend or its complementary. We keep considering dividend strategies, such as the maximization of the expected discounted future dividends. We will 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. We can study the duration of a negative surplus and consider Parisian ruin. |