## 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 |

Participants | Renata Alcoforado, Agnieszka Bergel, Rui M R Cardoso, Alfredo Egídio dos Reis (Principal Investigator), 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. Traditional 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 [see Rodriguez-M. et al. (2015)]. 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)]. We target developing more general models such as Phase-type. Also, we intend to introduce claim dependence. We will be evaluating ruin probabilities for the process free of dividends barrier, then we set an upper and reflecting dividend barrier and deal with different types of problems. Hence, we are in the presence of two barriers: the reflecting and dividend barrier and the absorbing ruin barrier. In this situation the probability of ultimate ruin is one, irrespective of having reached the dividend barrier, before or not. We want to evaluate the probability of getting a dividend or its complementary, the probability of ruin before reaching the dividend barrier. Then we consider dividend strategies, such as the maximization of the expected discounted future dividends. We intend to follow the lines given by Afonso et al. (2011) and Rodriguez-M. et al. (2015). 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. |