Evolutionary algorithms (EAs) are random optimization methods inspired by genetics and natural selection, resembling simulated annealing. We develop a method that can be used to find a meaningful tradeoff between the difficulty of the analysis and the algorithms' efficiency. Since the case of a discrete search space has been studied extensively, we develop a new stochastic model for the continuous n-dimensional case. Our model uses renewal processes to find global convergence conditions. A second goal of the paper is the analytical estimation of the computation time of EA with uniform mutation inside the (hyper)-sphere of volume 1, minimizing a quadratic function.
In this paper, we present recursive formulae for the ruin probability at or before a certain claim arrival instant for some particular continuous time risk model. The claim number process underlying this risk model is a renewal process with either Erlang or a mixture of exponentials inter-claim times (ICTs). The claim sizes (CSs) are independent and distributed in Erlang's family, i.e., they can have different parameters, which yields a non-homogeneous risk process. We present the corresponding recursive algorithm used to evaluate the above mentioned ruin probability and we illustrate it on several numerical examples in which we vary the model's parameters to assess the impact of the non-homogeneity on the resulting ruin probability.
KEYWORDSContinuous time risk process, ruin probability, renewal process, nonhomogeneous claim sizes, Erlang distribution, mixture of exponentials distribution.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.