Stochastic Process

In this paper we focus on the computational issues in the development of internal models, according to the technical requirements established by the Solvency II project. In particular, we consider the val-uation of profit-sharing life insurance policies. Numerical simulations must provide reliable estimates of the relevant quantities involved in the contracts; therefore, valuation processes have to be performed by accurate algorithms able to provide solutions in a suitable turnaround time. To gain in accuracy we propose a change of numéraire in the stochastic processes for risks sources, thus providing estimates under the forward risk-neutral measure. To speed-up the simulation process we use high performance computing environments. We develop algorithms based on the parallelization of Monte Carlo method, using both the risk-neutral and the forward measure, thus providing numerical procedures capable to trade-off accuracy and efficiency.

The extraction of modal parameters from a real structure represents an important step in modal analysis. When only the output signal is available in an experiment, the system identification process is referred as operation modal analysis (OMA). Applications of those cases are fond for structures where the ambient excitation (wind, traffic, waves, nearby systems, etc.) can not be removed or is the only possible one. Once the input signals can not be measured, some assumptions in their random nature are needed together with a stochastic modeling of the system. Among several methods, the stochastic subspace identification (SSI) has been shown to be a consistent one and, therefore, was chosen to be used in this paper. Here, the modal analysis of a system under wind load is studied. The fluid-structure interaction force is usually not easy to be represented and its whiteness (assumption made in most of OMA methods) can not be easily conformed. In this way, a two floor building model is used for experimental validation, where different fluid-structure interaction were created. The paper begins with a presentation of the discrete state space model followed by the SSI theory. Two popular SSI algorithms are presented: covariance-driven and data-driven. A efficient way to select the correct parameters for the method is discussed together with a procedure to analyze the results. To exemplify the identification process, experimental results are shown and the identified parameters are listed. As conclusion, the wind has been shown to be a good excitation source for OMA once the system has been correct identified.