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The aim of this paper is to calibrate the Longstaff, Mithal and Neis (2005) model (LMN model) based on the J-law (see Jerbi (2015) to implement the credit risk in the economic scenarios generator. The LMN model, based on the assumptions of the normality of the risks is used to establish a link between the spread, the probability of default and the liquidity risk. The related assumptions seem unrealistic given the depth of the distribution that characterizes the financial and economic data. In this context, we develop an LMN model based on the J-law taking into account the effects of Skewness and Kurtosis related to the two series of the CDS premium and the corporate bond prices. We use a simulated data that are from January 2009 to December 2016. We estimate the model parameters. The LMN model based on the J-law fit better with the reality than the one based on the normal Law.      

In recent years the financial markets known a rapid development and become more and more complex. So, many regulatory requirements, focused on banks as well as insurance sector, have been developed. These regulatory are concentrated essentially on business risk control and required capital to cover risks. These requirements have influenced the asset allocation issue in insurance industry. These requirements have influenced the asset allocation issue in insurance industry. This section is interested by this issue. In first time it highlights some research works in this issue. Then we will investigate the relation between Solvency and optimal asset allocation. Finally we will explore the principal used methods in modeling asset and in choosing the optimal portfolio composition.