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Speaker(s): Li Shen (Lyon Business School), Olivier Le Courtois (Lyon Business School)
This work discusses the profit testing for a life insurance company that issues modern life insurance contracts, which are participating contracts, universal life contracts and variable annuities with guarantees. Modern life insurance contracts are closely linked to the performance of investments.
The authors use Gaussian and non-Gaussian assumptions to model the performance. Specifically, the correlated Gaussian processes and the correlated Variance Gamma processes are considered. In order to decide which model is better, the authors compare the two models under four statistical tests: maximum values of the log-likelihood, Akaike Information Criterion, Schwarz Based Criterion and Vuong test.
The Variance Gamma model appears better than the Gaussian model according to all these statistical tests. Using the stochastic profit testing techniques introduced in Dickson, Hardy, and Waters (2013), we examine the influence of each parameter of the financial models and of the financial models themselves on the profit testing indexes. Higher net present values are anticipated with the higher asset returns, lower volatilities, larger positive jumps or smaller negative jumps. The Variance Gamma model results in more conservative predictions: it predicts lower expected values but larger standard deviations for net present values and it also predicts larger probabilities of negative net present values.