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Abstract. Actuarial theory in a stochastic interest rate environment is an active research area in life insurance. Installment joint life insurance actuarial theories are one of the key contents in actuarial theory. In this study, an interest force accumulation function model with a Wiener process and a Poisson process is proposed as the basis for the installment joint life insurance actuarial models. Then increasing life insurance actuarial models with the consumer price index are approximated. With the proposed model, the net single premium, net level premium, the reserves and the risk of loss model are provided. The actuarial models in the paper provide a feasible method to calculate the life insurance premium.

In the context of the global population aging, pension issue has become highly important and pressing national concerns. Therefore, to further improve and perfect pension system, especially for the pension insurance system, has a very important social value. From the following aspects of old-age insurance personal accounts actuarial model: The first, deduced fixed interest rate, monthly payment of personal accounts pension actuarial model; the second, taking into account the impact of different factors on interest rates, constructed in the form of joint modeling standard Wiener process and Poisson process personal accounts pension actuarial model formula is derived.

In order to quantify the demand elasticity of China's imported crude oil, a long-run stable relationship is estimated among the crude oil import, income and crude oil prices by the autoregressive distributed lag (ARDL) bound testing approach over the period 1999-2009. Empirical results show that the short and long-run price elasticities of imported crude oil are positive and inelastic, and the long-run income elasticity is near unity. Moreover, a stable equilibrium is established between the imported crude oil and its determinants by adding a break point into the model and providing evidence of the liability of the obtained elasticities. Finally, the corresponding reasons for the conclusions are presented.