Study On Pooled Annuity Fund With Non-Poisson Jump

Compared to private life annuity, pooled annuity funds provide another manner against economic risk that people may experience in their twilight years. To the elderly who facing retirement, annuity products are able to play a very active role. However, for both buyers and sellers, that the purchaser and (normally) the insurance company, there are still some problems in need of improvement about the traditional pension. In this paper first we introduce the main features of pooled annuity funds and some advantages. Then we describe the composition, enforcement and actual operation in practice. As pooled annuity funds create a few differences from other insurance products, this may bring us new questions, which explains the importance of establishing an accurate model. Next we'd work over the population model of pooled annuity funds, make changes on the original Poisson assumption in order to become closer to the actual situation and propose new mortality assumptions where exist only two states . On this basis we'll derive the distribution law of population groups and death progress under a certain survival probability, and establish a more realistic and more complex model. After that we consider the pooled annuity funds members'dynamic personal assets problem while in the money market and stock market involving some consumption level and investment rate, accounting a SDE with jumps by the effects of population change. Adopting the semi-martingale Itōformula under such cases we get the solution of personal assets following a simple analysis of its characteristics. During the final part we solve the optimal portfolio strategy with the CRRA utility. By using stochastic optimization theory we obtain the HJB equation, derive the optimal investment strategy and the ordinary differential equations that the optimal consumption strategy satisfies, further we discuss the optimal strategy of this issue under the exponential utility function.