Annuity, bequests, fertility and longevity in overlapping generations models

Our thesis has focused on the problem of ageing and by combination of theoretical and numerical methods we were able to show that to insure against the longevity risk, individual decisions are very different from macroeconomic optimal choices. Private annuities may be attractive to some healthy individuals but opening up an annuity market is by no means beneficial to the society. The value of annuities (annuity market) should be examined in a general equilibrium framework, in tandem with bequest motives. We also explored the optimal fertility for the society, which generally does not coincide with individual choices in {it laissez faire}. With Child taxes and intergenerational transfers, however, the government may induce individuals to choose the optimal quantity and quality of children the society needs. After all, with the prevalence of public pension programs, what provides a better insurance to the old generation than a well-educated right-sized population of the next generation?