On the scattering problem for infinitely many fermions in dimensions d≥3d\geq3 at positive temperature

In this paper, we study the dynamics of a system of infinitely many fermions in dimensions $d\geq3$ near thermal equilibrium and prove scattering in the case of small perturbation around equilibrium in a certain generalized Sobolev space of density operators. This work is a continuation of our previous paper, and extends the important recent result of M. Lewin and J. Sabin of a similar type for dimension d=2. In the work at hand, we establish new, improved Strichartz estimates that allow us to control the case $d\geq3$

The implication of the hyperbolic discount model for annuitisation decisions

The low demand for immediate annuities at retirement has been a long-standing puzzle. We show that a hyperbolic discount model can explain this behaviour and results in the attractiveness of long-term deferred annuities. With a set of benchmark assumptions, we find that retirees would be willing to pay a much higher price than the actuarial fair price for annuities with longer deferred periods. Moreover, if governments were to introduce a pre-commitment device which requires pensioners to make annuitisation decisions around ten years before retirement, the take up rate of annuities could become higher