At, in, or near retirement, investors need to make specific decisions about how they are going to use their savings to generate income during retirement. These decisions include deciding how much to invest in annuities, how to invest non-annuitized assets, and how much to withdraw from the non-annuitized assets each year. Retired investors face the risk of running out of assets while they still need the income. Since the income needs usually remain until death, this risk is often called “longevity risk.” Furthermore, many investors wish to leave some portion of their retirement accounts as part of their estates.
Retirement income management is choosing a combination of annuity, withdrawal, and investment strategies such that it is unlikely that the investor will run out of money before death while achieving the investor’s financial goals. In making these decisions, the investor must manage both market risk and longevity risk.
A lamination on a circle is an equivalence relation on the points of the circle. Laminations can be induced on a circle by a map that is continuous on the closed disc and injective in the interior. Such laminations are characterized topologically, as being flat and closed. In this paper we investigate the conditions under which a closed, flat lamination is induced by a conformal mapping.
A substantial body of research has documented increasing wage inequality in industrialized countries. Since the late 1970s and continuing through the mid-2000s, overall wage inequality has been increasing in the U.S. (e.g. Autor et al., 2008; Lemieux, 2006a), Germany (e.g. Dustmann et al., 2009), the UK (e.g. Machin and Van Reenen, 2008), Canada (e.g. Boudarbat et al., 2006), and Australia (e.g. ?). As possible explanations of these trends, most of the literature has focused on skill-biased technological change (SBTC), the supply of skilled workers, changes in institutions such as the decline in unionization and changes in the minimum wage, as well as changes in social norms. SBTC has been the most prominent explanation (see the survey by Katz and Autor, 1999), which argues that the increase in demand for skills is stronger than the simultaneous increase in the supply, leading to an increase in wage inequality.
