tailieunhanh - Library Introduction to The Economic Theory_7

cuốn sách có chứa nhiều công thức tính toán bảo hiểm hữu ích cho chức năng tử vong cụ thể (chẳng hạn như chức năng Gompert-Makeham) cung cấp một sự phù hợp tốt với các dữ liệu. Nó cũng xem xét tác động của lợi nhuận đầu tư ngẫu nhiên để định giá tiền trợ cấp hàng năm, một chủ đề không được thảo luận trong cuốn sách này | Introduction 11 References to Actuarial Finance An encyclopedic book of actuarial calculations with different mortality functions is Bowers et al. 1997 published by the Society of Actuaries. Duncan 1952 and Biggs 1969 provide formulas for variable annuities that is for annuities with stochastic returns. For an overview of life insurance formulas see Baldwin 2002 . Another useful book with rigorous mathematical derivations is Gerber 1990 . Milevsky s 2006 recent book contains many useful actuarial formulas for specific mortality functions such as the Gompertz-Makeham function that provide a good fit with the data. It also considers the implications of stochastic investment returns for annuity pricing a topic not discussed in this book. CHAPTER 16 Financial Innovation Refundable Annuities Annuity Options The Timing of Annuity Purchases In previous chapters in particular chapters 8 and 10 we have seen that in the presence of a competitive annuity market uncertainty with respect to the length of life can be perfectly insured by an optimum policy that invests all individual savings in long-term annuities. The implication of associating annuity purchases with savings is that the bulk of annuities are purchased throughout one s working life. This stands in stark contrast to empirical evidence that most private annuities are purchased at ages close to retirement in the United States the average age of annuity purchasers is 62 . A recent survey in the United Kingdom Gardner and Wadsworth 2004 reports that half of the individuals in the sample would given the option never annuitize. This attitude is independent of specific annuity terms and prices. By far the dominant reason given for the reluctance to annuitize was a preference for flexibility. For those willing to annuitize the major factors that affected their decisions were health those in good health were more likely to annuitize education household size less likely to annuitize as household size increases and