The Economic Theory of Annuities 3 pdf
The Economic Theory of Annuities by Eytan Sheshinski_1 pdf
... tends to mitigate the effects of adverse selection because,when bundled, the negative correlation between the costs of theseproducts reduces the overall variation of the costs of the bundle withindividual ... chapter15.tex 132 •Chapter 15bundles of annuities and long-term care insurance (at ages 65 and 75)and found that the cost of the hypothetical bundle was lower by 3 to 5percent compared to the cost of these ... y,(14.24)where a is the amount of annuities, z is expected lifetime, b is the amount of life insurance (=bequests), and y is the amount of the numeraire. Utility of consumption, u, and the utility from...
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The Economic Theory of Annuities by Eytan Sheshinski_6 pdf
... (x)F (x)dxdz(5 .33 )Optimum consumption decreases with age, its rate of decline beingequal to the product of the inverse of the coefficient of relative riskaversion and the hazard rate.Optimum ... totalconsumption in the second period. The second term is the sum of the expected utilities of two surviving individuals, while the third is the expected utility of one survivor. The budget constraint ... that in the absence of perfect pooling of longevity risks,individuals leave unintended bequests. The level of bequests depends on the age at death and hence is random. For an elaboration of the...
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The Economic Theory of Annuities by Eytan Sheshinski_3 ppt
... description of the motivation for and the stipulations of these annuities from a textbookfor actuaries:These are usually effected to avoid the disappointment that is often felt in the event of the ... to make the price of period-certain annuities commensurate with the price of regular annuities. These annuities are available in the United Kingdom, where they arecalled protected annuities. ... follow the standardassumption that the sign of the price of each good changes in the oppositedirection to the sign of profits from sales of this good. The following assumption about the relation...
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The Economic Theory of Annuities by Eytan Sheshinski_4 ppt
... 0.51 838 6 0. 639 64885 0 .31 8805 0.474641 0.479222 0.60267086 0.279 836 0. 435 065 0. 439 561 0.5 634 9187 0.242486 0 .39 4715 0 .39 9797 0.52227888 0.207251 0 .35 4020 0 .36 036 4 0.47 934 489 0.1745 63 0 .31 3509 ... 0 .32 1725 0. 435 21490 0.144767 0.2 737 76 0.28 433 8 0 .39 05 83 91 0.118099 0. 235 444 0.248 635 0 .34 625692 0.094678 0.199121 0.214996 0 .30 2021 93 0.074510 0.16 536 4 0.1 837 35 0.26088994 0.057496 0. 134 641 ... 0.1550 93 0.22 235 595 0.0 434 97 0.107 438 0.129260 0.18702096 0. 032 2 63 0.084018 0.10 633 2 0.15529297 0.0 234 72 0.0644 13 0.08 631 3 0.12 738 298 0.016760 0.0484 53 0.069084 0.1 032 2899 0.011757 0. 035 806...
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The Economic Theory of Annuities by Eytan Sheshinski_5 doc
... (4.4).When there is a positive rate of interest on assets, the competitive rate of return on annuities is equal to the rate of interest plus the hazard rate. The reason is obvious: The issuers of annuities ... condition the rate of return on annuities on the level of theseexpenditures by annuitants. Let the rate of return faced by individuals atAugust 3, 2007 Time: 04:13pm chapter07.texMoral Hazard• 53 age ... expectancy of the owners. The other risk class experiences aloss for the opposite reason.Another important implication of the fact that in equilibrium con-sumption is independent of the state of nature...
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The Economic Theory of Annuities by Eytan Sheshinski_8 potx
... accross states of nature). Sequential annuity marketequilibrium is characterized by the purchase of long-term annuities, shortsale of some of these annuities later on, or the purchase of additionalshort-term ... longevity risk. Further, to respond to the desire of individuals forflexibility, the model should allow for short sales of annuities purchasedearly or the purchase of additional short-term annuities ... variety of refundable annuities. Type ri≥ 0 annuities are annuities that each guar-antee a refund of riwhen presented by the holder in period 1. Thereare k types of such refundable annuities, ...
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The Economic Theory of Annuities_3 pdf
... andefficiency (1/εh) considerations. The implication of ( 13. 14) for the optimum pricing of annuities depends on the welfare function, W, and on the joint distribution of incomes, (y1, ,yH), and ... Pricing of Annuities •1 13 13. 3 Second-best Optimum Pricing of Annuities Governments do not engage, for well-known reasons, in unconstrainedlump-sum redistributions of incomes. In contrast, most annuities are ... distribution of bequests that become initial endowments of asubsequent generation. Thus, analysis of the long-term effects of changesin longevity has to focus on the (ergodic) evolution of the distributionof...
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The Economic Theory of Annuities_4 pdf
... follow the standardassumption that the sign of the price of each good changes in the oppositedirection to the sign of profits from sales of this good. The following assumption about the relation ... textbookfor actuaries:These are usually effected to avoid the disappointment that is often felt in the event of the early death of an annuitant. The calculation of yield closelyfollows the method used ... annuities. These annuities are available in the United Kingdom, where they arecalled protected annuities. It is interesting to quote a description of the motivation for and the stipulations of these annuities...
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Sample chapter for the economic theory of annuities_1 pdf
... Substituting the above definition of h(z,α,g),we obtain (12.4).August 18, 2007 Time: 11:06am chapter 13. texUtilitarian Pricing of Annuities •1 13 13. 3 Second-best Optimum Pricing of Annuities Governments ... fundamentalequation of stable population theory: ∞0e−gzF (z,α)b(z) dz = 1, (12.4)where b(z) is the age-specific birthrate (fertility) function. The magnitude of g depends implicitly on the form of the ... andefficiency (1/εh) considerations. The implication of ( 13. 14) for the optimum pricing of annuities depends on the welfare function, W, and on the joint distribution of incomes, (y1, ,yH), and...
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Sample chapter for the economic theory of annuities_2 pdf
... follow the standardassumption that the sign of the price of each good changes in the oppositedirection to the sign of profits from sales of this good. The following assumption about the relation ... annuities. These annuities are available in the United Kingdom, where they arecalled protected annuities. It is interesting to quote a description of the motivation for and the stipulations of these annuities ... textbookfor actuaries:These are usually effected to avoid the disappointment that is often felt in the event of the early death of an annuitant. The calculation of yield closelyfollows the method used...
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