Sample chapter for the economic theory of annuities 2 pdf
Sample chapter for the economic theory of annuities_1 pdf
... =− (1 + p 1 )(1 + p 2 )λ 2 W 2 1 W 2 2 [ W 11 W 2 2 − 2W 12 W 1 W 2 + W 22 W 2 1 ] −(1 + p 1 ) W 2 u (c ∗ 2 ) − (1 + p 2 ) W 1 u (c ∗ 1 ). (13A.3) Strict quasi-concavity of W implies that ... p 2 , (1 + p 2 ) c ∗ 2 ∂c ∗ 1 ∂p 2 = 1 (1 + p 1 )(1 + p 2 )[ W 11 u (c ∗ 1 ) 2 − W 22 u (c ∗ 2 ) 2 u(c ∗ 2 ) c ∗ 2 u (c ∗ 2 ) −W 12...
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Sample chapter for the economic theory of annuities_2 pdf
... the stipulations of these annuities from a textbook for actuaries: These are usually effected to avoid the disappointment that is often felt in the event of the early death of an annuitant. The ... the price of period-certain annuities commensurate with the price of regular annuities. (a) The Inferiority of Period-certain Annuities Under Full Information...
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Sample chapter for the economic theory of annuities_3 pdf
... 0.134641 0.155093 0 .22 2355 95 0.043497 0.107438 0. 129 260 0.187 020 96 0.0 322 63 0.084018 0.1063 32 0.15 529 2 97 0. 023 4 72 0.064413 0.086313 0. 127 3 82 98 0.016760 0.048453 0.069084 0.10 322 8 99 0.011757 0.035806 ... 0.174563 0.313509 0. 321 725 0.43 521 4 90 0.144767 0 .27 3776 0 .28 4338 0.390583 91 0.118099 0 .23 5444 0 .24 8635 0.34 625 6 92 0.094678 0.199 121 0 .21 4996 0....
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Sample chapter for the economic theory of annuities_4 potx
... probabilities. The reason for this inefficiency is that individuals disregard the effect of their actions on the equilibrium rate of return on annuities. The impact of individuals disregarding their actions ... owners. The other risk class experiences a loss for the opposite reason. Another important implication of the fact that in equilibrium con- sumption is indepe...
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Sample chapter for the economic theory of annuities_6 docx
... words, the rate of decrease of survival probabilities, d ln F(z) dz =− f (z) F (z) , 1 See, for example, Levy (1998) and the references therein. August 22 , 20 07 Time: 09:50am chapter0 1.tex 2 • Chapter ... The cause of the inefficiency is that individuals disregard the effect of their actions on the equilibrium rate of return on annuities. Essentially, these...
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Sample chapter for the economic theory of annuities_7 doc
... published by the Society of Actuaries. Duncan (19 52) and Biggs (1969) provide formulas for variable annuities, that is, for annuities with stochastic returns. For an overview of life insurance formulas, ... this book. August 18, 20 07 Time: 11 :25 am chapter1 6.tex 1 52 August 18, 20 07 Time: 11 :25 am chapter1 6.tex Chapter 16 • 151 Denote by ϕ expected profits in the...
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Sample chapter for the economic theory of annuities_8 potx
... in the theory of optimum income taxation. Review of Economic Studies 38 (2) : 175 20 8. August 2, 20 07 Time: 09:36am references.tex References Ahn, H., and C. Manski. 1993. Distribution theory for ... annuitization and, 23 24 ; longevity increase and, 35–38; no-arbitrage condition and, 24 25 ; normal retirement age (NRA) and, 37–38; optimum age for, 12 14, 21 22 , 27 2...
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The Economic Theory of Annuities by Eytan Sheshinski_1 pdf
... ε 11 = ˆ q a s 11 / ˆ a, ε 12 = ˆ q a s 12 / ˆ a, ε 21 = ˆ q b s 21 / ˆ b, ε 22 = ˆ q b s 22 / ˆ b: ε 11 ˆ t a + ε 12 ˆ t b =−θ − ˆ k 11 ˆ a ,ε 21 ˆ t a + ε 22 ˆ t b =−θ − ˆ k 12 ˆ b (14.30) August 18, 20 07 ... using the identities ε i0 + ε i1 + ε i2 = 0, i = 1, 2, where 0 denotes the untaxed numeraire, ˆ t a ˆ t b = ε 11 + ε 22 + ε 10 + ˆ k 11 ε...
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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 textbook for actuaries: These are usually effected to avoid the disappointment that is often felt in the event of the ... follow the standard assumption that the sign of the price of each good changes in the opposite direction to the sign of profits from sales of this good....
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The Economic Theory of Annuities by Eytan Sheshinski_4 ppt
... 0.134641 0.155093 0 .22 2355 95 0.043497 0.107438 0. 129 260 0.187 020 96 0.0 322 63 0.084018 0.1063 32 0.15 529 2 97 0. 023 4 72 0.064413 0.086313 0. 127 3 82 98 0.016760 0.048453 0.069084 0.10 322 8 99 0.011757 0.035806 ... 0.174563 0.313509 0. 321 725 0.43 521 4 90 0.144767 0 .27 3776 0 .28 4338 0.390583 91 0.118099 0 .23 5444 0 .24 8635 0.34 625 6 92 0.094678 0.199 121 0 .21 4996 0....
Ngày tải lên: 21/06/2014, 07:20