The Economic Theory of Annuities 2 pptx

... 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...

Ngày tải lên: 21/06/2014, 07:20

... 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 ... to make the price of period- certain annuities commensurate with the price of regular annuities. These annuities are available in the United Kingdom, where th...

Ngày tải lên: 21/06/2014, 07:20

... 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

... from (8 .21 ), the interpretation of this result is that the flow of returns from annuities held at age M can be matched, using the relevant risk-class survival function of the holder of the annuities, ... (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 ra...

Ngày tải lên: 21/06/2014, 07:20

... 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 is 2c 0 + ... survival probability, p. The couple maximizes the family’s expected utility, 2V c = 2u(c 0 ) + 2p 2 u(c 1 /2) + 2p(1 − p)u(c 1 ), where c 0 is per-capita consumption in...

Ngày tải lên: 21/06/2014, 07:20

... accross states of nature). Sequential annuity market equilibrium is characterized by the purchase of long-term annuities, short sale of some of these annuities later on, or the purchase of additional short-term ... invaluable, they will never sell all their long-term annuities; that is, a 0 − b 1 > 0. In period 2, annuities payout is a 0 + a 1 − b 1 if the holder of...

Ngày tải lên: 21/06/2014, 07:20

... year and there is no getting rid of it. —Jane Austen, Sense and Sensibility, chapter 2 (1811). vii August 22 , 20 07 Time: 09:47am prelims.tex The Economic Theory of Annuities i August 22 , 20 07 Time: ... prelims.tex The Economic Theory of Annuities xvii August 22 , 20 07 Time: 09:47am prelims.tex vi August 22 , 20 07 Time: 09:47am prelims.tex Preface This boo...

Ngày tải lên: 20/06/2014, 20:20

... 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 ... (14.30) for the tax rates, 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...

Ngày tải lên: 20/06/2014, 20:20

... 26 ; asymmetric, 6, 118 22 ; bequests and, 82; cost effects and, 119 20 ; full, 82, 87–88, 1 12; medical care and, 54; moral hazard and, 51–55; pooling equilibrium and, 119 22 ; private, 52 53, 82, ... of Economics 90: 624 –649. Salanie, B. 20 00. Microeconomics of Market Failure. Cambridge, MA: MIT Press. Salanie, B. 20 03. The Economics of Taxation. Cambridge, MA: MIT Press. She...

Ngày tải lên: 20/06/2014, 20:20

... accross states of nature). Sequential annuity market equilibrium is characterized by the purchase of long-term annuities, short sale of some of these annuities later on, or the purchase of additional short-term ... invaluable, they will never sell all their long-term annuities; that is, a 0 − b 1 > 0. In period 2, annuities payout is a 0 + a 1 − b 1 if the holder of...

Ngày tải lên: 21/06/2014, 00:20