Z Wikibooks, biblioteki wolnych podręczników.
Wzory teorii oprocentowania [ edytuj ]
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{\displaystyle 1=\delta {\bar {a}}_{{\overline {t}}|}+v^{t}}
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{\displaystyle \alpha (m)={\frac {i\cdot d}{i^{(m)}\cdot d^{(m)}}}\qquad \beta (m)={\frac {i-i^{(m)}}{i^{(m)}\cdot d^{(m)}}}}
Wzory do modelu demograficznego [ edytuj ] Współczynnikiem umieralności (central death rate ) nazywamy
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{\displaystyle m_{x}={\frac {q_{x}}{\int _{0}^{1}{}_{t}p_{x}dt}}}
Egzaminy aktuarialne w sieci [ edytuj ] Gotowce z angielskiej wikipedii [ edytuj ]
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{\displaystyle \,q_{x}=d_{x}/l_{x}\!}
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{\displaystyle \,{}_{t}p_{x}={\frac {l_{x+t}}{l_{x}}}}
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{\displaystyle \,_{n}q_{x}=_{n}d_{x}/l_{x}}
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{\displaystyle \,_{n}p_{x}=l_{x+n}/l_{x}}
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{\displaystyle \,e_{x}=\sum _{t=1}^{\infty }\ _{t}p_{x}}
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{\displaystyle \,l_{x+t}=(1-t)l_{x}+tl_{x+1}}
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{\displaystyle \,l_{x+1}=l_{x}\cdot (1-q_{x})=l_{x}\cdot p_{x}}
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{\displaystyle \,{l_{x+1} \over l_{x}}=p_{x}}
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{\displaystyle \,d_{x}=l_{x}-l_{x+1}}
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{\displaystyle \,{}_{t|k}q_{x}={}_{t}p_{x}\cdot {}_{k}q_{x+t}={l_{x+t}-l_{x+t+k} \over l_{x}}}
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{\displaystyle \,a_{{\overline {n|}}i}=v+v^{2}+\cdots +v^{n}={\frac {1-v^{n}}{i}}}
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{\displaystyle {\ddot {a}}_{{\overline {n|}}i}=1+v+\cdots +v^{n-1}={\frac {1-v^{n}}{d}}}
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{\displaystyle a_{{\overline {n|}}i}^{(m)}={\frac {1-v^{n}}{i^{(m)}}}}
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{\displaystyle {\ddot {a}}_{{\overline {n|}}i}^{(m)}={\frac {1-v^{n}}{d^{(m)}}}}
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{\displaystyle {\overline {a}}_{{\overline {n|}}i}={\frac {1-v^{n}}{\delta }}}
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{\displaystyle a_{{\overline {n|}}i}<a_{{\overline {n|}}i}^{(m)}<{\overline {a}}_{{\overline {n|}}i}<{\ddot {a}}_{{\overline {n|}}i}^{(m)}<{\ddot {a}}_{{\overline {n|}}i}}
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A
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{\displaystyle {}_{m|}{\ddot {a}}_{x}={}_{m}p_{x}v^{m}{\ddot {a}}_{x+m}=A_{x:{\overline {n}}|}^{\;\;\;1}{\ddot {a}}_{x+m}}
