Merge remote-tracking branch 'origin/master'

pmizel · pmizel · commit b37fd17f7c1b · 2019-07-08T16:16:39.000+02:00
diff --git a/en/depot/_spec-payment.tex b/en/depot/_spec-payment.tex
@@ -6,114 +6,114 @@ \section{Decentralized pension}
 
 \paragraph{Generic currency unit.} The design of the pension system is not tied to a specific currency unit such as ETH or BTC; instead, it uses the generic currency unit "\textbf{unit}". The unit must be replaced by a specific currency for the concrete implementation.
 
-\paragraph{Periods.} The pension system is divided into periods, which are defined as $P$. Each action within the pension system takes place in a period $P[p]$. The duration of a period ($P_{duration}$) is freely selectable. Within the following calculations we consider $P_{duration} = 1 month$.
+\paragraph{Periods.} The pension system is divided into periods, which are defined as $P$. Each action within the pension system takes place in a period $P_{p}$. The duration of a period ($P\_Duration$) is freely selectable. Within the following calculations we consider $P\_Duration = 1 month$.
 
-\paragraph{Users.} All users of the pension system are defined as $U$ and individual users are defined as $U[u]$. Each user has a state $U[u]_{state}$ which can be either \textbf{UC} (Contributor),
+\paragraph{Users.} All users of the pension system are defined as $U$ and individual users are defined as $U_{u}$. Each user has a state $U\_State_{u}$ which can be either \textbf{UC} (Contributor),
 \textbf{UP} (Pensioner), or \textbf{UD} (Done).
-The initial state of all users is $U[u]_{state} = UC$ 
+The initial state of all users is $U\_State_{u} = UC$ 
 
 \paragraph{Accounts.} The decentralized pension has two accounts: Savings ($W_{savings}$) and Laggards  ($W_{laggarts}$). Contributions and pension payments will be charged using these. The savings account contains the total amount of the managed contributions and is used for the monthly processing of deposits and withdrawals. The laggards account manages a reserve, which is paid to the last generation of the pension system.
 
 \subsection{Payment of contributions}
 
-Contributors can contribute in a period $P[p]$. The total amount per period and user is defined as $U[u]_{units[p]}$. The total number of periods in which a contributor has paid is defined as $U[u]_{contrib}$.
+Contributors can contribute in a period $P_{p}$. The total amount per period and user is defined as $U\_Units_{u,p}$. The total number of periods in which a contributor has paid is defined as $U\_Contrib_{u}$.
 
 \begin{equation}
-U[u]_{contrib} = \sum_{p=0}^{|P|} \begin{cases} 
-1 & _{if U[u]_{units[p]} > 0} \\
+U\_Contrib_{u} = \sum_{p=0}^{|P|} \begin{cases} 
+1 & _{if U\_Units_{u,p} > 0} \\
 0 & _{otherwise}
 \end{cases}
 \end{equation}
 
 
-All contribution payments of a period $P[p]$ are credited to the savings account $W_{savings}$.
-Entries from contributors who do not have any pension entitlement periods ($U[u]_{pensionperiods} = 0$) will also be credited to the $W_{laggarts}$ account.
+All contributions of a period $P_{p}$ are credited to the savings account $W_{savings}$.
+Entries from contributors who do not have any pension entitlement periods ($U\_Pensionperiods_{u} = 0$) will also be credited to the $W_{laggarts}$ account. Therefore, the sum of $W_{savings}-W_{laggarts}$ will be payed out in each period $P_{p}$ and only parts of $W_{laggarts}$ are used.
 
 
 \begin{equation}
-W_{savings} = W_{savings} + \sum_{u=0}^{|U|} U[u]_{units[p]}
+W_{savings} = W_{savings} + \sum_{u=0}^{|U|} U\_Units_{u,p}
 \end{equation}
 
 
 \begin{dmath}
 W_{laggarts} = W_{laggarts} + \sum_{u=0}^{|U|} \begin{cases} 
-U[u]_{units[p]} & _{if U[u]_{pensionperiods} = 0} \\
+U\_Units_{u,p} & _{if U\_Pensionperiods_{u} = 0} \\
 0 & _{otherwise}
 \end{cases}
 \end{dmath}
 
 \subsubsection{Pension entitlement periods}
-The pension entitlement periods ($U[u]_{pensionperiods}$) determines the number of periods, in which a pension payment is made. The higher the number of contribution periods
-$U[u]_{contrib}$, the higher the number of pension entitlement periods.
+The pension entitlement periods ($U\_Pensionperiods_{u}$) determines the number of periods, in which a pension payment is made. The higher the number of contribution periods
+$U\_Contrib_{u}$, the higher the number of pension entitlement periods.
 
-To incentivize a large number of contribution periods, a target value ($P_{target}$) is used
+To incentivize a large number of contribution periods, a target value ($P\_Target$) is used
 for the number of contribution periods. 
 
 \begin{equation}
-	P_{target} = 40 years \cdot 12 months
+	P\_Target = 40 years \cdot 12 months
 \end{equation}
 
 If the number of contribution periods corresponds to the target value, the number of pension entitlement periods should correspond exactly to the target value. If the number of contribution periods below or above the target value, the number of pension entitlement periods are correspondingly disproportionately smaller or larger.  
 
 The number of pension entitlement periods is defined as follows:
 
 \begin{equation}
-U[u]_{pensionperiods} = \frac{U[u]_{contrib}^2}{P_{target}}
+U\_Pensionperiods_{u} = \frac{U\_Contrib_{u}^2}{P\_Target}
 \end{equation}
 
 
 \subsubsection{Decentralized pension points}
 
-For the contributions paid for a period ($U[u]_{units[p]}$), a contributor receives decentralized pension points in the form of decentralized pension tokens ($DPT$). The total number of \gls{dpt} of a contributor at retirement age is used to calculate the amount of the pension payable.
+For the contributions paid for a period ($U\_Units_{u,p}$), a contributor receives decentralized pension points in the form of decentralized pension tokens ($DPT$). The total number of \gls{dpt} of a contributor at retirement age is used to calculate the amount of the pension payable.
 
 \begin{equation}
-U[u]_{dpt[p]} = DPT(u, p)
+U\_Dpt_{u,p} = DPT(u, p)
 \end{equation}
 
 \begin{equation}
-DPT(u, p) = DPT_{base}(u, p) \cdot DPT_{bonus}(p)
+DPT(u, p) = DPT\_Base(u, p) \cdot DPT\_Bonus(p)
 \end{equation}
 
 \paragraph*{Purchasing Power Index:}
 
-The purchasing power index ($PPI$) is calculated at the beginning of each period $P[n]$ and defined as $P[p]_{ppi}$. The $PPI$ is the reference value for a $DPT$ of the corresponding period.
+The purchasing power index ($PPI$) is calculated at the beginning of each period $P_{p}$ and is defined as $P\_Ppi_{p}$. The $PPI$ is the reference value for a $DPT$ of the corresponding period.
 
-To calculate the $PPI$ of the $P[p]$ period, the $PPI$ of the previous period $P[n-1]$ is used.
-If the difference between $PPI$ and the average contribution for the period $P[n-1]$ is greater than 10\%, the $PPI$ of the period $P[n]$ is increased or decreased by 10\% accordingly.
+To calculate the $PPI$ of the $P_{p}$ period, the $PPI$ of the previous period $P_{p-1}$ is used.
+If the difference between $PPI$ and the average contribution for the period $P_{p-1}$ is greater than 10\%, the $PPI$ of the period $P[n]$ is increased or decreased by 10\% accordingly.
 If the average contribution fluctuates sharply, the $PPI$ slowly feeds on the new average and large jumps are avoided.
 
 \begin{equation}
-P[p]_{units} = avg(\sum_{u=0}^{|U|} U[u]_{units[p]})
+P\_Units_{p} = avg(\sum_{u=0}^{|U|} U\_Units_{u,p})
 \end{equation}
 
 \begin{equation}
-P[p]_{ppi} = \begin{cases} 
-P[p]_{ppi} \cdot 1.1 & _{if P[p]_{units} \cdot 1.1 > P[p-1]_{ppi}} \\
-P[p]_{ppi} \cdot 0.9 & _{if P[p]_{units} \cdot 0.9 < P[p-1]_{ppi}} \\
-P[p]_{ppi} & _{otherwise}
+P\_Ppi_{p} = \begin{cases} 
+P\_Ppi_{p} \cdot 1.1 & _{if P\_Units_{p} \cdot 1.1 > P\_Ppi_{p-1}} \\
+P\_Ppi_{p} \cdot 0.9 & _{if P\_Units_{p} \cdot 0.9 < P\_Ppi_{p-1}} \\
+P\_Ppi_{p} & _{otherwise}
 \end{cases}
 \end{equation}
 
 \paragraph*{Decentralized pension points basis:}
 The pension points is the ERC20 tokenization of purchasing power in blockchain systems and is an abstraction to purchasing power where the $PPI$ value represents the reference as to how the willingness to pay was present in past periods. For a deposit equal to $PPI$, 1.0 DPT points are credited to the sender. Anything above the $PPI$ value will be credited with a maximum of 2.0 DPT, it is possible to pay more than twice the $PPI$ value. If the $PPI$ value is lower than the $PPI$ value, less DPT will be credited proportionally to the $min$ value.
 
 \begin{dmath}
-DPT_{base}(u, p) = \begin{cases} 
-min(\frac{U[u]_{units[p]}} {P[p]_{ppi}}, 2) 
-  & _{if U[u]_{units[p]} > P[p]_{ppi}} \\
-\frac{U[u]_{units[p]} - min} {P[p]_{ppi} - min} 
-  & _{if U[u]_{units[p]} < P[p]_{ppi}} \\
+DPT\_Base(u, p) = \begin{cases} 
+min(\frac{U\_Units_{u,p}} {P\_Ppi_{p}}, 2) 
+  & _{if U\_Units_{u,p} > P\_Ppi_{p}} \\
+\frac{U\_Units_{u,p} - min} {P\_Ppi_{p} - min} 
+  & _{if U\_Units_{u,p} < P\_Ppi_{p}} \\
 1.0 & _{otherwise}
 \end{cases}
 \end{dmath}
 
 \paragraph*{Decentralized pension points bonus:}
-Up to the period $P_{bonus} = 480$ additional bonus DPT ($DPT_{bonus}$) will be issued to contributors. Bonus DPT are intended to create an incentive for the first users of the pension system and thus reward the users who believed in and invested in the system at an early stage. The concept of Bonus DPT is based on the reduction of mining rewards known from the Bitcoin protocol.
+Up to the period $P\_Bonus = 480$ additional bonus DPT ($DPT\_Bonus$) will be issued to contributors. Bonus DPT are intended to create an incentive for the first users of the pension system and thus reward the users who believed in and invested in the system at an early stage. The concept of Bonus DPT is based on the reduction of mining rewards known from the Bitcoin protocol.
 
 \begin{equation}
-DPT_{bonus}(p) = \begin{cases} 
-1 + \frac{(P_{bonus} - P[p] + 1)^2}
-      {2 \cdot P_{bonus}^2} & _{if P[p] < P_{bonus}} \\
+DPT\_Bonus(p) = \begin{cases} 
+1 + \frac{(P\_Bonus - P_{p} + 1)^2}
+      {2 \cdot P\_Bonus^2} & _{if P_{p} < P\_Bonus} \\
 1 & _{otherwise} 
 \end{cases}
 \end{equation}
diff --git a/en/depot/_spec-payout.tex b/en/depot/_spec-payout.tex
@@ -1,14 +1,14 @@
 \subsection{Pension payment}
 
-Contributors are free to choose when they retire. If a contributor retires, no more contributions can be made and, depending on the contributions paid, pension payments can be made instead. The transition from contributor to pensioner is marked by the change of state $U[u]_{state} = UP$.
+Contributors are free to choose when they retire. If a contributor retires, no more contributions can be made and, depending on the contributions paid, pension payments can be made instead. The transition from contributor to pensioner is marked by the change of state $U\_State_{u} = UP$.
 
-The pension to be paid is calculated on the basis of the total number of DPTs of a pensioner ($U[u]_{dpt\_total}$).
+The pension to be paid is calculated on the basis of the total number of DPTs of a pensioner ($U\_Dpt\_total_{u}$).
 
 \begin{equation}
-U[u]_{dpt\_total} = \sum_{p=0}^{|P|} U[u]_{dpt[p]}
+U\_Dpt\_total_{u} = \sum_{p=0}^{|P|} U\_Dpt_{u,p}
 \end{equation}
 
-The pension entitlement periods $U[u]_{pensionperiods}$ determine in how many periods a pension is paid out. In which periods a pensioner claims his pension payments is left to the pensioner and can be freely chosen. If all pension payments have been claimed, the state will be replaced by $U[u]_{state} = UD$.
+The pension entitlement periods $U\_Pensionperiods_{u}$ determine in how many periods a pension is paid out. In which periods a pensioner claims his pension payments is left to the pensioner and can be freely chosen. If all pension payments have been claimed, the state will be replaced by $U\_State_{u} = UD$.
 
 If a pensioner has always paid the average contribution into the pension system in his contribution periods, his pension payment should also correspond to the average contribution payments of the current period and thus the purchasing power stored in $DPT$ should be restored.
 
@@ -17,85 +17,87 @@ \subsection{Pension payment}
 The pension payment is therefore defined as follows:
 
 \begin{dmath}
-U[u]_{pension[p]} = U[u]_{dpt\_total} \cdot (CPR(p) + SPR(p, W_{savings} - W_{laggarts}) + LPR(p, W_{laggarts}))
+U\_Pension_{u,p} = U\_Dpt\_total_{u} \cdot (CPR(p) + SPR(p, W_{savings} - W_{laggarts}) + LPR(p, W_{laggarts}))
 \end{dmath}
 
 \subsubsection{Contribution pension rate ($CPR$)}
-All contributions for a contribution period ($P[p]units$) are collected and paid out proportionately to pensioners. The contribution pension rate $CPR(p)$ defines the conversion rate from DPT to contributions.
+All contributions for a contribution period ($P\_Units_{p}$) are collected and paid out proportionately to pensioners. The contribution pension rate $CPR(p)$ defines the conversion rate from DPT to pension payouts.
 
 \begin{equation}
-P[p]_{units} = \sum_{u=0}^{|U|} U[u]_{units[p]}
+P\_Units_{p} = \sum_{u=0}^{|U|} U\_Units_{u,p}
 \end{equation}
 
 The pensions to be paid are determined by the average contribution payment of the 
-period ($avg(P[p]units)$) is capped. If there are more contributors than pensioners in the system, any surpluses are used as a reserve and are not paid out directly. If the contribution payments are not sufficient to pay the average contribution payment for the respective period, the contributions are distributed proportionally to all pensioners and pension payments using the DPT.
+period ($avg(P\_Units_{p})$) is capped. If there are more contributors than pensioners in the system, any surpluses are used as a reserve and are not paid out directly. If the contribution payments are not sufficient to pay the average contribution payment for the respective period, the contributions are distributed proportionally to all pensioners and pension payments using the DPT.
 
+\begin{subequations}
 \begin{dmath}
-P[p]_{dpt\_pensioner} = 
+P\_Dpt\_pensioner_{p} = 
 \sum_{u=0}^{|U|} \begin{cases} 
-U[u]_{dpt\_total[p]} & _{if U[u]_{state} = UP}\\
+U\_Dpt\_total_{u,p} & _{if U\_State_{u} = UP}\\
 0 & _{otherwise}
 \end{cases}
 \end{dmath}
 
-\begin{equation*}
-CPR_{a}(p) = \frac{avg(P[p]_{units})}{P_{target}}
-\end{equation*}
+\begin{equation}
+CPR\_A(p) = \frac{avg(P\_Units_{p})}{P\_Target}
+\end{equation}
 
-\begin{equation*}
-CPR_{b}(p) = \frac{P[p]_{units}} {P[p]_{dpt\_pensioner} \cdot avg(P[p]_{units}))}
-\end{equation*}
+\begin{equation}
+CPR\_B(p) = \frac{P\_Units_{p}} {P\_Dpt\_pensioner_{p} \cdot avg(P\_Units_{p}))}
+\end{equation}
 
 \begin{equation}
-CPR(p) = min(CPR_{a}(p), CPR_{b}(p))
+CPR(p) = min(CPR\_A(p), CPR\_B(p))
 \end{equation}
+\end{subequations}
 
 
 \subsubsection{Reserve pension rate ($SPR$)}
 
-Surplus contributions are reserved as a reserve and $P[p]$ is paid out proportionately in each period. The reserve is paid out in such a way that it is distributed evenly over all active users ($P[p]_{auc}$), their DPT and all active pension entitlement periods of the pension system $(P[p]_{tpep})$. The reserve pension rate $SPR(p, units)$ thus defines the conversion rate from DPT to reserves.
+Surplus contributions are reserved as a reserve and $P_{p}$ is paid out proportionately in each period. The reserve is paid out in such a way that it is distributed evenly over all active users ($P\_Auc_{p}$), their DPT and all active pension entitlement periods of the pension system $(P\_Tpep_{p})$. The reserve pension rate $SPR(p, units)$ thus defines the conversion rate from DPT to reserves.
 
 % auc = active user count
 
 \begin{equation}
-P[p]_{auc} = \sum_{u=0}^{|U|} \begin{cases} 
-0 & _{if U[u]_{state} = DP}\\
+P\_Auc_{p} = \sum_{u=0}^{|U|} \begin{cases} 
+0 & _{if U\_State_{u} = DP}\\
 1 & _{otherwise}
 \end{cases}
 \end{equation}
 
 \begin{equation}
-P[p]_{active\_dpt} = \sum_{u=0}^{|U|} \begin{cases} 
-0 & _{if U[u]_{state} = DP}\\
-U[u]_{dpt\_total} & _{otherwise}
+P\_Active\_dpt_{p} = \sum_{u=0}^{|U|} \begin{cases} 
+0 & _{if U\_State_{u} = DP}\\
+U\_Dpt\_total_{u} & _{otherwise}
 \end{cases}
 \end{equation}
 
-To calculate the total number of a pension entitlement periods of a given user $U[u]$, $TPEP(u)$ is defined as follows:
-
+To calculate the total number of active pension entitlement periods of a pensioner, we have to substract all periods in which a pension was already payed out. The already payed out pension periods are defined as follows:
+\begin{subequations}
 \begin{equation}
-TPEP(u) = \sum_{p=0}^{|P|} \begin{cases}
-1 & _{if U[u]_{pension[p]} > 0}\\
+IPEP(u) = \sum_{p=0}^{|P|} \begin{cases}
+1 & _{if U\_Pension_{u,p} > 0}\\
 0 & _{otherwise}\\
 \end{cases}
 \end{equation}
 
 
-% tpep = total pension entitlement periods
+% ipep = inactive pension entitlement periods
 
-\begin{equation}
-P[p]_{tpep} = \sum_{u=0}^{|U|} \begin{cases}
-P_{target} - TPEP(u)  & _{if U[u]_{state} = DP}\\
-P_{target} & _{if U[u]_{state} = DC}\\
+\begin{dmath}
+P\_Tpep_{p} = \sum_{u=0}^{|U|} \begin{cases}
+P\_Target - IPEP(u)  & _{if U\_State_{u} = DP}\\
+P_{target} & _{if U\_State_{u} = DC}\\
 0 & _{otherwise}
 \end{cases}
-\end{equation}
+\end{dmath}
 
 \begin{equation}
-SPR(p, units) = \frac{units} {P[p]_{active\_dpt} \dot {\frac{P[p]_{tpep}} {P[p]_{auc}}}
+SPR(p, units) = \frac{units} {P\_Active\_dpt_{p} \dot {\frac{P\_Tpep_{p}} {P\_Auc_{p}}}
 }
 \end{equation}
-
+\end{subequations}
 
 \subsubsection{Laggards pension rate ($LPR$)}
 
@@ -105,14 +107,14 @@ \subsubsection{Laggards pension rate ($LPR$)}
 
 \begin{equation}
 total\_pensioners =  \sum_{u=0}^{|U|} \begin{cases} 
-1  & _{if U[u]_{state} = DP}\\
+1  & _{if U\_State_{u} = DP}\\
 0 & _{otherwise}
 \end{cases}
 \end{equation}
 
 \begin{equation}
 LPR(p, units) =  \begin{cases} 
-SPR(p, units)  & _{if \frac{total_pensioners} {P[p]_{tpep}} = 1}\\
+SPR(p, units)  & _{if \frac{total\_pensioners} {P\_Tpep_{p}} = 1}\\
 0 & _{otherwise}
 \end{cases}
 \end{equation}$  $
diff --git a/en/depot/asure.depot.en.tex b/en/depot/asure.depot.en.tex
@@ -33,14 +33,14 @@
 description={A technical standard used for smart contracts on the Ethereum blockchain for implementing tokens.}}
 \newglossaryentry{smartcontract}{name={SmartContract},plural={SmartContract},
 description={A smart contract is a computer protocol intended to digitally facilitate, verify, or enforce the negotiation or performance of a contract. Smart contracts allow the performance of credible transactions without third parties. These transactions are trackable and irreversible.}}
-\newglossaryentry{account}{name={account},plural={accounts},
-description={A hash of a public key which can hold values. Hold values can only be accessed by knowing the corresponding private key.}}
+\newglossaryentry{account}{name={Account},plural={Accounts},
+description={A hash of a public key which can hold values. Values hold by an account can only be accessed by knowing the corresponding private key.}}
 \newglossaryentry{gdpr}{name={GDPR},plural={GDPR},
 description={The General Data Protection Regulation (EU) 2016/679 ("GDPR") is a regulation in EU law on data protection and privacy for all individuals within the European Union (EU).}}
 \newglossaryentry{payg}{name={PAYG},plural={PAYG},
-description={a method of financing social insurance, especially old-age provision, but also health insurance and unemployment insurance. The paid-in contributions are used directly to finance the beneficiaries, ie they are paid back to them.}}
+description={A method of financing social insurance, especially old-age provision, but also health insurance and unemployment insurance. The paid-in contributions are used directly to finance the beneficiaries, ie they are paid back to them.}}
 \newglossaryentry{cpr}{name={CPR},plural={CPR},
-description={The contribution pension rate  defines the conversion rate from DPT to contributions.}}
+description={The contribution pension rate  defines the conversion rate from DPT to pension payouts.}}
 \newglossaryentry{dpt}{name={DPT},plural={DPT},
 description={Decentralized pension tokens represent the contributed amounts relative to all other contributions of a given period.}}
 \newglossaryentry{ppi}{name={PPI},plural={PPI},
