[lmi-commits] [lmi] master 51cd822 5/5: Discount list-bill premiums for tabulation

[Greg Chicares]

branch: master
commit 51cd822a2540678e10860439c289ebc3670236fe
Author: Gregory W. Chicares <address@hidden>
Commit: Gregory W. Chicares <address@hidden>

    Discount list-bill premiums for tabulation
---
 Makefile.am   |  2 ++
 financial.cpp | 91 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 financial.hpp | 12 ++++++++
 objects.make  |  2 ++
 4 files changed, 107 insertions(+)

diff --git a/Makefile.am b/Makefile.am
index 5a522f6..78788ca 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -383,6 +383,7 @@ libantediluvian_la_LIBADD = \
 liblmi_la_SOURCES = \
     authenticity.cpp \
     commutation_functions.cpp \
+    financial.cpp \
     fund_data.cpp \
     gpt_input.cpp \
     gpt_server.cpp \
@@ -678,6 +679,7 @@ test_file_command_CXXFLAGS = $(AM_CXXFLAGS)
 test_financial_SOURCES = \
   $(common_test_objects) \
   facets.cpp \
+  financial.cpp \
   financial_test.cpp \
   null_stream.cpp \
   stratified_algorithms.cpp \
diff --git a/financial.cpp b/financial.cpp
new file mode 100644
index 0000000..13f003b
--- /dev/null
+++ b/financial.cpp
@@ -0,0 +1,91 @@
+// Financial functions.
+//
+// Copyright (C) 2017 Gregory W. Chicares.
+//
+// This program is free software; you can redistribute it and/or modify
+// it under the terms of the GNU General Public License version 2 as
+// published by the Free Software Foundation.
+//
+// This program is distributed in the hope that it will be useful,
+// but WITHOUT ANY WARRANTY; without even the implied warranty of
+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with this program; if not, write to the Free Software Foundation,
+// Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
+//
+// http://savannah.nongnu.org/projects/lmi
+// email: <address@hidden>
+// snail: Chicares, 186 Belle Woods Drive, Glastonbury CT 06033, USA
+
+#include "pchfile.hpp"
+
+#include "financial.hpp"
+
+#include "calendar_date.hpp"
+
+#include <algorithm>                    // std::generate(), std::min()
+#include <cmath>                        // std::pow()
+#include <numeric>                      // std::inner_product()
+#include <vector>
+
+/// Possibly off-anniversary premium to be shown on list bill.
+///
+/// Motivation: Group UL certificates may be issued on any date, but
+/// plan sponsors want to pay for all certificates on the same date.
+///
+/// Calculate a certificate's discounted premium for a billing cycle,
+/// during which a certificate anniversary might occur and insurance
+/// age might therefore change. The billing interval is any of the
+/// customary life-insurance payment modes. For the maximum billing
+/// period of one year, the demographic notation used on page 129 of
+/// Batten, _Mortality Table Construction_, 1978 (ISBN 0-13-601302-3)
+/// would be:
+///   - (delta)premium(x)   [here, prem_ante] for monthly charges at
+///     age x from the bill date to the anniversary age change;
+///   - (alpha)premium(x+1) [here, prem_post] for monthly charges at
+///     age x+1 from the anniversary age change to the end of the
+///     billing year (zero if the certificate matures at age x+1).
+/// Construct a monthly vector of delta or alpha premiums as the
+/// case may be, then discount them, at an interest rate given as
+/// v upper twelve, for the period defined by the given mode.
+///
+/// Return the discounted value, which is to be rounded by the caller.
+///
+/// Implementation notes:
+///  - p0 is a vector of premiums, one for each month in the billing
+///    cycle: zero or more delta values, followed by zero or more
+///    alpha values.
+///  - v is a vector of discount factors v12^0, v12^1, v12^2... .
+
+double list_bill_premium
+    (double               prem_ante
+    ,double               prem_post
+    ,mcenum_mode          mode
+    ,calendar_date const& cert_date
+    ,calendar_date const& bill_date
+    ,double               v12
+    )
+{
+    // Bill nothing for a not-yet-issued certificate. Alternatively,
+    // the condition tested here might be asserted.
+    if(bill_date < cert_date) return 0.0;
+    // Number of alpha months in the twelvemonth starting on bill date.
+    int const inforce_months_mod_12 = years_and_months_since
+        (cert_date, bill_date).second
+        ;
+    // Number of delta months in the twelvemonth starting on bill date.
+    int const months_ante = 12 - inforce_months_mod_12;
+    // Transform frequency to wavelength:
+    //   mode {1, 2, 4, 12} --> m {12, 6, 3, 1}
+    int const m = 12 / static_cast<int>(mode);
+    std::vector<double> p0(std::min(m, months_ante), prem_ante);
+    std::vector<double> p1(m - p0.size(), prem_post);
+    p0.insert(p0.end(), p1.begin(), p1.end());
+    int i = 0;
+    std::vector<double> v(p0.size());
+    std::generate(v.begin(), v.end(), [&i, v12] {return std::pow(v12, i++);});
+    return std::inner_product(p0.begin(), p0.end(), v.begin(), 0.0);
+}
+
diff --git a/financial.hpp b/financial.hpp
index c719ff0..12b2c22 100644
--- a/financial.hpp
+++ b/financial.hpp
@@ -25,8 +25,11 @@
 #include "config.hpp"
 
 #include "assert_lmi.hpp"
+#include "mc_enum_type_enums.hpp"       // mcenum_mode
 #include "zero.hpp"
 
+class calendar_date;
+
 // TODO ?? Things to reconsider later:
 //
 // v*v*v...*v != v^n because of floating-point roundoff.
@@ -248,5 +251,14 @@ void irr
         );
 }
 
+double list_bill_premium
+    (double               prem_ante
+    ,double               prem_post
+    ,mcenum_mode          mode
+    ,calendar_date const& cert_date
+    ,calendar_date const& bill_date
+    ,double               v12
+    );
+
 #endif // financial_hpp
 
diff --git a/objects.make b/objects.make
index 6b5d658..fcc54bc 100644
--- a/objects.make
+++ b/objects.make
@@ -273,6 +273,7 @@ lmi_common_objects := \
   $(common_common_objects) \
   authenticity.o \
   commutation_functions.o \
+  financial.o \
   fund_data.o \
   gpt_input.o \
   gpt_server.o \
@@ -601,6 +602,7 @@ file_command_test$(EXEEXT): \
 financial_test$(EXEEXT): \
   $(common_test_objects) \
   facets.o \
+  financial.o \
   financial_test.o \
   null_stream.o \
   stratified_algorithms.o \