actuary.py

#!/usr/bin/python
import sys
import datetime

# Calculates death probabilities based on Social Security
# actuarial tables for a given group of people.

# Run with a list of ages/genders and an optional timespan (or year in the future):

# python actuary.py 63m 80m 75f 73m 10

# or:

# python actuary.py 63m 80m 75f 73m 2022

# This will give statistics for that group, including
# various probabilities over 10 years. Years can be
# ommitted and it will still give some statistics.
# If "Years" exceeds the current calendar year, it will be interpreted as a date.


# replaced with Japanese one
# http://www.mhlw.go.jp/toukei/saikin/hw/life/21th/index.html
bothtables=[[0.00037, 0.00026, 0.00018, 0.00013, 0.00011, 0.00010, 0.00009, 0.00008, 0.00008, 0.00008, 0.00010, 0.00011, 0.00013, 0.00015, 0.00019, 0.00024, 0.00030, 0.00038, 0.00045, 0.00051, 0.00057, 0.00061, 0.00064, 0.00064, 0.00064, 0.00065, 0.00066, 0.00067, 0.00068, 0.00069, 0.00071, 0.00074, 0.00077, 0.00081, 0.00085, 0.00090, 0.00098, 0.00108, 0.00118, 0.00128, 0.00140, 0.00152, 0.00166, 0.00181, 0.00198, 0.00216, 0.00238, 0.00263, 0.00289, 0.00317, 0.00347, 0.00381, 0.00419, 0.00461, 0.00507, 0.00558, 0.00612, 0.00669, 0.00732, 0.00810, 0.00888, 0.00961, 0.01037, 0.01121, 0.01214, 0.01319, 0.01434, 0.01553, 0.01685, 0.01842, 0.02023, 0.02227, 0.02466, 0.02753, 0.03087, 0.03478, 0.03919, 0.04420, 0.04974, 0.05568, 0.06208, 0.06937, 0.07793, 0.08752, 0.09785, 0.10827, 0.11926, 0.13135, 0.14503, 0.16041, 0.17569, 0.19195, 0.20922, 0.22755, 0.24695, 0.26744, 0.28905, 0.31177, 0.33560, 0.36051, 0.38649, 0.41348, 0.44142, 0.47023, 0.49980, 0.53002, 0.56075, 0.59182, 0.62304, 0.65422], [0.00033, 0.00023, 0.00015, 0.00011, 0.00009, 0.00008, 0.00008, 0.00007, 0.00006, 0.00006, 0.00006, 0.00007, 0.00008, 0.00010, 0.00012, 0.00014, 0.00016, 0.00019, 0.00021, 0.00024, 0.00025, 0.00026, 0.00026, 0.00026, 0.00026, 0.00027, 0.00028, 0.00031, 0.00034, 0.00036, 0.00038, 0.00040, 0.00042, 0.00045, 0.00048, 0.00052, 0.00056, 0.00061, 0.00066, 0.00071, 0.00076, 0.00082, 0.00091, 0.00100, 0.00108, 0.00115, 0.00124, 0.00138, 0.00153, 0.00167, 0.00179, 0.00191, 0.00204, 0.00219, 0.00236, 0.00254, 0.00273, 0.00292, 0.00313, 0.00340, 0.00370, 0.00401, 0.00434, 0.00465, 0.00498, 0.00537, 0.00584, 0.00634, 0.00692, 0.00767, 0.00856, 0.00961, 0.01083, 0.01224, 0.01381, 0.01558, 0.01763, 0.02006, 0.02284, 0.02600, 0.02956, 0.03371, 0.03867, 0.04458, 0.05155, 0.05937, 0.06837, 0.07843, 0.08949, 0.10160, 0.11490, 0.12964, 0.14628, 0.16458, 0.18367, 0.20330, 0.22398, 0.24573, 0.26854, 0.29242, 0.31734, 0.34328, 0.37021, 0.39806, 0.42678, 0.45627, 0.48643, 0.51715, 0.54827, 0.57965, 0.61112, 0.64247, 0.67352, 0.70404]]

def deathprob(age, years):
    #negative ages = female
    act=[]
    if age<0:
        act=bothtables[1]
        age=-1*age
    else:
        act=bothtables[0]
    while(len(act)<int(age+years+2)): # slower/bloaiter but keeps things clean
        act.append(act[-1]**0.5)
    liveprob=1
    i=0
    iage=int(age)
    fage=age%1
    while i<=years-1:
        thisyear=(1-fage)*act[iage+i]+fage*act[iage+i+1]
        liveprob*=1-thisyear
        i+=1
    if years%1: # Amortizes risk of dying over a partial year, which is
                # 1-P(living last full year)^(year fraction)
        lastyear=(1-fage)*act[iage+i]+fage*act[iage+i+1]
        lastyearlive=1-lastyear
        lastyearlive=lastyearlive**((years%1))
        liveprob*=lastyearlive
    return 1-liveprob

def proballdie(ages, years):
    probsliving=[]
    for i in ages:
        probsliving.append(1-deathprob(i, years))
    prod=1
    for i in probsliving:
        prod*=(1-i)
    return prod

def probanydie(ages, years):
    probsliving=[]
    for i in ages:
        probsliving.append(1-deathprob(i, years))
    prod=1
    for i in probsliving:
        prod*=i
    return 1-prod

def calcexp(ages, prob, flag):
    i=0
    for interval in (10, 1, 0.1, 0.01):
        probs=0
        while(probs<prob):
            i+=interval
            if flag==0:
                probs=proballdie(ages, i)
            else:
                probs=probanydie(ages, i)
        i-=interval
    return i

ages=[]
# print sys.argv[1:]
for arg in sys.argv[1:]:
    gender=1
    years=1.0
    if arg[-1]=='m' or arg[-1]=='M':
        try:
            ages.append(1*float(arg[:-1]))
        except:
            print "Error parsing argument", arg
    elif arg[-1]=='f' or arg[-1]=='F':
        try:
            ages.append(-1*float(arg[:-1]))
        except:
            print "Error parsing argument", arg
    else:
        try:
            years=float(arg)
            break
        except:
            print "Error parsing argument", arg

if not sys.argv[1:]:
    print "The format is 'actuary.py 15m 80f 23', with a list of ages and a number of years to run the projections."
    raise SystemExit
if not ages:
    print "No ages specified.  Format is 12m, 17f, etc."
    raise SystemExit

# print "Ages:", ages
# print "Years:", years

(datetime.date.today()+datetime.timedelta(days=365.242191*1)).year
someone_years=[calcexp(ages, 0.05, 1),
               calcexp(ages, 0.5, 1),
               calcexp(ages, 0.95, 1)]
someone_dates=[(datetime.date.today()+datetime.timedelta(days=365.242191*someone_years[0])).year,
               (datetime.date.today()+datetime.timedelta(days=365.242191*someone_years[1])).year,
               (datetime.date.today()+datetime.timedelta(days=365.242191*someone_years[2])).year]
print "There is a 5%  chance of someone dying within", someone_years[0], "years (by", str(someone_dates[0])+")."
print "There is a 50% chance of someone dying within", someone_years[1], "years (by", str(someone_dates[1])+")."
print "There is a 95% chance of someone dying within", someone_years[2], "years (by", str(someone_dates[2])+")."
print ""

if len(ages)>1:
    everyone_years=[calcexp(ages, 0.05, 0),
                   calcexp(ages, 0.5, 0),
                   calcexp(ages, 0.95, 0)]
    everyone_dates=[(datetime.date.today()+datetime.timedelta(days=365.242191*everyone_years[0])).year,
                   (datetime.date.today()+datetime.timedelta(days=365.242191*everyone_years[1])).year,
                   (datetime.date.today()+datetime.timedelta(days=365.242191*everyone_years[2])).year]
    print "There is a 5%  chance of everyone dying within", everyone_years[0], "years (by", str(everyone_dates[0])+")."
    print "There is a 50% chance of everyone dying within", everyone_years[1], "years (by", str(everyone_dates[1])+")."
    print "There is a 95% chance of everyone dying within", everyone_years[2], "years (by", str(everyone_dates[2])+")."


if years:
    yearword="years"
    if years==1:
        yearword="year"

    print ""
    if years>datetime.date.today().year:
        years=years-datetime.date.today().year
    if len(ages)>1:
        p=100*proballdie(ages, years)
        printable=""
        if p<0.001:
            printable="<0.001"
        elif p>99.99:
            printable=">99.99"
        else:
            printable=str(p)[:5]
        print "Probability of all dying in", years, yearword+":  ", printable+"%"
    p=100*probanydie(ages, years)
    printable=""
    if p<0.001:
        printable="<0.001"
    elif p>99.99:
        printable=">99.99"
        print p
    else:
        printable=str(p)[:5]
    print "Probability of a death within", years, yearword+":", printable+"%"
raise SystemExit