Examples

This page contains comprehensive examples demonstrating ACTUNEO’s capabilities.

Example 1: Complete Mortality Analysis

import numpy as np
import matplotlib.pyplot as plt
from actuneo.mortality import MortalityTable, SurvivalFunctions

# Create a mortality table with realistic rates
ages = np.arange(0, 121)

# Gompertz-Makeham formula parameters
A = 0.0001
B = 0.00035
c = 1.085

qx = A + B * c ** ages
qx = np.clip(qx, 0, 1)  # Ensure rates are between 0 and 1

mt = MortalityTable(ages, qx, name="Gompertz-Makeham Table")

# Calculate various metrics
print(f"Life expectancy at birth: {mt.life_expectancy(0):.2f} years")
print(f"Life expectancy at age 65: {mt.life_expectancy(65):.2f} years")

# Plot survival curve
sf = SurvivalFunctions(mt, interest_rate=0.05)
ages_plot = np.arange(0, 101)
survival_probs = [sf.npx(0, age) for age in ages_plot]

plt.figure(figsize=(10, 6))
plt.plot(ages_plot, survival_probs)
plt.xlabel('Age')
plt.ylabel('Survival Probability')
plt.title('Survival Curve')
plt.grid(True)
plt.show()

Example 2: Pension Valuation

from actuneo.mortality import MortalityTable, SurvivalFunctions
from actuneo.life import Annuities
import numpy as np

# Create a mortality table
ages = np.arange(20, 101)
qx = 0.001 * (ages - 20) / 80
mt = MortalityTable(ages, qx, name="Pension Table")

# Initialize annuity calculator
ann = Annuities(mt, interest_rate=0.05)

# Calculate pension liability for a member retiring at 65
# Annual pension: $50,000
retirement_age = 65
annual_pension = 50000

# Present value of whole life annuity
annuity_factor = ann.whole_life_annuity_due(retirement_age)
pension_liability = annual_pension * annuity_factor

print(f"Annuity factor: {annuity_factor:.4f}")
print(f"Pension liability: ${pension_liability:,.2f}")

# Calculate liability for different interest rates
print("\nSensitivity to interest rates:")
for rate in [0.03, 0.04, 0.05, 0.06, 0.07]:
    ann_temp = Annuities(mt, interest_rate=rate)
    factor = ann_temp.whole_life_annuity_due(retirement_age)
    liability = annual_pension * factor
    print(f"  Rate {rate:.1%}: ${liability:,.2f}")

Example 3: Life Insurance Premium Calculation

from actuneo.mortality import MortalityTable
from actuneo.life import LifeAssurance
import numpy as np

# Create mortality table
ages = np.arange(20, 101)
qx = 0.001 * (ages - 20) / 80
mt = MortalityTable(ages, qx, name="Standard Table")

# Initialize life assurance calculator
la = LifeAssurance(mt, interest_rate=0.05)

# Policyholder details
age = 35
sum_assured = 500000
term = 20

# Calculate premiums for different product types
print(f"Premiums for age {age}, sum assured ${sum_assured:,}")
print(f"\nProduct comparisons:")

# Whole life
wl_premium = la.whole_life_assurance(age, sum_assured=sum_assured)
print(f"  Whole Life: ${wl_premium:,.2f} per year")

# Term assurance
term_premium = la.term_assurance(age, term, sum_assured=sum_assured)
print(f"  {term}-Year Term: ${term_premium:,.2f} per year")

# Endowment
endow_premium = la.endowment_assurance(age, term, sum_assured=sum_assured)
print(f"  {term}-Year Endowment: ${endow_premium:,.2f} per year")

# Calculate total premiums paid
print(f"\nTotal premiums over {term} years:")
print(f"  Term: ${term_premium * term:,.2f}")
print(f"  Endowment: ${endow_premium * term:,.2f}")

Example 4: Yield Curve Analysis

from actuneo.finance import YieldCurve, DurationConvexity
import numpy as np
import matplotlib.pyplot as plt

# Create a yield curve
maturities = [0.25, 0.5, 1, 2, 3, 5, 7, 10, 20, 30]
yields = [0.025, 0.028, 0.030, 0.035, 0.038, 0.042, 0.045, 0.048, 0.052, 0.053]

yc = YieldCurve(maturities, yields)

# Interpolate for all maturities
all_maturities = np.linspace(0.25, 30, 100)
interpolated_yields = [yc.get_yield(m) for m in all_maturities]

# Plot yield curve
plt.figure(figsize=(12, 6))
plt.plot(all_maturities, [y * 100 for y in interpolated_yields], 'b-', linewidth=2)
plt.scatter(maturities, [y * 100 for y in yields], color='red', s=50, zorder=5)
plt.xlabel('Maturity (years)')
plt.ylabel('Yield (%)')
plt.title('Yield Curve')
plt.grid(True, alpha=0.3)
plt.show()

# Calculate discount factors
print("\nDiscount Factors:")
for mat in [1, 5, 10, 20, 30]:
    df = yc.discount_factor(mat)
    print(f"  {mat}-year: {df:.6f}")

Example 5: Reserve Calculation

from actuneo.mortality import MortalityTable
from actuneo.life import LifeAssurance, Reserves
import numpy as np

# Setup
ages = np.arange(20, 101)
qx = 0.001 * (ages - 20) / 80
mt = MortalityTable(ages, qx, name="Reserve Table")

la = LifeAssurance(mt, interest_rate=0.05)
res = Reserves(mt, interest_rate=0.05)

# Policy details
issue_age = 30
sum_assured = 100000
term = 20

# Calculate annual premium
annual_premium = la.endowment_assurance(issue_age, term, sum_assured=sum_assured)

print(f"Endowment Assurance Policy")
print(f"Issue age: {issue_age}")
print(f"Term: {term} years")
print(f"Sum assured: ${sum_assured:,}")
print(f"Annual premium: ${annual_premium:,.2f}\n")

# Calculate reserves at each policy anniversary
print("Policy Reserves:")
print("Year | Age | Reserve")
print("-" * 30)

for t in range(0, term + 1, 5):
    current_age = issue_age + t
    reserve = res.reserve_endowment(issue_age, term, t, annual_premium)
    print(f" {t:2d}  | {current_age} | ${reserve:,.2f}")

More Examples

For more examples and tutorials, visit:

• GitHub Repository

• Examples Directory

Contributing Examples

If you have examples you’d like to share, please submit them via pull request or open an issue on GitHub!