A simple life insurance

DataCamp

Valuation of Life Insurance Products in R

VALUATION OF LIFE INSURANCE PRODUCTS IN R

A simple life insurance Roel Verbelen, Ph.D. Postdoctoral researcher, KU Leuven

DataCamp

The life insurance

Valuation of Life Insurance Products in R

DataCamp

A simple life insurance The product is sold to (x) at time 0.

Valuation of Life Insurance Products in R

DataCamp

Valuation of Life Insurance Products in R

A simple life insurance Expected Present Value:

The EPV is k∣1 Ax

= 1 ⋅ v(k + 1) ⋅ k px ⋅ qx+k = 1 ⋅ v(k + 1) ⋅ k∣ qx .

DataCamp

Valuation of Life Insurance Products in R

A simple life insurance in R Compute 5∣1 A65 = 1 ⋅ v(6) ⋅ 5∣ q65 = 1 ⋅ v(6) ⋅ 5 p 65 ⋅ q70 for constant i = 3%. > # Mortality rates and one-year survival probabilities > qx px # 5-year deferred mortality probability of (65) > kpx kqx kqx [1] 0.02086664 > # Discount factor > discount_factor discount_factor [1] 0.8374843 > # EPV of the simple life insurance > 1 * discount_factor * kqx [1] 0.01747548

DataCamp

Valuation of Life Insurance Products in R

VALUATION OF LIFE INSURANCE PRODUCTS IN R

Let's practice!

DataCamp

Valuation of Life Insurance Products in R

VALUATION OF LIFE INSURANCE PRODUCTS IN R

The whole, temporary and deferred life insurance Katrien Antonio, Ph.D.

Professor, KU Leuven and University of Amsterdam

DataCamp

A series of one-year contracts

What if? The benefit is bk EUR instead of 1 EUR? A series of one-year contracts instead of just one?

Valuation of Life Insurance Products in R

DataCamp

Valuation of Life Insurance Products in R

General setting A life insurance on (x) with death benefit vector (b0 , b1 , … , b k , …) Series of one-year contracts: each with bk ⋅ v(k + 1) ⋅ k px ⋅ qx+k as Expected Present Value (EPV) together: +∞

+∞

k=0

k=0

∑ bk ⋅ v(k + 1) ⋅ k px ⋅ qx+k = ∑ bk ⋅ v(k + 1) ⋅ k∣ qx the EPV.

DataCamp

Whole life insurance Whole life insurance: lifelong.

Valuation of Life Insurance Products in R

DataCamp

Temporary life insurance Temporary (or: term) life insurance: maximum of n years.

Valuation of Life Insurance Products in R

DataCamp

Valuation of Life Insurance Products in R

Deferred whole life insurance Deferred whole life insurance: no payments in first u years.

DataCamp

Life insurances in R Compute A35 for constant interest rate i = 3%. > # Whole-life insurance of (35) > kpx kqx discount_factors benefits sum(benefits * discount_factors * kqx) [1] 0.2880872

Now do 20∣ A35 . > # Deferred whole-life insurance of (35) > kpx kqx discount_factors benefits sum(benefits * discount_factors * kqx) [1] 0.2552956

Valuation of Life Insurance Products in R

DataCamp

Valuation of Life Insurance Products in R

VALUATION OF LIFE INSURANCE PRODUCTS IN R

Let's practice!

DataCamp

Valuation of Life Insurance Products in R

VALUATION OF LIFE INSURANCE PRODUCTS IN R

Combined benefits Roel Verbelen, Ph.D. Postdoctoral researcher, KU Leuven

DataCamp

Endowment insurance

Valuation of Life Insurance Products in R

DataCamp

Valuation of Life Insurance Products in R

Sending baby Incredible to college









Mrs. Incredible is 35 years old. She wants to save money to send her baby to college. She needs 75,000 EUR when he gets 18. Given her dangerous lifestyle as a superhero, at the same time she wants to cover her life. The sum insured is 50,000 euro. Can you design this type of life insurance policy?

DataCamp

Valuation of Life Insurance Products in R

Sending baby Incredible to college pictured

DataCamp

Valuation of Life Insurance Products in R

Sending baby Incredible to college in R She is 35-years-old, living in Belgium, year 2013. Interest rate is 3%. > i kqx discount_factors benefits EPV_death_benefits EPV_death_benefits [1] 870.8815

DataCamp

Valuation of Life Insurance Products in R

Sending baby Incredible to college in R Pure endowment (using the survival probability 18 p35 ) > EPV_pure_endowment EPV_pure_endowment [1] 42975.86

Premium pattern rho (using the survival probabilities 0 p35 to 17 p 35 ) > # Premium pattern rho > kpx discount_factors rho EPV_rho EPV_rho [1] 14.06193

DataCamp

Valuation of Life Insurance Products in R

Sending baby Incredible to college in R Actuarial equivalence EPV(death benefits) + EPV(pure endowment) P = . EPV(rho) > # Premium level > (EPV_death_benefits + EPV_pure_endowment) / EPV_rho [1] 3118.116

DataCamp

Valuation of Life Insurance Products in R

VALUATION OF LIFE INSURANCE PRODUCTS IN R

Let's practice!

DataCamp

Valuation of Life Insurance Products in R

VALUATION OF LIFE INSURANCE PRODUCTS IN R

Congratulations! Katrien Antonio and Roel Verbelen Professor, KU Leuven and University of Amsterdam Postdoctoral researcher, KU Leuven

DataCamp

What you've learned Valuation of cash flows Life tables Life annuities Life insurances

Valuation of Life Insurance Products in R

DataCamp

Want to know more?

Valuation of Life Insurance Products in R

DataCamp

What else is there? More advanced life insurance products. Loss models for frequencies and severities. Data science in insurance.

Valuation of Life Insurance Products in R

DataCamp

Valuation of Life Insurance Products in R

VALUATION OF LIFE INSURANCE PRODUCTS IN R

Enjoy your journey as an actuary!