Life Insurance - C4-C5

Core Assumptions and Notation

The Standard Ultimate Survival Model

Life Insurance Overview

PV (cont, discrete) + symbol for APV

Pure Endowment

The Endowment Rule

The Deferral Rule

The Whole Life Split

The Deferred Term Trick

Annual → Continuous or 1/mthly life

Concepts and Their Ideas

Annual → Continuous or 1/mthly life

Multipliers & Don’t …

General Valuation Principle

Differing Insurance Benefits

Increasing Insurance

Differing Insurance Benefits

Geometric Progression

Note on Select Lives

Annuity Certain

Annuity Certain

3 types + formulas

Annuity Types

Annuity Certain

1/m-thly

r.v. representing PV of the whole life annuity-due for (x)

• Using the insurance present value random variable

• Summing EPVs of individual payments

• Using the probability function for K_x

Finding Whole Life Annuity Formulae

Using the insurance present value random variable

Finding Whole Life Annuity Formulae

Summing EPVs of individual payments

Finding Whole Life Annuity Formulae

Using the probability function for K_x

Term Annuity-Due

WL Annuity-Due → WL Immediate Annuity

Term Immediate Life Annuity

Continuous Whole Life Annuity

Continuous Term Annuity

Annuities Payable 1/m-thly

Properties

Whole Life 1/m-thly annuity-due

PV r.v.

Whole Life 1/m-thly annuity-due

EPV

Whole Life 1/m-thly immediate annuity

Term Life 1/m-thly annuity-due

Term life immediate annuity payable 1/m-thly

Comparison of sizes PV annuities

Deferred Annuities

Guaranteed Annuities

Increasing Annuities

Arithmetically increasing annuities

Geometrically increasing annuities

Evaluating Annuity Functions

Evaluating Annuity Functions

Recursions

Evaluating Annuity Functions

Applying the UDD assumption

Numerical Illustrations and Method Comparison

Contenders

Numerical Illustrations and Method Comparison

Verdict

Functions for select lives

Annuities

Overview

EPV:

Continuous Whole Life Annuity

Discrete Whole Life Annuity-Due

Discrete Whole Life Annuity-Immediate