Table of Contents

## What do you mean by force of mortality?

In actuarial science, force of mortality represents the instantaneous rate of mortality at a certain age measured on an annualized basis. It is identical in concept to failure rate, also called hazard function, in reliability theory.

## What was Benjamin Gompertz main discovery with respect to mortality rates?

The probabilty of death within in a certain time period. -Benjamin Gompertz discovered within a given population, the rate of change in the natural log of mortality rates is fairly constant across all ages.

**What is the Balducci assumption?**

The Balducci assumption implies a decreasing mortality rate over [x, x+1] and Uniform distribution gives an increasing mortality rate. For a given number of deaths over the period, the estimated exposure would be highest if we assumed an increasing mortality rate.

### What is the Curtate expectation of life?

e , curtate expectation of life : – expectation of life where only complete years of life count. mx , the central death rate :- defined as mx= dx/L. x .

### How do you use force of mortality?

The force of mortality becomes µx = qx 1 − (1 − s)qx . The mortality rate qx = P[ a person who has lived to age x dies before reaching age x+1] provides a direct comparison of the risk of death at different ages.

**Can force of mortality exceed 1?**

Although can never exceed 1, both and can do so. Consider, for example, a cohort in which 8 members reach age x, of whom 7 die within 12 months. In a cohort, the central death rate relates to all deaths between the exact age x and the exact age .

## What is Gompertz formula?

In the Gompertz model, the value at inflection (Wi) is locked at 36.8% of the upper asymptote, and is calculated as Wi = A/ℯ.

## Is Gompertz exponential?

The Gompertz distributon , named for Benjamin Gompertz, is a continuous probability distribution on that has exponentially increasing failure rate. Unfortunately, the death rate of adult humans increases exponentially, so the Gompertz distribution is widely used in actuarial science.

**What is UDD assumption?**

i) UDD method is based on the assumption that for integer x and 0 ≤ t ≤ 1, the function. tpx.µx+tis a constant. i.e. for an individual exactly aged x(integer) the probability of dying on. any one particular day over the next year is same as that of dying on any other day over the. next year.

### How do you calculate LX on a life table?

Lx The number of person-years lived between exact ages x and x+1. The average number of years of life remaining at exact age x. l0 = 100,000 lx = lx-1 • (1 – qx-1) x = 1, 2, 3, … dx = lx • qx x = 0, 1, 2, 3, …

### What is complete expectation of life?

The complete expectation of life, typically for a new-born life, is often used to compare the general level of health in different populations. The random variable is used to represent the curtate future lifetime for a life of exact age (i.e. the number of complete years lived after age ).

**How is actuarial present value calculated?**

Suppose the death benefit is payable at the end of year of death. Then T(G, x) := ceiling(G – x) is the number of “whole years” (rounded upwards) lived by (x) beyond age x, so that the actuarial present value of one unit of insurance is given by: is the probability that (x+t) dies within one year.