# Dying board

the dying board says x /math for each <reached> age< math> out, with which probability an individual of a certain collective (person's group) the age [itex] x+1< /math> reached. The probability of one [itex] x< /math> - year old person, before reaching the age [itex] x+1< /math> to die, /math becomes as <probability of dying> math< q_x> designated.

Frequently for men and women usually own dying boards are used. From the dying board the life expectancy of a newborn child and the so-called leave themselves. further life expectancy, thus the life expectancy of a person at the age [itex] for x< /math>, calculate.

Apart from the probabilities of dying [itex] q_x< /math> become for each age [itex] x< /math> usually the number [itex] l_x< /math> the living persons and the number at the age [itex] of x< /math> deceasing persons [itex] d_x< /math> tabulated. One usually goes to 100,000 [/itex] from math l_0< => or [itex] l_0 = 1.000.000< /math> newborn persons out. Thus one can explain descriptive, how a person collective in the model reduces by the deaths. It applies:

[itex] q_x = \ frac {d_x} {l_x}< /math>
[itex] d_x = l_x - l_ {x+1}< /math>

The calculation of private life insurances (the risk for the insurer consists of it furnishing with death of the insured person (premature) a capital achievement) and old age pension insurances (the risk consists the pension for the insurer of it that the person deceases not early, but long years refers) different dying boards are the basis. So the German registrar combination has registered association. (DAV) different dying boards develops:

• With the board DAV 1994 T can be calculated insurance with a death character (thus life insurances on death and case of experiencing, risk insurance). For safety reasons the probabilities of dying are increased in relation to the reality.
• The dying board DAV 2004 R is for insurance with an experiencing drop character (old age pension insurances) a suitable basis of calculation. For safety reasons the probabilities of dying are degraded in relation to the reality.

Both DAV boards may be consulted also for the reservation of the obligations ( covering resetting), which can be proven in the balance. The older board DAV 1994 R may be against it no more basis of the computation of the covering resetting considered by old age pension insurances, there it the trend of the improvement of the number of deaths (because of medical progress, improvement of the life circumstances) for persons born later from today's viewpoint not sufficiently.

The final age of the dying board becomes usually with the Greek letter [itex] \ omega< /math> designated (e.g. DAV 1994 T: [itex] \ omega = 100< /math>; DAV 2004 R: [itex] \ omega = 120< /math>, clearly longer, there hereby old age pension insurances to be thus calculated).

In the insurance economy period dying boards are often used. Agespecific mortalnesses is determined from at the same time living persons. Period boards describe therefore modelful number of deaths conditions of at the same time living generations within a relatively short observation period.

In contrast to it Kohortensterbetafeln , which describe a dying Geburtsjahrganges, are unsuitable due to the long observation period for the calculation of old age pension insurances.

By a generation dying board one understands a dying board, with that the number of deaths not only about the age (and possibly of the sex), but additionally about Geburtsjahrgang depends. Thereby the rising life expectancy for persons born later can be considered. Generation boards are the basis therefore the calculation of old age pension insurances. Above the boards DAV already mentioned 1994 R and DAV 2004 R are generation boards. Sometimes birth year dependence is illustrated simplifying by the fact that classes for the calculation, born later, become “younger made” by a simple age shift.

Partially also insuring dying boards are used. These consider that the number of deaths of the insuring collective of that the population e.g. due to a health examination or the self selection deviates.

The method of the dying board computation belongs to the not-parametric procedures of the event analysis (analysis event).