Ruin Theory
Overview
In the insurance, the event that occurs when an insurance company becomes insolvent is called "ruin". It is a core concern of an
insurer to be able to minimize and control the probability of ruin. This requires a set of models sometimes called
"theory of ruin" or ruin theory.
Definitions
Set {% R(t) %} to the reserve of the company at time t. The time of ruin, {% \tau %} is defined as
{% \tau = inf\{ t:R(t) < 0 \} %}
Then the probability of ruin is
{% Prob = \mathbb{P} (\tau \leq T) %}
In the context of
measure theory,
the time of ruin is a
stopping time
Models
