Ruin probability via several numerical methods

In this thesis, ruin probabilities of insurance companies are studied. Ruin proba- bility in finite time is considered because it is more realistic compared with infinite time ruin probabilities. However, infinite time methods are also mentioned in order to compare them with the finite time methods. The thesis will initially provide some information about ruin probability of a risk process in finite and infinite time, and then the Markov chain and quantum mechan- ics approaches will be shown in order to compute the ruin probability. Using a reinsurance agreement, which is a risk sharing tool in actuarial science, the ruin probability of a modified surplus process in finite time via the quantum mechanics approach is studied. Furthermore, some optimization problems about capital injections, withdrawals and reinsurance premiums are taken into considera- tion in order to minimise the ruin probability. Finally, the thesis compares the finite time method under the reinsurance agreement in terms of the ruin probability and total injections amount with an infinite time counterpart method.