Computing The Joint Distribution Of The Surplus Before Ruin And The Deficit At Ruin

The word "risk" is known to all of us, it exists in our daily life. In order to avoid it, insurance industry comes into the world. Simultaneously, the insurance companies themselves are in face of the risk of ruin, so we focus on the problem how to operate the company stably and to keep a good solvency. In recent years, research on ruin theory is a pop task. There are a vast amount of literature on solving the upper and the lower bounds of the ruin probability, computing and simulating ruin probability, calculating the distribution of the surplus before ruin and the distribution of the deficit at ruin, also their joint distribution. This paper is based on the former's research, simplifies the ruin probability when the claim times follow a Poisson process and the claims have a Pareto distribution, then computes the joint distribution of the surplus before ruin and the deficit at ruin. Besides, we simulating the ruin probability when the claims have a mix-subexponential distribution and then computes the joint distribution of the surplus before ruin and the deficit at ruin. Prom doing this, we generalize the question to a field of quantitative research.