FINITE TIME RUIN PROBABILITY USING HAWKES VARIABLE MEMORY COUNTING PROCESS WITH EXPONENTIAL DISTRIBUTION CLAIMS

The finite time ruin probability in actuarial science and in companies throughout their operating lives remains a major and very complex concern for the latter. Given the complexity of the occurrence of natural risk phenomena, the mathematical determination of this probability can prove particularly complex. This mathematical complexity represents a considerable obstacle for researchers in this field. Previous research has mainly focused on risk models constructed from Markovian processes. In this paper, we address the modeling risk where the number of claims is approximated by a variable memory counting process based on a self-excited Hawkes process. We subsequently considered that the claim amounts are independent random variables and identically distributed following an exponential law. This allowed us to determine an expression for the probability of ruin in finite time. We proposed a simulation to visualize the evolution of the probability of ruin as a function of the initial reserve and time.