Event Details
- Conferencia: 12 horas día 29 de octubre (Sala de Conferencias, IMAG)
- Conferenciante: Dmitriy Kim, Kazakh National University, Kazakhstan
- Título: Ruin probability for a process with switching
- Short bio: Dmitriy Kim received the Bachelor degree in mathematics from Kazakh National University, Kazakhstan, in 2000, the Master's and Doctoral degrees in probability theory and mathematical statistics from Novosibirsk State University, Russia, in 2002 and 2005, respectively. He has been a researcher at a number of Kazakhstani and European universities and since 2017 he has been working at the School of Digital Technologies, Narxoz University, Almaty, Kazakhstan. Dmitriy Kim specializes in the boundary problems for random processes and in application of probabilistic methods for modeling complex systems.
- Abstract: We consider a class of stochastic processes defined by a partition of the real line into two disjoint sets, each associated with its own probability distribution. When the process takes a value in one of these sets, its subsequent increment follows the distribution corresponding to that set. Such processes are referred to as a processes with one level of switching. The ruin probability is studied for a process with one level of switching between two independent Lévy processes, one being spectrally negative and the other a compound Poisson process with drift. Explicit representations for the ruin probability are obtained in terms of ladder height distributions. As a consequence, results are derived for a risk process in which the premium rate and the claim size distribution depend on whether the current reserve lies above or below a specified threshold.
