General methods for bounding multidimensional ruin probabilities in regime-switching models

Abstract

We present a universal methodology for bounding multidimensional ultimate ruin probabilities in regime-switching models. Some new lower and upper bounds on are given. The considered methods are applicable to several discrete-and continuous time risk models. As an example, we construct a variety of new two-sided operator bounds which converge to with an exponential rate. Several numerical examples are also provided.

Optimal Surplus-Dependent Reinsurance under Regime-Switching in a Brownian Risk Model

“…In financial literature, regime-switching models have become very popular because they take into account possible macroeconomic changes. Originally proposed by Hamilton to model stock returns, this class of models has been adopted also in insurance mathematics, see, e.g., Asmussen (1989); Bargès et al (2013); Bäuerle and Kötter (2007); Gajek and Rudź (2020); Jiang and Pistorius (2012). In this connection, one should not forget the models containing hidden information.…”