This work investigates the dynamics of competitive Kolmogorov systems formulated in a semi-Markov regime-switching framework. The conditional holding time each environmental regime is allowed to follow arbitrary probability distribution on nonnegative half-line sense approximations. Sharp sufficient conditions coexistence and exclusion species are established, case ...

Using a Markov‐switching VAR, we show that the effects of uncertainty shocks on output are four times higher in regime economic distress than tranquil regime. We then provide structural interpretation these facts. To do so, develop business cycle model which agents aware possibility changes when forming expectations. The is estimated using Bayesian minimum distance estimator minimizes, over set...

The probability of a stochastic process to first breach an upper and/or a lower level is an important quantity for optimal control and risk management. We present those probabilities for regime switching Brownian motion. In the 2and 3-state model, the Laplace transform of the (single and double barrier) first-passage times is – up to the roots of a polynomial of degree 4 (respectively 6) – deri...

Econometric literature on financial durations has been popularized by the introduction of the Autoregressive Conditional Duration model. In the latest years, a lot of refinements have been suggested. Following financial market microstructure arguments, it is argued that a Pareto distribution is a meaningful representation for durations. The model is analyzed under the hypothesis of regime-switc...

This work focuses on numerical methods for finding optimal investment, dividend payment, and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections. The surplus is modeled by a regime-switching jump diffusion process subject to both regular and singular controls. Using dynamic programming principle, ...

We consider a Markovian regime-switching risk model (also called the Markov-modulated risk model) with stochastic premium income, in which the premium income and the claim occurrence are driven by the Markovian regime-switching process. The purpose of this paper is to study the integral equations satisfied by the expected discounted penalty function. In particular, the discount interest force p...

This work focuses on regime-switching jump diffusions, which include three classes of random processes, Brownian motions, Poisson processes, and Markov chains. First, a scalar linear system is treated as a benchmark model. Then stabilization of systems with one-sided linear growth is considered. Next, nonlinear systems that have a finite explosion time are treated, in which regularization (expl...