This special issue, edited by Alexander Zeifman, Victor Korolev, and Alexander Sipin, focuses on recent advances in the theory and applications of stochastic processes. It includes 15 original research articles that cover various aspects of stochastic processes, particularly in queueing theory, Markov processes, risk theory, Monte Carlo methods, and probability models in meteorological phenomena. The articles were contributed by researchers from Belarus, China, Finland, Iran, Italy, Korea, and Russia. One of the key contributions is a new generalized Gerber–Shiu discounted penalty function for a compound Poisson risk model, which is used to study the moments of the ruin time. The authors propose a recursion method using Laplace transform to calculate the generalized Gerber–Shiu discounted penalty function and derive explicit expressions for exponential claim distributions. Numerical examples illustrate the effects of parameters on the function. Another significant article discusses the valuation of guaranteed minimum death benefits (GMDB) using the Fourier cosine series expansion (COS) method. The authors express the value of GMDB through the discounted density function approach and approximate the valuation equations using the COS method. They provide explicit equations for the cosine coefficients when the distribution of the time-until-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential Lévy process. Numerical experiments demonstrate the efficiency of the proposed method. The special issue aims to provide valuable insights into the latest developments in stochastic processes and their applications, making it a valuable resource for researchers and practitioners in probability theory and related fields.This special issue, edited by Alexander Zeifman, Victor Korolev, and Alexander Sipin, focuses on recent advances in the theory and applications of stochastic processes. It includes 15 original research articles that cover various aspects of stochastic processes, particularly in queueing theory, Markov processes, risk theory, Monte Carlo methods, and probability models in meteorological phenomena. The articles were contributed by researchers from Belarus, China, Finland, Iran, Italy, Korea, and Russia. One of the key contributions is a new generalized Gerber–Shiu discounted penalty function for a compound Poisson risk model, which is used to study the moments of the ruin time. The authors propose a recursion method using Laplace transform to calculate the generalized Gerber–Shiu discounted penalty function and derive explicit expressions for exponential claim distributions. Numerical examples illustrate the effects of parameters on the function. Another significant article discusses the valuation of guaranteed minimum death benefits (GMDB) using the Fourier cosine series expansion (COS) method. The authors express the value of GMDB through the discounted density function approach and approximate the valuation equations using the COS method. They provide explicit equations for the cosine coefficients when the distribution of the time-until-death random variable is approximated by a combination of exponential distributions and the price of the fund is modeled by an exponential Lévy process. Numerical experiments demonstrate the efficiency of the proposed method. The special issue aims to provide valuable insights into the latest developments in stochastic processes and their applications, making it a valuable resource for researchers and practitioners in probability theory and related fields.