Title: Hybrid Risk Processes: A Robust Framework for Modern Ruin Problems
Abstract: We introduce a novel class of risk processes based on hybrid stochastic differential equations, providing a unified framework that captures a wide range of actuarial models. This class accommodates both jump and diffusion dynamics, allowing for features such as reserve-dependent adjustments, dividend strategies, and other structural complexities commonly encountered in insurance risk modeling. The framework also facilitates the analysis of generalized notions of ruin, including Parisian, Omega, and Poissonian ruin. Moreover, it enables efficient computation of key risk measures, making it a versatile tool for both theoretical and practical applications.
Bio: Dr. Oscar Peralta is an applied probabilist with research interests in actuarial science, finance, operations research, and statistics. In particular, he is interested in the interplay between probabilistic arguments, their theoretical foundations, and their applications in other branches of mathematics. After completing his Ph.D. in 2019 at the Technical University of Denmark under the supervision of Professors Bo Friis Nielsen and Mogens Bladt, he became a Research Associate at the University of Adelaide in Australia, working with Dr. Giang Nguyen on hybrid stochastic differential equations. Subsequently, he secured a position as a Senior Researcher at the University of Lausanne in Switzerland, collaborating with Professor Hansjoerg Albrecher on mathematical problems in life and non-life insurance. Following this, he accepted a Postdoctoral Researcher position at Cornell University, working with Professor Andreea Minca to explore new questions in risk management. In 2024, Dr. Oscar Peralta joined the Department of Actuarial Science and Insurance at the Autonomous Technical Institute of Mexico (ITAM) as an Assistant Professor.