Abstract
Inspired by a duration-dependent life insurance model, we explore continuous-time semi-Markov jump processes. We develop approximations using time-homogeneous Markov jump processes conditioned on a high-intensity Poissonian grid (grid-conditional). Our approach leverages a recent adaptation of the uniformization principle, resulting in a strongly pathwise convergent sequence of jump processes. Unlike traditional methods that rely on solving integro-differential equations to compute value functions, our approximations yield straightforward, implementable expressions. This makes them particularly useful for scenarios where evaluating pathwise distributional functionals of the original semi-Markov process proves challenging.
Bio:
Andreea Minca is a Professor in the School of Operations Research and Information Engineering at Cornell University. She holds degrees from Sorbonne University (PhD in Applied Mathematics) and Ecole Polytechnique (Diplome de l'Ecole Polytechnique).
In recognition of "her fundamental research contributions to the understanding of financial instability, quantifying and managing systemic risk, and the control of interbank contagion", Andreea received the 2016 SIAM Activity Group on Financial Mathematics and Engineering Early Career Prize. Andreea is also a recipient of the NSF CAREER Award (2017), a Research Fellow of the Global Association of Risk Professionals (GARP) (2014), and an AXA Research Fund Awardee (2020).
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