Some PDE results in Heston model with applications
Abstract
We present here some results for the PDE related to the logHeston model. We present different regularity results and prove a verification theorem that shows that the solution produced via the Feynman-Kac theorem is the unique viscosity solution for a wide choice of initial data (even discontinuous) and source data. In addition, our techniques do not use Feller’s condition at any time. In the end, we prove a convergence theorem to approximate this solution by means of a hybrid (finite differences/tree scheme) approach.
Type
This work is driven by the results in my previous paper on LLMs.
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Authors
Quantitative Researcher, Ph.D.
I am a Quantitative Researcher and Applied Mathematician with a Ph.D. from École des Ponts ParisTech and University of Roma Tor Vergata. My expertise lies at the intersection of stochastic calculus, high-performance computing, and numerical methods. I specialize in modeling complex stochastic dynamics and building high-performance numerical solutions in C++ and Python, transforming advanced mathematical theory into fast, accurate pricing and risk infrastructure. With prior industry experience as a Quantitative Analyst at Enel and Risk Analyst at AXA, I am passionate about applying advanced mathematical techniques, Monte Carlo simulations, and data-driven methods to solve complex pricing, risk, and alpha-generation problems in financial markets.