Solution of the space-fractional diffusion equation on bounded domains of superdiffusive phenomena

DA Monroy, EP Raposo - Physical Review E, 2024 - APS
Space-fractional diffusion equations find widespread application in nature. They govern the
anomalous dynamics of many stochastic processes, generalizing the standard diffusion …

Pricing, risk and volatility in subordinated market models

JP Aguilar, JL Kirkby, J Korbel - Risks, 2020 - mdpi.com
We consider several market models, where time is subordinated to a stochastic process.
These models are based on various time changes in the Lévy processes driving asset …

Closed-form option pricing for exponential Lévy models: a residue approach

JP Aguilar, JL Kirkby - Quantitative Finance, 2023 - Taylor & Francis
Exponential Lévy processes provide a natural and tractable generalization of the classic
Black–Scholes–Merton model which account for several stylized features of financial …

On the quantitative properties of some market models involving fractional derivatives

JP Aguilar, J Korbel, N Pesci - Mathematics, 2021 - mdpi.com
We review and discuss the properties of various models that are used to describe the
behavior of stock returns and are related in a way or another to fractional pseudo-differential …