19 citations · 26 across the 3 of their papers we have counts for
3 papers
q-fin.PR2023
Black-Scholes without stochastics or PDEs
Richard J. Martin
We show how to derive the Black-Scholes model and its generalisation to the `exchange-option' (to exchange one asset for another) via the continuum limit of the Binomial tree. No k…
math-ph2018★ 19 cited
Long- and short-time asymptotics of the first-passage time of the Ornstein-Uhlenbeck and other mean-reverting processes
R. J. Martin, M. J. Kearney, R. V. Craster
The first-passage problem of the Ornstein-Uhlenbeck process to a boundary is a long-standing problem with no known closed-form solution except in specific cases. Taking this as a s…
math-ph2018★ 7 cited
Analytical approximation to the multidimensional Fokker--Planck equation with steady state
R. J. Martin, R. V. Craster, A. Pannier +1
The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to spec…