Numerical approximations for stochastic differential equations
JM Foster - 2020 - ora.ox.ac.uk
In this thesis, we consider problems related to the numerical simulation of stochastic
differential equations (SDEs). In particular, we are interested in methods that use both …
differential equations (SDEs). In particular, we are interested in methods that use both …
Robust option pricing with volatility term structure--An empirical study for variance options
AMG Cox, AM Grass - arXiv preprint arXiv:2312.09201, 2023 - arxiv.org
The robust option pricing problem is to find upper and lower bounds on fair prices of
financial claims using only the most minimal assumptions. It contrasts with the classical …
financial claims using only the most minimal assumptions. It contrasts with the classical …
Delayed switching identities and multi-marginal solutions to the Skorokhod embedding problem
AMG Cox, AM Grass - arXiv preprint arXiv:2312.04218, 2023 - arxiv.org
In this article, we consider a generalisation of the Skorokhod embedding problem (SEP) with
a delayed starting time. In the delayed SEP, we look for stopping times which embed a given …
a delayed starting time. In the delayed SEP, we look for stopping times which embed a given …
Perkins embedding for general starting laws
A Grass - arXiv preprint arXiv:2307.03618, 2023 - arxiv.org
The Skorokhod embedding problem (SEP) is to represent a given probability measure as a
Brownian motion $ B $ at a particular stopping time. In recent years particular attention has …
Brownian motion $ B $ at a particular stopping time. In recent years particular attention has …
The Nonlocal Stefan Problem via a Martingale Transport
We study the nonlocal Stefan problem, where the phase transition is described by a
nonlocal diffusion as well as the change of enthalpy functions. By using a stochastic …
nonlocal diffusion as well as the change of enthalpy functions. By using a stochastic …
The Stefan problem and free targets of optimal Brownian martingale transport
We formulate and solve a free target optimal Brownian stopping problem from a given
distribution while the target distribution is free and is conditioned to satisfy a given density …
distribution while the target distribution is free and is conditioned to satisfy a given density …
Optimal stopping of stochastic transport minimizing submartingale costs
Given a stochastic state process $(X_t) _t $ and a real-valued submartingale cost process
$(S_t) _t $, we characterize optimal stopping times $\tau $ that minimize the expectation of …
$(S_t) _t $, we characterize optimal stopping times $\tau $ that minimize the expectation of …
On the continuity of the root barrier
E Bayraktar, T Bernhardt - Proceedings of the American Mathematical …, 2022 - ams.org
On the continuity of the root barrier Page 1 PROCEEDINGS OF THE AMERICAN
MATHEMATICAL SOCIETY Volume 150, Number 7, July 2022, Pages 3133–3145 https://doi.org/10.1090/proc/15765 …
MATHEMATICAL SOCIETY Volume 150, Number 7, July 2022, Pages 3133–3145 https://doi.org/10.1090/proc/15765 …
Shadows and barriers
M Brückerhoff, M Huesmann - The Annals of Applied Probability, 2024 - projecteuclid.org
In this article, we show an intimate connection between two objects in probability theory,
which received some attention in the last years: shadows of measures and barrier solutions …
which received some attention in the last years: shadows of measures and barrier solutions …
Switching identities by probabilistic means
Switching identities have a long history in potential theory and stochastic analysis. In recent
work of Cox and Wang, a switching identity was used to connect an optimal stopping …
work of Cox and Wang, a switching identity was used to connect an optimal stopping …