no code implementations • 15 Aug 2023 • Abdul-Lateef Haji-Ali, Jonathan Spence
Under strong convergence criteria on approximations to $X$ and $Y$, randomised multilevel Monte Carlo techniques can be used to construct unbiased Monte Carlo estimates of $U_1$, which can be paired with an antithetic MLMC estimate of $U_0$ to recover order $\varepsilon^{-2}$ computational cost.
no code implementations • 14 Jan 2023 • Michael B. Giles, Abdul-Lateef Haji-Ali, Jonathan Spence
Associated risk measures, such as the value-at-risk of an underlying valuation adjustment, play an important role in managing these risks.
1 code implementation • 19 Jul 2021 • Abdul-Lateef Haji-Ali, Jonathan Spence, Aretha Teckentrup
We consider the numerical approximation of $\mathbb{P}[G\in \Omega]$ where the $d$-dimensional random variable $G$ cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations $\{G_\ell\}_{\ell\in\mathbb{N}}$ which can be sampled.
no code implementations • 4 Jan 2021 • Abdul-Lateef Haji-Ali, Håkon Hoel, Raúl Tempone
By employing a system of interacting stochastic particles as an approximation of the McKean--Vlasov equation and utilizing classical stochastic analysis tools, namely It\^o's formula and Kolmogorov--Chentsov continuity theorem, we prove the existence and uniqueness of strong solutions for a broad class of McKean--Vlasov equations.
Probability Numerical Analysis Numerical Analysis 65C05, 62P05
1 code implementation • 11 Dec 2019 • Michael B. Giles, Abdul-Lateef Haji-Ali
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different risk scenarios and (b) evaluating the loss of the portfolio is expensive and the cost increases with its size.
