38 citations · 70 across the 29 of their papers we have counts for
4 papers · 1 filter
On the Admissibility of Linear Stochastic Volterra Operators
John A. D. Appleby, John A. Daniels, David W. Reynolds
Conditions guaranteeing convergence of linear stochastic Volterra operators are studied. Necessary and sufficient conditions for mean square convergence are established, while almo…
A Black--Scholes Model with Long Memory
John A. D. Appleby, John A. Daniels, Katja Krol
This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stat…
Necessary and sufficient conditions for periodic decaying resolvents in linear discrete convolution Volterra equations and applications to ARCH processes
John A. D. Appleby, John A. Daniels
We define a class of functions which have a known decay rate coupled with a periodic fluctuation. We identify conditions on the kernel of a linear summation convolution Volterra eq…
Long run behaviour of the autocovariance function of ARCH() models
John A. D. Appleby, John A. Daniels
The asymptotic properties of the memory structure of ARCH() equations are investigated. This asymptotic analysis is achieved by expressing the autocovariance function of AR…