## Leeds-Liverpool joint workshop

This is a 1 day event held virtually at the University of Liverpool and jointly organized by Tiziano de Angelis (University of Leeds) and Julia Eisenberg and Ehsan Azmoodeh (University of Liverpool).

### Programme

 Time Speaker Title of the Talk 14:00 – 14:35 Konstantinos Dareiotis (University of Leeds) Approximation of SDEs - a stochastic sewing approach 14:40 – 14:50 Coffee break 14:50 – 15:25 Hirbod Assa (University of Liverpool) Commodity price modeling by optimal storage time 15:25 – 16:00 Conclusions and remarks

Konstantinos Dareiotis

Title: Approximation of SDEs - a stochastic sewing approach

Abstract: :We give a new take on the error analysis of approximations of stochastic differential equations (SDEs), utilising the stochastic sewing lemma [K. Le, ’18] . This approach allows one to exploit regularisation by noise effects in obtaining convergence rates. In our first application we show convergence (to our knowledge for the first time) of the Euler-Maruyama scheme for SDEs driven by fractional Brownian motions with non-regular drift. When the Hurst parameter is $H\in(0,1)$ and the drift is $C^\alpha$, $\alpha>2-1/H$, we show the strong $L_p$ and almost sure rates of convergence to be $(1/2+\alpha H) \wedge 1-$. As another application we consider the approximation of SDEs driven by multiplicative standard Brownian noise where we derive the almost optimal rate of convergence $1/2-$ of the Euler-Maruyama scheme for $C^\alpha$ drift, for any $\alpha>0$.

Hirbod Assa

Title: Commodity price modeling by optimal storage time

Abstract: The purpose of this paper is threefold. First, by assuming that in a commodity market all producers have the possibility to store goods, we introduced a continuous time speculative storage model that is based on a basic version of a model developed in Deaton and Laroque (1992); Deaton and Laroque (1995); Deaton and Laroque (1996); Deaton and Laroque (2003). This model incorporates speculative storage into the demand and establishes the concept of speculative demand. Second, we prove that the speculators' expectation price converges to a stationary rational expectations equilibrium (SREE). Finally, we estimate the model parameters values with and without storage for real data, and by running a likelihood ratio test we will observe that for the real data introducing storage in the model makes a statistically significant difference.