Massoud Heidari

Ali Hirsa, Massoud Heidari

Individual trade orders are often bunched into a block order for processing efficiency, where in post execution, they are allocated into individual accounts. Since Regulators have not mandated any specific post trade allocation practice or methodology, entities try to rigorously follow internal policies and procedures to meet the minimum Regulatory ask of being procedurally fair and equitable. However, as many have found over the years, there is no simple solution for post trade allocation between accounts that results in a uniform distribution of returns. Furthermore, in many instances, the divergences between returns do not dissipate with more transactions, and tend to increase in some cases. This paper is the first systematic treatment of trade allocation risk. We shed light on the reasons for return divergence among accounts, and we present a solution that supports uniform allocation of return irrespective of number of accounts and trade sizes.

Nicholas G. Polson, Brandon T. Willard, Massoud Heidari

In this paper we develop a statistical theory and an implementation of deep learning models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers optimises a deep learning objective. We allow for non-smooth non-convex regularisation penalties to induce sparsity in parameter weights. We provide a link between traditional shallow layer statistical models such as principal component and sliced inverse regression and deep layer models. We also define the degrees of freedom of a deep learning predictor and a predictive MSE criteria to perform model selection for comparing architecture designs. We focus on deep multiclass logistic learning although our methods apply more generally. Our results suggest an interesting and previously under-exploited relationship between deep learning and proximal splitting techniques. To illustrate our methodology, we provide a multi-class logit classification analysis of Fisher's Iris data where we illustrate the convergence of our algorithm. Finally, we conclude with directions for future research.