Resurgence of large order relations

We model the execution of a large uninformed sell order in the presence of strategic competitive market makers. We solve for the unique symmetric equilibrium of the model in closed form. Analysis of this equilibrium reveals that large orders unequivocally benefit market makers, while smaller investors stand to benefit only if the order trades with a sufficiently high intensity. The equilibrium results further provide a rationale for the empirically observed patterns of (i) shorter orders trading at higher intensities, and (ii) price pressures potentially subsiding before large orders stop executing.

The optimal execution of stock trades is a relevant and interesting problem as it is key in maximizing profits and reducing risks when investing in the stock market. In the case of large orders, the problem becomes even more complex as the impact of the order in the market has to be taken into account. The usual solution is to split large orders into a set of smaller suborders that must be executed within a prescribed time window. This leads to the problem of deciding when in the time window execute each suborder. There are popular ways of executing the trading of these split orders like those which try to track the “Time Weighted Average Price” and the “Volume Weighted Average Price”, usually called TWAP and VWAP orders. This paper presents a strategy to optimize the splitting of large trade orders over a given time window. The strategy is based on the solution of an optimization problem that is applied following a receding horizon approach. This approach reduces the impact of prediction errors due to the uncertain market dynamics, by using new values of the price time series as they are available as time goes on. Suborder size constraints are taken into account in both market and limit orders. The strategy relies on price and traded volume forecast but it is independent of the prediction technique used. The performance index weighs not only the financial cost of the suborders, but also the impact on the market and the forecasting accuracy. A tailored optimization algorithm is proposed for efficiently solving the corresponding optimization problem. Most of the computations of the algorithm can be parallelized. Finally, the proposed approach has been tested through a case study composed by stocks of the Chinese A-share market.

The proprietary trading pattern is investigated around the large order events of individual, foreign, institution and insider investors to examine whether they front run other investors’ large orders, using the data from the Stock Exchange of Thailand (SET) during March 2007 to December 2009. The proprietary investors have statistically significant daily abnormal volume, in the same direction with the impending large orders, before the event date of the individual and insider large order events. The results suggest the evidence of front running in aggregate, after removing other explanations. Moreover, the daily abnormal returns and cumulative abnormal returns (CAR) around the large order events of each investor type suggest that the profits from front running the individual large orders are inconclusive. For the insider large order event, the proprietary investors gain on average according to the insider large buy event, while they not only have no profit but also lose the opportunities to gain according to the insider large sell event.

A simple power-series method is developed to calculate to large order the Rayleigh-Schr\odinger perturbation expansions for energy levels of a hydrogen atom with a Yukawa-type screened Coulomb potential. Perturbation series for the 1s, 2s, and 2p levels, shown not to be of the Stieltjes type, are calculated to 100th order. Nevertheless, the poles of the Pad\'e approximants to these series generally avoid the region of the positive real axis 0${\ensuremath{\lambda}}^{\mathrm{*}}$, where ${\ensuremath{\lambda}}^{\mathrm{*}}$ represents the coupling constant threshold. As a result, the Pad\'e sums afford accurate approximations to E(\ensuremath{\lambda}) in this domain. The continued-fraction representations to these perturbation series have been accurately calculated to large (100th) order and demonstrate a curious ``quasioscillatory,'' but non-Stieltjes, behavior. Accurate values of E(\ensuremath{\lambda}) as well as ${\ensuremath{\lambda}}^{\mathrm{*}}$ for the 1s, 2s, and 2p levels are reported.

Large Orders in Small Markets: On Optimal Execution with Endogenous Liquidity Supply

The correct functioning of parametric focusing techniques [e.g., MUltiple SIgnal Classification (MUSIC)] require a proper selection of the model order. For such aim, a methodology based on the Kullback-Leibler information criterion is commonly employed. These methods perform well due to its propensity to choose relatively large model orders, which tend to retrieve good-fitted responses when the data generating mechanism is more complex than the models used to fit. However, some solutions can be misleading, since only the most proper model order (i.e., the actual number of targets) guaranties best performance. As an alternative, this work suggests employing statistical regularization instead of model order selection (MOS) approaches. First, a model with large order is chosen to perform focusing via parametric methods; subsequently, statistical regularization is applied, seeking to attain good-fitted solutions. To demonstrate the capabilities of the addressed novel strategy, Synthetic Aperture Radar (SAR) Tomography (TomoSAR) is considered as application.

One of the main challenges of graph filters is the stability of their design. While classical graph filters allow for a stable design using optimal polynomial approximation theory, generalized graph filters tend to suffer from the ill-conditioning of the involved system matrix. This issue, accentuated for increasing graph filter orders, naturally leads to very large (small) filter coefficients or error saturation, casting a shadow on the benefits of these richer graph filter structures. In addition to this, data-driven design/learning of graph filters with large filter orders, even in the case of classical graph filters, suffers from the eigenvalue spread of the input data covariance matrix and mode coupling, leading to convergence-related issues as the ones observed when identifying time-domain filters with large orders. To alleviate these conditioning and convergence problems, and to reduce the overall design complexity, in this work, we propose a cascaded implementation of generalized graph filters and an efficient algorithm for designing the graph filter coefficients in both model- and data-driven settings. Further, we establish the connections of this implementation with so-called graph convolutional neural networks and demonstrate the performance of the proposed structure in different network applications. By the proposed approach, further error reduction and better design stability are achieved.

Anjan and his firm Greendzine Technologies Pvt. Ltd. (GTPL) have created a unique eco-friendly green electric vehicle called IrrwayTM as a personal mobility solution to cater to the underserved market segment of “In-Campus mobility” in India. They have created enough stir in some of the market segments like Golf Courses and Gated communities with the product, however there have not been any large orders from customers in these segments. All attempts to get venture capitalists and angel investors to invest in the company have not been very fruitful as well. With no big ticket investors investing in the company and no large sales orders to date, they need to be able to decide whether to take a shot with the upcoming opportunity to serve the mall segment for “Mobile Branding” activity and also find other target segments which they can concentrate on to give immediate boost to the sales of the product, thus improving the financial position of the firm. This will also hopefully bring enough investors to the company. Anjan and his team want to device a marketing strategy which revolves around the utility, fun aspect and green nature of the product to be able to achieve better sales and open up new opportunities for the company.

On hazard rate ordering of the sums of heterogeneous geometric random variables

Ordering properties of convolutions of heterogeneous Erlang and Pascal random variables

We apply the larger sieve to bound the number of 2×2 matrices not having large order when reduced modulo the primes in an interval. Our motivation is the relation with linear recursive congruential generators. Basically our results establish that the probability of finding a matrix with large order modulo many primes drops drastically when a certain threshold involving the number of primes and the order is exceeded. We also study, for a given prime and a matrix, the existence of nearby non-similar matrices having large order. In this direction we find matrices of large order when the trace is restricted to take values in a short interval.

Large Order Size Liquidity in Treasury Markets

Large orders for corporate bonds get preferential treatment unlike large orders for stocks on the NYSE. A structural explanation, namely, that the corporate bond market is dealer‐dominated, has been offered for the favorable pricing. In this paper, we offer an additional explanation, namely, that the improved pricing for large orders is due to the net impact such orders have on a market maker's costs. Using a data sample that is substantially free of timing mismatch, we support our assertion by sorting the sample into ‘brokered’ trades, which are trades where the dealer merely crosses buy and sell orders and ‘inventoried’ trades, where the dealer trades out of his inventory. We find that large orders raise information costs, but lower inventory costs for ‘inventoried’ trades. The net result is a smaller price advantage than received by large orders on ‘brokered’ trades which are not subject to these costs.

It is commonly observed that in order to understand various biological phenomenon and operation of medical devices, mathematical modelling is done that usually give rise to large order dynamical system. Such large order dynamical system becomes computationally heavy and creates storage problems too. These problems can be tackled if the order of large order system is reduced such that the input/output characteristics are nearly preserved. The reduced order models make the simulation possible and their control practically feasible. This paper shows reduction of pacemaker electrode problem that forms a large order system. A pacemaker electrode forms a part of an artificial pacemaker that is actually responsible for transmitting the electrical impulses to the heart tissue and regulates the beating of the heart. Being very large order problem, it gets difficult to carry out multiple simulations to find out optimum design parameters such as the electrode tip radius and the input excitation that plays an important role in current and voltage distribution on and around the pacemaker electrode. Reduced order model presented in this paper enables multiple simulations at reduced computational cost.

The aim of this article is to shed light on the relationship between buy/sell imbalances and daily stock returns for the CAC 40 stocks. Using detailed intraday data from Euronext Paris, we find a weak positive relation between directional trades of the whole market and the current individual stock returns. We distinguish between trades initiated by large orders and trades initiated by small orders. Results reveal a strong positive relation between daily returns and the direction of trades initiated by large orders, that is, increases in stock prices occur during periods of high-buying activity and stock prices decreases are accompanied by selling imbalances. The above relation becomes negative if we consider only trades initiated by small orders. Our empirical evidence indicates that small orders are submitted by noise traders, and that large orders are strongly associated with stock price movements. Finally, our findings are consistent with the absence of inventory control phenomenon on Euronext Paris. Indeed, there is no significant relation between stock returns and lagged imbalances.