ON GUNDERSEN''''S QUESTION FOR THE UNICITY OF MEROMORPHIC FUNCTIONS

The uniqueness of meromorphic functions that share four values are investigated, some results are obtained to show that if two nonconstant entire functions share three finite values IM, then the functions necessarily share all three values CM.     

Bank-level estimates of market power

The aim of this study is to provide an empirical methodology for the estimation of market power of individual banks. The new method employs the well-known model of Panzar and Rosse (1987) and proposes its estimation using the local regression technique. Local regression yields coefficient estimates equal to the number of observations and, thus, market power is estimated for each bank at each point in time. In addition, a number of restrictive assumptions regarding the properties of the production function of banks are relaxed. A panel of banks from transition countries that has been recently employed by Delis (2010) to obtain market power estimates using the Panzar and Rosse model at the country level is used for comparative purposes. We find that country averages of the bank-level results exhibit a very close relationship with standard, industry-level Panzar-Rosse estimates. However, the empirical results suggest that many banks in countries with fairly competitive banking systems deviate significantly from the country averages and that market power varies substantially across banks in each country.     

Characterizing limit order prices

A computational model of a limit order book is used to study the effect of different limit order distribution offsets. Reference prices such as same side/contra side best market prices and last traded price are considered in combination with different price offset distributions. We show that when characterizing limit order prices, varying the offset distribution only produces different behavior when the reference price is the contra side best price. Irrespective of the underlying mechanisms used in computing the limit order prices, the shape of the price graph and the behavior of the average order book profile distribution are strikingly similar in all the considered reference prices/offset distributions. This implies that existing averaging methods can cancel variabilities in limit order book shape/attributes and may be misleading.     

Optimal Basket Liquidation for CARA Investors is Deterministic

Abstract

We consider the problem faced by an investor who must liquidate a given basket of assets over a finite time horizon. The investor's goal is to maximize the expected utility of the sales revenues over a class of adaptive strategies. We assume that the investor's utility has constant absolute risk aversion (CARA) and that the asset prices are given by a very general continuous-time, multiasset price impact model. Our main result is that (perhaps surprisingly) the investor does no worse if he narrows his search to deterministic strategies. In the case where the asset prices are given by an extension of the nonlinear price impact model of Almgren [(2003) Applied Mathematical Finance, 10, pp. 1–18], we characterize the unique optimal strategy via the solution of a Hamilton equation and the value function via a nonlinear partial differential equation with singular initial condition.     

Deep Reinforcement Learning for Market Making in Corporate Bonds: Beating the Curse of Dimensionality

ABSTRACT

In corporate bond markets, which are mainly OTC markets, market makers play a central role by providing bid and ask prices for bonds to asset managers. Determining the optimal bid and ask quotes that a market maker should set for a given universe of bonds is a complex task. The existing models, mostly inspired by the Avellaneda-Stoikov model, describe the complex optimization problem faced by market makers: proposing bid and ask prices for making money out of the difference between them while mitigating the market risk associated with holding inventory. While most of the models only tackle one-asset market making, they can often be generalized to a multi-asset framework. However, the problem of solving the equations characterizing the optimal bid and ask quotes numerically is seldom tackled in the literature, especially in high dimension. In this paper, we propose a numerical method for approximating the optimal bid and ask quotes over a large universe of bonds in a model à la Avellaneda–Stoikov. As classical finite difference methods cannot be used in high dimension, we present a discrete-time method inspired by reinforcement learning techniques, namely, a model-based deep actor-critic algorithm.     

Using store level scanner data to improve category management decisions: Developing positioning maps

This paper provides evidence of the usefulness of aggregated point-of-sale scanner data to infer the positioning of competing brands, providing valuable information for category management and hence facilitating decision making. Specifically, the authors propose a methodology to study the internal market structure based on market share models with latent heterogeneity when only macro-level time series data (not individual choices) are available. The proposed approach assumes a multidimensional decomposition, latent in the preference structure that is implicit to these types of models. By empirically applying this approach, the authors (1) simultaneously identify both latent dimensions of competing brands and latent segments with different brand preferences, (2) explain the competitive positioning of brands without using disaggregated consumer panel data, and (3) achieve greater predictive performance. The findings offer insights to academics and practitioners interested in improving the practice of category management.     

Ranking efficient decision making units in data envelopment analysis based on reference frontier share

Data envelopment analysis (DEA) is a powerful technique for performance evaluation of decision making units (DMUs). Ranking efficient DMUs based on a rational analysis is an issue that yet needs further research. The impact of each efficient DMU in evaluation of inefficient DMUs can be considered as additional information to discriminating among efficient DMUs. The concept of reference frontier share is introduced in which the share of each efficient DMU in construction of the reference frontier for evaluating inefficient DMUs is considered. For this purpose a model for measuring the reference frontier share of each efficient DMU associated with each inefficient one is proposed and then a total measure is provided based on which the ranking is made. The new approach has the capability for ranking extreme and non-extreme efficient DMUs. Further, it has no problem in dealing with negative data. These facts are verified by theorems, discussions and numerical examples.     

中国螺纹钢期货市场价格发现功能研究

螺纹钢期货价格发现功能研究对我国钢铁行业提高竞争力,争取钢铁成品和铁矿石定价权,引导螺纹钢期货市场健康发展具有重要作用。本文在向量误差修正模型(VEC)中引入剔除残差相关性的最小二乘算法,构建了用于测度期现货市场价格发现功能的永久短暂PT和信息份额IS共同因子模型,弥补了现有VEC模型由于求得的期现货残差序列相关性较大,导致PT和IS模型测算的信息贡献度存在较大差异的不足。在此基础上,利用2011年1月至2014年11月中国螺纹钢期现货市场933个日交易数据,验证了模型的有效性。     

基于动机的联合风险投资收益分配契约设计(A2016-0158)

从联合风险投资的领导者采取联合投资的动机出发,考虑分配给跟随者的收益份额是否能达到目的,运用优化理论建立了联合投资双方的收益分配模型,提出了联合风险投资机构之间的收益分配契约设计的一种可供参考的方法,并用实例说明了模型方法的应用。研究还表明,潜在的市场竞争可能对领导者造成的损失越大,领导者越愿意给予跟随者更多的收益份额;当项目质量信息的不确定性越高,单独投资将存在较大风险的时候,为了获得项目质量信息的补充,也使得领导者愿意给予跟随者更多的收益份额。     

Does Bitcoin dominate the price discovery of the Cryptocurrencies market? A time-varying information share analysis

Using a time-varying vector error correction model (VECM), we examine the dynamic information shares of the top four Cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Ripple (XRP) and Litecoin (LTC) over 1/1/2016–31/12/2019. Although steadily decreasing, the information share of BTC is still the largest as of end-2019. The individual dominances of market capitalization and trading volume can explain 20% of variations of the BTC information share but only 6% of those for ETH.