Comparison Between the Mean-Variance Optimal and the Mean-Quadratic-Variation Optimal Trading Strategies

ABSTRACT

We compare optimal liquidation policies in continuous time in the presence of trading impact using numerical solutions of Hamilton–Jacobi–Bellman (HJB) partial differential equations (PDEs). In particular, we compare the time-consistent mean-quadratic-variation strategy with the time-inconsistent (pre-commitment) mean-variance strategy. We show that the two different risk measures lead to very different strategies and liquidation profiles. In terms of the optimal trading velocities, the mean-quadratic-variation strategy is much less sensitive to changes in asset price and varies more smoothly. In terms of the liquidation profiles, the mean-variance strategy is much more variable, although the mean liquidation profiles for the two strategies are surprisingly similar. On a numerical note, we show that using an interpolation scheme along a parametric curve in conjunction with the semi-Lagrangian method results in significantly better accuracy than standard axis-aligned linear interpolation. We also demonstrate how a scaled computational grid can improve solution accuracy.     

Training Multilayer Perceptron with Genetic Algorithms and Particle Swarm Optimization for Modeling Stock Price Index Prediction

Predicting stock market (SM) trends is an issue of great interest among researchers, investors and traders since the successful prediction of SMs’ direction may promise various benefits. Because of the fairly nonlinear nature of the historical data, accurate estimation of the SM direction is a rather challenging issue. The aim of this study is to present a novel machine learning (ML) model to forecast the movement of the Borsa Istanbul (BIST) 100 index. Modeling was performed by multilayer perceptron–genetic algorithms (MLP–GA) and multilayer perceptron–particle swarm optimization (MLP–PSO) in two scenarios considering Tanh (x) and the default Gaussian function as the output function. The historical financial time series data utilized in this research is from 1996 to 2020, consisting of nine technical indicators. Results are assessed using Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE) and correlation coefficient values to compare the accuracy and performance of the developed models. Based on the results, the involvement of the Tanh (x) as the output function, improved the accuracy of models compared with the default Gaussian function, significantly. MLP–PSO with population size 125, followed by MLP–GA with population size 50, provided higher accuracy for testing, reporting RMSE of 0.732583 and 0.733063, MAPE of 28.16%, 29.09% and correlation coefficient of 0.694 and 0.695, respectively. According to the results, using the hybrid ML method could successfully improve the prediction accuracy.     

Molecular simulations of entangled defect structures around nanoparticles in nematic liquid crystals

We investigate the defect structures forming around two nanoparticles in a Gay–Berne nematic liquid crystal using molecular simulations. For small separations, disclinations entangle both particles forming the figure of eight, the figure of omega and the figure of theta. These defect structures are similar in shape and occur with a comparable frequency to micron-sized particles studied in experiments. The simulations reveal fast transitions from one defect structure to another suggesting that particles of nanometre size cannot be bound together effectively. We identify the ‘three-ring’ structure observed in previous molecular simulations as a superposition of the different entangled and non-entangled states over time and conclude that it is not itself a stable defect structure.     

The effect of explanations on mathematical reasoning tasks

Studies in mathematics education often point to the necessity for students to engage in more cognitively demanding activities than just solving tasks by applying given solution methods. Previous studies have shown that students that engage in creative mathematically founded reasoning to construct a solution method, perform significantly better in follow up tests than students that are given a solution method and engage in algorithmic reasoning. However, teachers and textbooks, at least occasionally, provide explanations together with an algorithmic method, and this could possibly be more efficient than creative reasoning. In this study, three matched groups practiced with either creative, algorithmic, or explained algorithmic tasks. The main finding was that students that practiced with creative tasks did, outperform the students that practiced with explained algorithmic tasks in a post-test, despite a much lower practice score. The two groups that got a solution method presented, performed similarly in both practice and post-test, even though one group got an explanation to the given solution method. Additionally, there were some differences between the groups in which variables predicted the post-test score.     

Concentrated Equilibrium and Intraday Patterns in Financial Markets

Abstract

We introduce endogenous participation of market makers into a Kyle-type model with long-lived asymmetric information. In our model with plausible parameter values, the trading volume and price volatility show a U-shaped intraday pattern, often observed in actual financial markets. It will be shown that the pattern is caused not only by the trading behaviour of liquidity traders but also by that of market makers. Our findings shed new light on the stylized fact of the trade concentration at the opening and closing periods.     

Algorithmic Information Distortions in Node-Aligned and Node-Unaligned Multidimensional Networks

In this article, we investigate limitations of importing methods based on algorithmic information theory from monoplex networks into multidimensional networks (such as multilayer networks) that have a large number of extra dimensions (i.e., aspects). In the worst-case scenario, it has been previously shown that node-aligned multidimensional networks with non-uniform multidimensional spaces can display exponentially larger algorithmic information (or lossless compressibility) distortions with respect to their isomorphic monoplex networks, so that these distortions grow at least linearly with the number of extra dimensions. In the present article, we demonstrate that node-unaligned multidimensional networks, either with uniform or non-uniform multidimensional spaces, can also display exponentially larger algorithmic information distortions with respect to their isomorphic monoplex networks. However, unlike the node-aligned non-uniform case studied in previous work, these distortions in the node-unaligned case grow at least exponentially with the number of extra dimensions. On the other hand, for node-aligned multidimensional networks with uniform multidimensional spaces, we demonstrate that any distortion can only grow up to a logarithmic order of the number of extra dimensions. Thus, these results establish that isomorphisms between finite multidimensional networks and finite monoplex networks do not preserve algorithmic information in general and highlight that the algorithmic information of the multidimensional space itself needs to be taken into account in multidimensional network complexity analysis.     

有负荷约束的指派问题

通过组合最优化的理论和方法,研究机器有负荷(时间)限制的指派问题,证明其NP困难性,并建立多项式可解的特殊情形算法及一般情形的隐枚举算法.     

Market oscillations induced by the competition between value-based and trend-based investment strategies

We consider financial market using mathematical models which incorporate an excess demand function that depends not only upon the price but on the price derivative. The classical (value-based) motivation for purchasing the equity is augmented with a trend-based strategy of buying due to rising prices. An analysis (based on money flow and the finiteness of assets) of the supply, demand and price as a function of time leads to a system of ordinary differential equations which is mathematically complete. The numerical study of our equations exhibits overshooting, abrupt reversals and oscillations in prices. We examine our models within the context of real markets and economic laboratory experiments by comparing its predictions with a set of Porter and Smith experiments and with all US stock market “crashes” since 1929.     

Using conditional probability to identify trends in intra-day high-frequency equity pricing

By examining the conditional probabilities of price movements in a popular US stock over different high-frequency intra-day timespans, varying levels of trend predictability are identified. This study demonstrates the existence of predictable short-term trends in the market; understanding the probability of price movement can be useful to high-frequency traders. Price movement was examined in trade-by-trade (tick) data along with temporal timespans between 1 s to 30 min for 52 one-week periods for one highly-traded stock. We hypothesize that much of the initial predictability of trade-by-trade (tick) data is due to traditional market dynamics, or the bouncing of the price between the stock’s bid and ask. Only after timespans of between 5 to 10 s does this cease to explain the predictability; after this timespan, two consecutive movements in the same direction occur with higher probability than that of movements in the opposite direction. This pattern holds up to a one-minute interval, after which the strength of the pattern weakens.     

政府补贴方式下排放许可交易生产优化

从学术上探讨了政府补贴方式下有排放许可交易的生产优化问题.分析了配额和补贴方式效果在管理上的差异,给出了补贴方式下的各经济核算关系及模型,给出了最低净化水平定理的证明;给出优化计算,求解了最优净化水平,并探讨了其与最优产量和企业最优收益间的关系;给出仿真计算,并对企业生产在这种支持方式下的优化管理进行了分析.研究表明:企业将对生产中产生的全部排放物进行相同净化水平α的处理时,所需要的处理费用最低;在线性反需求函数下,最优产量的变化量只与净化成本函数、排放交易价格、补助价格等几个量相关,最优收益与最优产量的平方成正比.