Quantitative Finance
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New submissions for Thu, 22 Aug 19
 [1] arXiv:1908.07626 [pdf, other]

Title: Optimal Investment with Correlated Stochastic Volatility FactorsSubjects: Mathematical Finance (qfin.MF); Probability (math.PR)
The problem of portfolio allocation in the context of stocks evolving in random environments, that is with volatility and returns depending on random factors, has attracted a lot of attention. The problem of maximizing a power utility at a terminal time with only one random factor can be linearized thanks to a classical distortion transformation. In the present paper, we address the problem with several factors using a perturbation technique around the case where these factors are perfectly correlated reducing the problem to the case with a single factor. We illustrate our result with a particular model for which we have explicit formulas. A rigorous accuracy result is also derived using sub and supersolutions of the HJB equation involved. In order to keep the notations as explicit as possible, we treat the case with one stock and two factors and we describe an extension to the case with two stocks and two factors.
 [2] arXiv:1908.07659 [pdf, other]

Title: Myopic robust index tracking with Bregman divergenceSubjects: Portfolio Management (qfin.PM); Methodology (stat.ME)
Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward looking approach is more suitable, whereby the tracking error is expressed as expectation of a function of the difference between the returns of the index and of the portfolio. We also assume that there is an uncertainty in the distribution of the assets, hence a robust version of the optimization problem needs to be adopted. We use Bregman divergence in describing the deviation between the nominal and actual distribution of the components of the index. In this scenario, we derive the optimal robust index tracking strategy in a semianalytical form as a solution of a system of nonlinear equations. Several numerical results are presented that allow us to compare the performance of this robust strategy with the optimal nonrobust strategy. We show that, especially during market downturns, the robust strategy can be very advantageous.
 [3] arXiv:1908.07813 [pdf, other]

Title: Relationship between optimal portfolios which can maximize and minimize the expected returnAuthors: Takashi ShinzatoSubjects: Portfolio Management (qfin.PM)
In recent years, the evaluation of the minimal investment risk of the quenched disordered system of a portfolio optimization problem and the investment concentration of the optimal portfolio has been actively investigated using the analysis methods of statistical mechanical informatics. However, the work to date has not sufficiently compared the optimal portfolios of different portfolio optimization problems. Therefore, in this paper, we use the Lagrange undetermined multiplier method and replica analysis to examine the relationship between the optimal portfolios of the expected return maximization problem and the expected return minimization problem with constraints of budget and investment risk. In particular, we derive the mean square error and the correlation coefficient of the optimal portfolios of these maximization and minimization problems as functions of a variable (the degree of risk tolerance) that can characterize the feasible subspace defined by the two constraints.
 [4] arXiv:1908.07870 [pdf, other]

Title: A complex net of intertwined complements: Measuring interdimensional dependence among the poorAuthors: Felipe Del Canto M (Pontifical University of Chile, Institute of Economics)Comments: 19 pages, 2 figuresSubjects: General Economics (econ.GN)
The choice of appropriate measures of deprivation, identification and aggregation of poverty has been a challenge for many years. The works of Sen, Atkinson and others have been the cornerstone for most of the literature on poverty measuring. Recent contributions have focused in what we now know as multidimensional poverty measuring. Current aggregation and identification measures for multidimensional poverty make the implicit assumption that dimensions are independent of each other, thus ignoring the natural dependence between them. In this article a variant of the usual method of deprivation measuring is presented. It allows the existence of the forementioned connections by drawing from geometric and networking notions. This new methodology relies on previous identification and aggregation methods, but with small modifications to prevent arbitrary manipulations. It is also proved that this measure still complies with the axiomatic framework of its predecessor. Moreover, the general form of latter can be considered a particular case of this new measure, although this identification is not unique.
 [5] arXiv:1908.07998 [pdf, other]

Title: Decisionfacilitating information in hiddenaction setups: An agentbased approachComments: 27 pages, 11 figuresSubjects: General Economics (econ.GN); Theoretical Economics (econ.TH)
The hidden action model captures a fundamental problem of principalagent theory and provides an optimal sharing rule when only the outcome but not the effort can be observed. However, the hidden action model builds on various explicit and also implicit assumptions about the information of the contracting parties. This paper relaxes key assumptions regarding the availability of information included the hidden action model in order to study whether and, if so, how fast the optimal sharing rule is achieved and how this is affected by the various types of information employed in the principalagent relation. Our analysis particularly focuses on information about the environment and feasible actions for the agent to carry out the task. For this, we follow an approach to transfer closedform mathematical models into agentbased computational models. The results show that the extent of information about feasible options to carry out a task only has an impact on performance, if decisionmakers are well informed about the environment, and that the decision whether to perform exploration or exploitation when searching for new feasible options only affects performance in specific situations. Having good information about the environment, in contrary, appears to be crucial in almost all situations.
 [6] arXiv:1908.07999 [pdf, other]

Title: HATS: A Hierarchical Graph Attention Network for Stock Movement PredictionSubjects: Statistical Finance (qfin.ST); Artificial Intelligence (cs.AI); Computational Engineering, Finance, and Science (cs.CE)
Many researchers both in academia and industry have long been interested in the stock market. Numerous approaches were developed to accurately predict future trends in stock prices. Recently, there has been a growing interest in utilizing graphstructured data in computer science research communities. Methods that use relational data for stock market prediction have been recently proposed, but they are still in their infancy. First, the quality of collected information from different types of relations can vary considerably. No existing work has focused on the effect of using different types of relations on stock market prediction or finding an effective way to selectively aggregate information on different relation types. Furthermore, existing works have focused on only individual stock prediction which is similar to the node classification task. To address this, we propose a hierarchical attention network for stock prediction (HATS) which uses relational data for stock market prediction. Our HATS method selectively aggregates information on different relation types and adds the information to the representations of each company. Specifically, node representations are initialized with features extracted from a feature extraction module. HATS is used as a relational modeling module with initialized node representations. Then, node representations with the added information are fed into a taskspecific layer. Our method is used for predicting not only individual stock prices but also market index movements, which is similar to the graph classification task. The experimental results show that performance can change depending on the relational data used. HATS which can automatically select information outperformed all the existing methods.
Crosslists for Thu, 22 Aug 19
 [7] arXiv:1908.07978 (crosslist from cs.LG) [pdf, other]

Title: QCNN: Quantile Convolutional Neural NetworkAuthors: Gábor PetneháziSubjects: Machine Learning (cs.LG); Computational Finance (qfin.CP); Machine Learning (stat.ML)
A dilated causal onedimensional convolutional neural network architecture is proposed for quantile regression. The model can forecast any arbitrary quantile, and it can be trained jointly on multiple similar time series. An application to Value at Risk forecasting shows that QCNN outperforms linear quantile regression and constant quantile estimates.
Replacements for Thu, 22 Aug 19
 [8] arXiv:1801.07595 (replaced) [pdf, other]

Title: Gaussian Approximation of a Risk Model with NonStationary Hawkes Arrivals of ClaimsComments: 21 pages,3 figures. arXiv admin note: text overlap with arXiv:1607.06624, arXiv:1702.05852, arXiv:1309.7621 by other authorsJournalref: Methodology and Computing in Applied Probability 2019Subjects: Risk Management (qfin.RM); Probability (math.PR)
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