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Hao Xing

Publications and source records attributed to Hao Xing.

At least 37 records · Page 2Linked to original sources

Global Context Enhanced Social Recommendation with Hierarchical Graph Neural Networks

Social recommendation which aims to leverage social connections among users to enhance the recommendation performance. With the revival of deep learning techniques, many efforts have been devoted to developing various neural network-based social recommender systems, such as attention mechanisms and graph-based message passing frameworks. However, two important challenges have not been well addressed yet: (i) Most of existing social recommendation models fail to fully explore the multi-type user-item interactive behavior as well as the underlying cross-relational inter-dependencies. (ii) While the learned social state vector is able to model pair-wise user dependencies, it still has limited representation capacity in capturing the global social context across users. To tackle these limitations, we propose a new Social Recommendation framework with Hierarchical Graph Neural Networks (SR-HGNN). In particular, we first design a relation-aware reconstructed graph neural network to inject the cross-type collaborative semantics into the recommendation framework. In addition, we further augment SR-HGNN with a social relation encoder based on the mutual information learning paradigm between low-level user embeddings and high-level global representation, which endows SR-HGNN with the capability of capturing the global social contextual signals. Empirical results on three public benchmarks demonstrate that SR-HGNN significantly outperforms state-of-the-art recommendation methods. Source codes are available at: https://github.com/xhcdream/SR-HGNN.

cs.IR↗

Robust Event Detection based on Spatio-Temporal Latent Action Unit using Skeletal Information

This paper propose a novel dictionary learning approach to detect event action using skeletal information extracted from RGBD video. The event action is represented as several latent atoms and composed of latent spatial and temporal attributes. We perform the method at the example of fall event detection. The skeleton frames are clustered by an initial K-means method. Each skeleton frame is assigned with a varying weight parameter and fed into our Gradual Online Dictionary Learning (GODL) algorithm. During the training process, outlier frames will be gradually filtered by reducing the weight that is inversely proportional to a cost. In order to strictly distinguish the event action from similar actions and robustly acquire its action unit, we build a latent unit temporal structure for each sub-action. We evaluate the proposed method on parts of the NTURGB+D dataset, which includes 209 fall videos, 405 ground-lift videos, 420 sit-down videos, and 280 videos of 46 otheractions. We present the experimental validation of the achieved accuracy, recall and precision. Our approach achieves the bestperformance on precision and accuracy of human fall event detection, compared with other existing dictionary learning methods. With increasing noise ratio, our method remains the highest accuracy and the lowest variance.

cs.CV↗

Radner equilibrium and systems of quadratic BSDEs with discontinuous generators

Motivated by an equilibrium problem, we establish the existence of a solution for a family of Markovian backward stochastic differential equations with quadratic nonlinearity and discontinuity in $Z$. Using unique continuation and backward uniqueness, we show that the set of discontinuity has measure zero. In a continuous-time stochastic model of an endowment economy, we prove the existence of an incomplete Radner equilibrium with nondegenerate endogenous volatility.

math.PR↗

Product Image Recognition with Guidance Learning and Noisy Supervision

This paper considers recognizing products from daily photos, which is an important problem in real-world applications but also challenging due to background clutters, category diversities, noisy labels, etc. We address this problem by two contributions. First, we introduce a novel large-scale product image dataset, termed as Product-90. Instead of collecting product images by labor-and time-intensive image capturing, we take advantage of the web and download images from the reviews of several e-commerce websites where the images are casually captured by consumers. Labels are assigned automatically by the categories of e-commerce websites. Totally the Product-90 consists of more than 140K images with 90 categories. Due to the fact that consumers may upload unrelated images, it is inevitable that our Product-90 introduces noisy labels. As the second contribution, we develop a simple yet efficient \textit{guidance learning} (GL) method for training convolutional neural networks (CNNs) with noisy supervision. The GL method first trains an initial teacher network with the full noisy dataset, and then trains a target/student network with both large-scale noisy set and small manually-verified clean set in a multi-task manner. Specifically, in the stage of student network training, the large-scale noisy data is supervised by its guidance knowledge which is the combination of its given noisy label and the soften label from the teacher network. We conduct extensive experiments on our Products-90 and public datasets, namely Food101, Food-101N, and Clothing1M. Our guidance learning method achieves performance superior to state-of-the-art methods on these datasets.

cs.CV↗

Capital allocation under the Fundamental Review of Trading Book

Facing the FRTB, banks need to allocate their capital to each business units or risk positions to evaluate the capital efficiency of their strategies. This paper proposes two computationally efficient allocation methods which are weighted according to liquidity horizon. Both methods provide more stable and less negative allocations under the FRTB than under the current regulatory framework.

q-fin.RM↗

BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data

We provide a stochastic representation for a general class of viscous Hamilton-Jacobi (HJ) equations, which has convexity and superlinear nonlinearity in its gradient term, via a type of backward stochastic differential equation (BSDE) with constraint in the martingale part. We compare our result with the classical representation in terms of (super)quadratic BSDE, and show in particular that existence of a solution to the viscous HJ equation can be obtained under more general growth assumptions on the coefficients, including both unbounded diffusion coefficient and terminal data.

math.PR↗

A class of globally solvable Markovian quadratic BSDE systems and applications

We establish existence and uniqueness for a wide class of Markovian systems of backward stochastic differential equations (BSDE) with quadratic nonlinearities. This class is characterized by an abstract structural assumption on the generator, an a-priori local-boundedness property, and a locally-Hölder-continuous terminal condition. We present easily verifiable sufficient conditions for these assumptions and treat several applications, including stochastic equilibria in incomplete financial markets, stochastic differential games, and martingales on Riemannian manifolds.

math.PR↗

Incomplete stochastic equilibria for dynamic monetary utility

We study existence and uniqueness of continuous-time stochastic Radner equilibria in an incomplete market model among a group of agents whose preference is characterized by cash invariant time-consistent monetary utilities. An assumption of "smallness" type is shown to be sufficient for existence and uniqueness. In particular, this assumption encapsulates settings with small endowments, small time-horizon, or a large population of weakly heterogeneous agents. Central role in our analysis is played by a fully-coupled nonlinear system of quadratic BSDEs.

math.PR↗

Convex duality for stochastic differential utility

This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and stochastic differential utility. For Epstein-Zin utility, duality between the primal and dual problems is established. Consequently the optimal strategy of the consumption and investment problem is identified without assuming several technical conditions on market model, utility specification, and agent's admissible strategy. Meanwhile the minimizer of the dual problem is identified as the utility gradient of the primal value and is economically interpreted as the "least favorable" completion of the market.

q-fin.MF↗

Consumption investment optimization with Epstein-Zin utility in incomplete markets

In a market with stochastic investment opportunities, we study an optimal consumption investment problem for an agent with recursive utility of Epstein-Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations. The supperdifferential of indirect utility is also obtained, meeting demands from applications in which Epstein-Zin utilities were used to resolve several asset pricing puzzles. The empirically relevant utility specification introduces difficulties to the optimization problem due to the fact that the Epstein-Zin aggregator is neither Lipschitz nor jointly concave in all its variables.

math.PR↗

Asymptotic Glosten Milgrom equilibrium

This paper studies the Glosten Milgrom model whose risky asset value admits an arbitrary discrete distribution. Contrast to existing results on insider's models, the insider's optimal strategy in this model, if exists, is not of feedback type. Therefore a weak formulation of equilibrium is proposed. In this weak formulation, the inconspicuous trade theorem still holds, but the optimality for the insider's strategy is not enforced. However, the insider can employ some feedback strategy whose associated expected profit is close to the optimal value, when the order size is small. Moreover this discrepancy converges to zero when the order size diminishes. The existence of such a weak equilibrium is established, in which the insider's strategy converges to the Kyle optimal strategy when the order size goes to zero.

q-fin.TR↗

Long Term Optimal Investment in Matrix Valued Factor Models

Long term optimal investment problems are studied in a factor model with matrix valued state variables. Explicit parameter restrictions are obtained under which, for an isoelastic investor, the finite horizon value function and optimal strategy converge to their long-run counterparts as the investment horizon approaches infinity. This convergence also yields portfolio turnpikes for general utilities. By using results on large time behaviour of semi-linear partial differential equations, our analysis extends affine models, where the Wishart process drives investment opportunities, to a non-affine setting. Furthermore, in the affine setting, an example is constructed where the value function is not exponentially affine, in contrast to models with vector-valued state variables.

q-fin.MF↗

Robust Portfolios and Weak Incentives in Long-Run Investments

When the planning horizon is long, and the safe asset grows indefinitely, isoelastic portfolios are nearly optimal for investors who are close to isoelastic for high wealth, and not too risk averse for low wealth. We prove this result in a general arbitrage-free, frictionless, semimartingale model. As a consequence, optimal portfolios are robust to the perturbations in preferences induced by common option compensation schemes, and such incentives are weaker when their horizon is longer. Robust option incentives are possible, but require several, arbitrarily large exercise prices, and are not always convex.

q-fin.PM↗

Large time behavior of solutions to semi-linear equations with quadratic growth in the gradient

This paper studies the large time behavior of solutions to semi-linear Cauchy problems with quadratic nonlinearity in gradients. The Cauchy problem considered has a general state space and may degenerate on the boundary of the state space. Two types of large time behavior are obtained: i) pointwise convergence of the solution and its gradient; ii) convergence of solutions to associated backward stochastic differential equations. When the state space is R^d or the space of positive definite matrices, both types of convergence are obtained under growth conditions on model coefficients. These large time convergence results have direct applications in risk sensitive control and long term portfolio choice problems.

math.AP↗

Stability of the exponential utility maximization problem with respect to preferences

This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semimartingale model where random endowments are present, a sequence of utilities defined on R converges to the exponential utility. Under a uniform condition on their marginal utilities, convergence of value functions, optimal payoffs and optimal investment strategies are obtained, their rate of convergence are also determined. Stability of utility-based pricing is studied as an application. Second, a sequence of utilities defined on R_+ converges to the exponential utility after shifting and scaling. Their associated optimal strategies, after appropriate scaling, converge to the optimal strategy for the exponential hedging problem. This complements Theorem 3.2 in \textit{M. Nutz, Probab. Theory Relat. Fields, 152, 2012}, which establishes the convergence for a sequence of power utilities.

q-fin.PM↗

Point process bridges and weak convergence of insider trading models

We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time 1 value satisfies a specific constraint. This construction allows us to show the existence of Glosten-Milgrom equilibrium and its associated optimal trading strategy for the insider. In the equilibrium the insider employs a mixed strategy to randomly submit two types of orders: one type trades in the same direction as noise trades while the other cancels some of the noise trades by submitting opposite orders when noise trades arrive. The construction also allows us to prove that Glosten-Milgrom equilibria converge weakly to Kyle-Back equilibrium, without the additional assumptions imposed in \textit{K. Back and S. Baruch, Econometrica, 72 (2004), pp. 433-465}, when the common intensity of the Poisson processes tends to infinity.

math.PR↗

Long-term and blow-up behaviors of exponential moments in multi-dimensional affine diffusions

This paper considers multi-dimensional affine processes with continuous sample paths. By analyzing the Riccati system, which is associated with affine processes via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time. In these two cases, we also compute the long-term growth rate and the explosion rate for exponential moments. These results provide a handle to study implied volatility asymptotics in models where returns of stock prices are described by affine processes whose exponential moments do not have an explicit formula.

q-fin.PR↗

Regularity of the Optimal Stopping Problem for Jump Diffusions

The value function of an optimal stopping problem for jump diffusions is known to be a generalized solution of a variational inequality. Assuming that the diffusion component of the process is nondegenerate and a mild assumption on the singularity of the Lévy measure, this paper shows that the value function of this optimal stopping problem on an unbounded domain with finite/infinite variation jumps is in $W^{2,1}_{p, loc}$ with $p\in(1, \infty)$. As a consequence, the smooth-fit property holds.

math.OC↗