Dynamic behaviour of optimal portfolio with stochastic volatility

In the existing literature, little is known about the dynamic behaviour of the optimal portfolio in terms of market inputs and arbitrary stochastic factor dynamics in an incomplete market with a stochastic volatility. In this paper, to study optimal portfolio behaviour, we compute and analyze the mean and the variance of the optimal portfolio and of their adjustment speed in terms of market inputs in an incomplete market. The incompleteness arises from the additional source of uncertainty of the volatility in Heston’s stochastic volatility model. Conducting sensitivity analysis for the mean and the variance of the optimal portfolio process as well as its adjustment speed to the market parameters, we find several interesting behavioural patterns of investors towards asset price and its volatility shocks. Our results are robust and convergent by the agreement from two simulation methods for different time step increments and the number of Monte Carlo simulation paths

Impacts of road network expansion on landscape ecological risk in a megacity, China: A case study of Beijing

AbstractRoad networks affect the spatial structure of urban landscapes, and with continuous expansion, it will also exert more widespread influences on the regional ecological environment. With the support of geographic information system (GIS) technology, based on the application of various spatial analysis methods, this study analyzed the spatiotemporal changes of road networks and landscape ecological risk in the research area of Beijing to explore the impacts of road network expansion on ecological risk in the urban landscape. The results showed the following: 1) In the dynamic processes of change in the overall landscape pattern, the changing differences in landscape indices of various landscape types were obvious and were primarily related to land-use type. 2) For the changes in a time series, the expansion of the road kernel area was consistent with the extension of the sub-low-risk area in the urban center, but some differences were observed during different stages of development. 3) For the spatial position, the expanding changes in the road kernel area were consistent with the grade changes of the urban central ecological risk, primarily because both had a certain spatial correlation with the expressways. 4) The influence of road network expansion on the ecological risk in the study area had obvious spatial differences, which may be closely associated with the distribution of ecosystem types

DyG2Vec: Representation Learning for Dynamic Graphs with Self-Supervision

Temporal graph neural networks have shown promising results in learning inductive representations by automatically extracting temporal patterns. However, previous works often rely on complex memory modules or inefficient random walk methods to construct temporal representations. In addition, the existing dynamic graph encoders are non-trivial to adapt to self-supervised paradigms, which prevents them from utilizing unlabeled data. To address these limitations, we present an efficient yet effective attention-based encoder that leverages temporal edge encodings and window-based subgraph sampling to generate task-agnostic embeddings. Moreover, we propose a joint-embedding architecture using non-contrastive SSL to learn rich temporal embeddings without labels. Experimental results on 7 benchmark datasets indicate that on average, our model outperforms SoTA baselines on the future link prediction task by 4.23% for the transductive setting and 3.30% for the inductive setting while only requiring 5-10x less training/inference time. Additionally, we empirically validate the SSL pre-training significance under two probings commonly used in language and vision modalities. Lastly, different aspects of the proposed framework are investigated through experimental analysis and ablation studies.Comment: Proceedings of the 19th International Workshop on Mining and Learning with Graphs (MLG

Dynamic Embedding Size Search with Minimum Regret for Streaming Recommender System

With the continuous increase of users and items, conventional recommender systems trained on static datasets can hardly adapt to changing environments. The high-throughput data requires the model to be updated in a timely manner for capturing the user interest dynamics, which leads to the emergence of streaming recommender systems. Due to the prevalence of deep learning-based recommender systems, the embedding layer is widely adopted to represent the characteristics of users, items, and other features in low-dimensional vectors. However, it has been proved that setting an identical and static embedding size is sub-optimal in terms of recommendation performance and memory cost, especially for streaming recommendations. To tackle this problem, we first rethink the streaming model update process and model the dynamic embedding size search as a bandit problem. Then, we analyze and quantify the factors that influence the optimal embedding sizes from the statistics perspective. Based on this, we propose the \textbf{D}ynamic \textbf{E}mbedding \textbf{S}ize \textbf{S}earch (\textbf{DESS}) method to minimize the embedding size selection regret on both user and item sides in a non-stationary manner. Theoretically, we obtain a sublinear regret upper bound superior to previous methods. Empirical results across two recommendation tasks on four public datasets also demonstrate that our approach can achieve better streaming recommendation performance with lower memory cost and higher time efficiency.Comment: Accepted for publication on CIKM202

Bidirectional Learning for Offline Infinite-width Model-based Optimization

In offline model-based optimization, we strive to maximize a black-box objective function by only leveraging a static dataset of designs and their scores. This problem setting arises in numerous fields including the design of materials, robots, DNA sequences, and proteins. Recent approaches train a deep neural network (DNN) on the static dataset to act as a proxy function, and then perform gradient ascent on the existing designs to obtain potentially high-scoring designs. This methodology frequently suffers from the out-of-distribution problem where the proxy function often returns poor designs. To mitigate this problem, we propose BiDirectional learning for offline Infinite-width model-based optimization (BDI). BDI consists of two mappings: the forward mapping leverages the static dataset to predict the scores of the high-scoring designs, and the backward mapping leverages the high-scoring designs to predict the scores of the static dataset. The backward mapping, neglected in previous work, can distill more information from the static dataset into the high-scoring designs, which effectively mitigates the out-of-distribution problem. For a finite-width DNN model, the loss function of the backward mapping is intractable and only has an approximate form, which leads to a significant deterioration of the design quality. We thus adopt an infinite-width DNN model, and propose to employ the corresponding neural tangent kernel to yield a closed-form loss for more accurate design updates. Experiments on various tasks verify the effectiveness of BDI. The code is available at https://github.com/GGchen1997/BDI.Comment: NeurIPS2022 camera-ready version; AI4Science; Drug discovery; Offline model-based optimization; Neural tangent kernel; Bi-level optimizatio