The cold-start problem remains a significant challenge in recommendation systems, particularly for new users or unseen items with little to no historical data. Existing methods, including graph neural networks, often struggle in such scenarios. Inspired by the success of transformer models in natural language processing, we propose G-TRAC (Graph-Textual Representations Alignment for Cold-start Recommendations), a novel approach that integrates transformer-based textual modeling with graph neural networks. By effectively leveraging both textual and structural information, G-TRAC addresses cold-start challenges more effectively. Extensive experiments demonstrate its ability to enhance recommendation quality and generalize well across diverse scenarios.

A multitude of interconnected risk eventsranging from regulatory changes to geopolitical tensions-can trigger ripple effects across firms.Identifying inter-firm risk relations is thus crucial for applications like portfolio management and investment strategy.Traditionally, such assessments rely on expert judgment and manual analysis, which are, however, subjective, labor-intensive, and difficult to scale.To address this, we propose a systematic method for extracting inter-firm risk relations using Form 10-K filings-authoritative, standardized financial documents-as our data source.Leveraging recent advances in natural language processing, our approach captures implicit and abstract risk connections through unsupervised fine-tuning based on chronological and lexical patterns in the filings.This enables the development of a domain-specific financial encoder with a deeper contextual understanding and introduces a quantitative risk relation score for transparency, interpretable analysis.Extensive experiments demonstrate that our method outperforms strong baselines across multiple evaluation settings.

Modern information retrieval (IR) systems, powered by bi-encoder architectures and pretrained language models, rely on effective negative sampling for contrastive learning. While easy negatives are computationally simple, they fail to challenge the model, whereas hard negatives-selected via methods like BM25, ANCE, or ADORE-can be overly difficult and misleading. To this end, this paper proposes dynamic margin-based contrastive learning (DMCL), which adaptively adjusts the decision boundary based on query-negative similarity, ensuring consistent exposure to moderately hard negatives. Experiments across diverse datasets and models show that DMCL outperforms traditional methods, achieving state-of-the-art retrieval performance with minimal computational cost.

Tags play a critical role in enhancing product discoverability, optimizing search results, and enriching recommendation systems on e-commerce platforms. Despite the recent advancements in large language models (LLMs), which have shown proficiency in processing and understanding textual information, their application in tag generation remains an under-explored yet complex challenge. To this end, we introduce a novel method for automatic product tagging using LLMs to create behavior-enhanced tags (BETags). Specifically, our approach begins by generating base tags using an LLM. These base tags are then refined into BETags by incorporating user behavior data. This method aligns the tags with users' actual browsing and purchasing behavior, enhancing the accuracy and relevance of tags to user preferences. By personalizing the base tags with user behavior data, BETags are able to capture deeper behavioral insights, which is essential for understanding nuanced user interests and preferences in e-commerce environments. Moreover, since BETags are generated offline, they do not impose real-time computational overhead and can be seamlessly integrated into downstream tasks commonly associated with recommendation systems and search optimization. Our evaluation of BETag across three datasets--- Amazon (Scientific), MovieLens-1M, and FreshFood---shows that our approach significantly outperforms both human-annotated tags and other automated methods. These results highlight BETag as a scalable and efficient solution for personalized automated tagging, advancing e-commerce platforms by creating more tailored and engaging user experiences.

In this paper, we examine the existence of the Rényi divergence between two time invariant hidden Markov models with arbitrary positive initial distributions. By making use of a Markov chain representation of the probability distribution for the hidden Markov model and eigenvalue for the associated Markovian operator, we obtain, under some regularity conditions, convergence of the Rényi divergence. By using this device, we also characterize the Rényi divergence and obtain the Kullback–Leibler divergence as $$\alpha \rightarrow 1$$ of the Rényi divergence. Several examples, including classical finite state hidden Markov models, Markov switching models, and recurrent neural networks, are given for illustration. Moreover, we develop a non-Monte Carlo method that computes the Rényi divergence of two-state Markov switching models via the underlying invariant probability measure, which is characterized by the Fredholm integral equation.

This paper enhances option pricing accuracy by incorporating financial expertise into a neural network (NN) design and optimizing data sample quality through cleaning and synthesis. Instead of directly estimating option values (OVs) with NNs, we leverage the concept of control variate by decomposing OVs as time values (TVs) estimated by NNs, plus the analytically solvable intrinsic values (IVs). TV surface can be decomposed into two scenarios with very different properties, and we design two NNs according to our derived no-arbitrage constraints for these two scenarios. To alleviate learning inaccuracy due to the kink of the TV surface along the scenario boundary, we synthesize training samples based on our derived constraints to smoothly extend the surface for each scenario. On the other hand, irrational option quotes commonly found in illiquid markets incur uneven surfaces, significantly deteriorating NN predictability. We develop a learnable data-cleaning method to remove potentially irrational quotes spotted by no-arbitrage constraints properly. Besides, unnecessary data syntheses proposed in previous literature can also be removed by incorporating corresponding constraints into our NN to enhance training efficiency. Comprehensive experiments on liquid S&P 500 and illiquid TAIEX option markets examine the superiority of our approach.

This paper introduces SARA, a semantic-assisted reinforced active learning framework for enhancing entity alignment (EA) under limited supervision scenarios. SARA addresses the challenges of EA in real-world scenarios, including knowledge graph heterogeneity and limited training ground truth. SARA effectively selects valuable entity pairs with limited labeled data by combining reinforced active learning and semantic information. It utilizes a pair-wise language model based on Sentence-BERT to learn informative name embeddings that capture entity name semantics. These embeddings are combined with structural embeddings and trained using a novel semantic-assisted alignment loss. Extensive experiments on benchmark datasets and a real-world dataset demonstrate the superiority of SARA over existing approaches, particularly in limited labeled data scenarios. The paper also provides insights into fine-tuning strategies, presents ablation studies, and conducts sensitivity analyses to validate the effectiveness of SARA.

In this paper, we address the challenge of discovering financial signals in narrative financial reports.As these documents are often lengthy and tend to blend routine information with new information, it is challenging for professionals to discern critical financial signals.To this end, we leverage the inherent nature of the year-to-year structure of reports to define a novel signal-highlighting task; more importantly, we propose a compare-andcontrast multistage pipeline that recognizes different relationships between the reports and locates relevant rationales for these relationships.We also create and publicly release a humanannotated dataset for our task.Our experiments on the dataset validate the effectiveness of our pipeline, and we provide detailed analyses and ablation studies to support our findings.

This paper presents ConvRerank, a conversational passage re-ranker that employs a newly developed pseudo-labeling approach. Our proposed view-ensemble method enhances the quality of pseudo-labeled data, thus improving the fine-tuning of ConvRerank. Our experimental evaluation on benchmark datasets shows that combining ConvRerank with a conversational dense retriever in a cascaded manner achieves a good balance between effectiveness and efficiency. Compared to baseline methods, our cascaded pipeline demonstrates lower latency and higher top-ranking effectiveness. Furthermore, the in-depth analysis confirms the potential of our approach to improving the effectiveness of conversational search.

Default analysis plays an essential role in financial markets because it narrows the information gap between borrowers and lenders. Of late, machine learning-based methods have found their way to default analysis and typically view it as a risk classification task by slotting obligors into risk categories. The quality of such an approach is assessed by its prediction accuracy in risk rankings. Rarely considered but important are issues on the predicted numbers of default occurrences and the term structure of cumulative default probabilities for which classification tools are by nature silent. In this paper, we depart from the typical practice of risk classification and focus on employing machine learning to estimate the term structure of cumulative default probabilities—a structured estimation that contains default probabilities from short-term to long-term periods. To this end, we formulate the task as a problem of parametric family learning via a neural model consisting of two segments: parameter generation and parametric family determination. The proposed neural approach offers added flexibility in improving long-term default predictions. Moreover, the carefully designed model successfully maintains vital economic characteristics of its predictions. Experiments on a US corporate default dataset show that our approach achieves measurably better prediction performance in both risk classification and matching the predicted numbers of default occurrences with the actual ones.

In this demonstration, we present RecDelta, an interactive tool for the cross-model evaluation of top-k recommendation. RecDelta is a web-based information system where people visually compare the performance of various recommendation algorithms and their recommended items. In the proposed system, we visualize the distribution of the δ scores between algorithms--a distance metric measuring the intersection between recommendation lists. Such visualization allows for rapid identification of users for whom the items recommended by different algorithms diverge or vice versa; then, one can further select the desired user to present the relationship between recommended items and his/her historical behavior. RecDelta benefits both academics and practitioners by enhancing model explainability as they develop recommendation algorithms with their newly gained insights. Note that while the system is now online at https://cfda.csie.org/recdelta, we also provide a video recording at https://tinyurl.com/RecDelta to introduce the concept and the usage of our system.

Explicit feedback---user input regarding their interest in an item---is the most helpful information for recommendation as it comes directly from the user and shows their direct interest in the item. Most approaches either treat the recommendation given such feedback as a typical regression problem or regard such data as implicit and then directly adopt approaches for implicit feedback; both methods, however,tend to yield unsatisfactory performance in top-k recommendation. In this paper, we propose interaction-level preference ranking(IPR), a novel pairwise ranking embedding learning approach to better utilize explicit feedback for recommendation. Experiments conducted on three real-world datasets show that IPR yields the best results compared to six strong baselines.

Item concept modeling is commonly achieved by leveraging textual information. However, many existing models do not leverage the inferential property of concepts to capture word meanings, which therefore ignores the relatedness between correlated concepts, a phenomenon which we term conceptual “correlation sparsity.” In this paper, we distinguish between word modeling and concept modeling and propose an item concept modeling framework centering around the item concept network (ICN). ICN models and further enriches item concepts by leveraging the inferential property of concepts and thus addresses the correlation sparsity issue. Specifically, there are two stages in the proposed framework: ICN construction and embedding learning. In the first stage, we propose a generalized network construction method to build ICN, a structured network which infers expanded concepts for items via matrix operations. The second stage leverages neighborhood proximity to learn item and concept embeddings. With the proposed ICN, the resulting embedding facilitates both homogeneous and heterogeneous tasks, such as item-to-item and concept-to-item retrieval, and delivers related results which are more diverse than traditional keyword-matching-based approaches. As our experiments on two real-world datasets show, the framework encodes useful conceptual information and thus outperforms traditional methods in various item classification and retrieval tasks.

Predicting extreme weather events such as tropical and extratropical cyclones is of vital scientific and societal importance. Of late, machine learning methods have found their way to weather analysis and prediction, but mostly, these methods use machine learning merely as a complement to traditional numerical weather prediction models. Although some pure machine learning and data-driven approaches for weather prediction have been developed, they mainly formulate the problem similar to pattern recognition or follow the train of thought of traditional time-series models for extreme weather event forecasting; for the former, this usually yields only single-step ahead prediction, and for the latter, this lacks the flexibility to account for observed weather features as such methods concern only the patterns of the extreme weather occurrences. In this paper, we depart from the typical practice of pattern recognition and time-series approaches and focus on employing machine learning to estimate the probabilities of extreme weather occurrences in a multi-step-ahead (MSA) fashion given information on both weather features and the realized occurrences of extreme weather. Specifically, we propose a Markov conditional forward (MCF) model that adopts the Markov property between the occurrences of extreme weather for MSA extreme weather forecasting. Moreover, for better long-term prediction, we propose three novel cube perturbation methods to address error accumulation in our model. Experimental results on a real-world extreme weather dataset show the superiority of the proposed MCF model in terms of prediction accuracy for both short-term and long-term forecasting; moreover, the three cube perturbation methods successfully increase the fault tolerance and generalization ability of the MCF model, yielding significant improvements for long-term prediction.

In this demonstration, we develop an interactive tool, HIVE, to demonstrate the ability and versatility of an explainable risk ranking model with a special focus on financial use cases. HIVE is a web-based tool that provides users with automated highlighted financial statements, and HIVE is designed for making comparing statements rather more efficient. Moreover, with the proposed tool, users can find related reports at ease, and we believe that HIVE can benefit both academics and practitioners in finance as they can work around deep learning models with their newly gained insights.

Recently, much progress in natural language processing has been driven by deep contextualized representations pretrained on large corpora. Typically, the fine-tuning on these pretrained models for a specific downstream task is based on single-view learning, which is however inadequate as a sentence can be interpreted differently from different perspectives. Therefore, in this work, we propose a text-to-text multi-view learning framework by incorporating an additional view---the text generation view---into a typical single-view passage ranking model. Empirically, the proposed approach is of help to the ranking performance compared to its single-view counterpart. Component analysis is also reported in the paper.

Considering the temporal order of user-item interactions for recommendation forms a novel class of recommendation algorithms in recent years, among which sequential recommendation models are the most popular approaches. Although, theoretically, such fine-grained modeling should be beneficial to the recommendation performance, these sequential models in practice greatly suffer from the issue of data sparsity as there are a huge number of combinations for item sequences. To address the issue, we propose LSTPR, a graph-based matrix factorization model that incorporates both high-order graph information and long short-term user preferences into the modeling process. LSTPR explicitly distinguishes long-term and short-term user preferences and enriches the sparse interactions via random surfing on the user-item graph. Experiments on three recommendation datasets with temporal user-item information demonstrate that the proposed LSTPR model achieves significantly better performance than the seven baseline methods.

Conversational search plays a vital role in conversational information seeking. As queries in information seeking dialogues are ambiguous for traditional ad hoc information retrieval (IR) systems due to the coreference and omission resolution problems inherent in natural language dialogue, resolving these ambiguities is crucial. In this article, we tackle conversational passage retrieval, an important component of conversational search, by addressing query ambiguities with query reformulation integrated into a multi-stage ad hoc IR system. Specifically, we propose two conversational query reformulation (CQR) methods: (1) term importance estimation and (2) neural query rewriting. For the former, we expand conversational queries using important terms extracted from the conversational context with frequency-based signals. For the latter, we reformulate conversational queries into natural, stand-alone, human-understandable queries with a pretrained sequence-to-sequence model. Detailed analyses of the two CQR methods are provided quantitatively and qualitatively, explaining their advantages, disadvantages, and distinct behaviors. Moreover, to leverage the strengths of both CQR methods, we propose combining their output with reciprocal rank fusion, yielding state-of-the-art retrieval effectiveness, 30% improvement in terms of NDCG@3 compared to the best submission of Text REtrieval Conference (TREC) Conversational Assistant Track (CAsT) 2019.

Textual data is common and informative auxiliary information for recommender systems. Most prior art utilizes text for rating prediction, but rare work connects it to top-recommendation. Moreover, although advanced recommendation models capable of incorporating auxiliary information have been developed, none of these are specifically designed to model textual information, yielding a limited usage scenario for typical user-to-item recommendation. In this work, we present a framework of text-aware preference ranking (TPR) for top- recommendation, in which we comprehensively model the joint association of user-item interaction and relations between items and associated text. Using the TPR framework, we construct a joint likelihood function that explicitly describes two ranking structures: 1) item preference ranking (IPR) and 2) word relatedness ranking (WRR), where the former captures the item preference of each user and the latter captures the word relatedness of each item. As these two explicit structures are by nature mutually dependent, we propose TPR-OPT, a simple yet effective learning criterion that additionally includes implicit structures, such as relatedness between items and relatedness between words for each user for model optimization. Such a design not only successfully describes the joint association among users, words, and text comprehensively but also naturally yields powerful representations that are suitable for a range of recommendation tasks, including user-to-item, item-to-item, and user-to-word recommendation, as well as item-to-word reconstruction. In this paper, extensive experiments have been conducted on eight recommendation datasets, the results of which demonstrate that by including textual information from item descriptions, the proposed TPR model consistently outperforms state-of-the-art baselines on various recommendation tasks.

While internalized "implicit knowledge" in pretrained transformers has led to fruitful progress in many natural language understanding tasks, how to most effectively elicit such knowledge remains an open question.Based on the text-to-text transfer transformer (T5) model, this work explores a template-based approach to extract implicit knowledge for commonsense reasoning on multiple-choice (MC) question answering tasks.Experiments on three representative MC datasets show the surprisingly good performance of our simple template, coupled with a logit normalization technique for disambiguation.Furthermore, we verify that our proposed template can be easily extended to other MC tasks with contexts such as supporting facts in open-book question answering settings.Starting from the MC task, this work initiates further research to find generic natural language templates that can effectively leverage stored knowledge in pretrained models.

We propose the use of a word-level sentiment bidirectional LSTM in tandem with the self-attention mechanism for sentence-level sentiment prediction. In addition to the proposed model, we also present a finance report dataset for sentence-level financial risk detection. Experiments conducted on the proposed dataset together with two public review datasets attest the effectiveness of our model for sentence sentiment prediction.

In this paper, we propose a novel optimization criterion that leverages features of the skew normal distribution to better model the problem of personalized recommendation. Specifically, the developed criterion borrows the concept and the flexibility of the skew normal distribution, based on which three hyperparameters are attached to the optimization criterion. Furthermore, from a theoretical point of view, we not only establish the relation between the maximization of the proposed criterion and the shape parameter in the skew normal distribution, but also provide the analogies and asymptotic analysis of the proposed criterion to maximization of the area under the ROC curve. Experimental results conducted on a range of large-scale real-world datasets show that our model significantly outperforms the state of the art and yields consistently best performance on all tested datasets.

We present FRIDAYS, a financial risk information detecting and analyzing system that enables financial professionals to efficiently comprehend financial reports in terms of risk and domain-specific sentiment cues. Our system is designed to integrate multiple NLP models trained on financial reports but on different levels (i.e., word, multi-word, and sentence levels) and to illustrate the prediction results generated by the models. The system is available online at https://cfda.csie.org/FRIDAYS/.

Customer reviews on platforms such as TripAdvisor and Amazon provide rich information about the ways that people convey sentiment on certain domains. Given these kinds of user reviews, this paper proposes UGSD, a representation learning framework for constructing domain-specific sentiment dictionaries from online customer reviews, in which we leverage the relationship between user-generated reviews and the ratings of the reviews to associate the reviewer sentiment with certain entities. The proposed framework has the following three main advantages. First, no additional annotations of words or external dictionaries are needed for the proposed framework; the only resources needed are the review texts and entity ratings. Second, the framework is applicable across a variety of user-generated content from different domains to construct domain-specific sentiment dictionaries. Finally, each word in the constructed dictionary is associated with a low-dimensional dense representation and a degree of relatedness to a certain rating, which enable us to obtain more fine-grained dictionaries and enhance the application scalability of the constructed dictionaries as the word representations can be adopted for various tasks or applications, such as entity ranking and dictionary expansion. The experimental results on three real-world datasets show that the framework is effective in constructing high-quality domain-specific sentiment dictionaries from customer reviews.

This paper attempts to conduct a sentence-level sentiment analysis with respect to financial risk on a collection of financial reports. Specifically, we first propose a simple yet efficient algorithm to generate financial sentiment phrases (senti-phrases), and then with the obtained senti-phrases, we utilize multiple sentence embedding models for better learning the representations of financial risk sentences. In order to verify the performance of the proposed approach, we conduct a risk classification task of financial sentences on a sentence-level labeled dataset of finance reports. Experimental results show that incorporating the obtained senti-phrases into the embedding-based models improves the classification performance.

In the Age of Big Data, graph embedding has received increasing attention for its ability to accommodate the explosion in data volume and diversity, which challenge the foundation of modern recommender systems. Respectively, graph facilitates fusing complex systems of interactions into a unified structure and distributed embedding enables efficient retrieval of entities, as in the case of approximate nearest neighbor (ANN) search. When combined, graph embedding captures relational information beyond entity interaction and towards a problem's underlying structure, as epitomized by struct2vec [20] and PinSage [26]. This session will start by brushing up on the basics about graphs and embedding methods and discussing their merits. We then quickly dive into using the mathematical formulation of graph embedding to derive the modular framework: Sampler-Mapper-Optimizer for Recommendation, or SMORe. We demonstrate existing models used for recommendation, such as MF and BPR, can all be assembled using three basic components: sampler, mapper, and optimizer. The tutorial is accompanied by a hands-on session, where we show how graph embedding can model complex systems through the multi-task learning and the cross-platform data sparsity alleviation tasks.

We present collaborative similarity embedding (CSE), a unified framework that exploits comprehensive collaborative relations available in a user-item bipartite graph for representation learning and recommendation. In the proposed framework, we differentiate two types of proximity relations: direct proximity and k-th order neighborhood proximity. While learning from the former exploits direct user-item associations observable from the graph, learning from the latter makes use of implicit associations such as user-user similarities and item-item similarities, which can provide valuable information especially when the graph is sparse. Moreover, for improving scalability and flexibility, we propose a sampling technique that is specifically designed to capture the two types of proximity relations. Extensive experiments on eight benchmark datasets show that CSE yields significantly better performance than state-of-the-art recommendation methods.

Recommender systems are vital ingredients for many e-commerce services. In the literature, two of the most popular approaches are based on factorization and graph-based models; the former approach captures user preferences by factorizing the observed direct interactions between users and items, and the latter extracts indirect preferences from the graphs constructed by user-item interactions. In this paper we present HOP-Rec, a unified and efficient method that incorporates the two approaches. The proposed method involves random surfing on a graph to harvest high-order information among neighborhood items for each user. Instead of factorizing a transition matrix, our method introduces a confidence weighting parameter to simulate all high-order information simultaneously, for which we maintain a sparse user-item interaction matrix and enrich the matrix for each user using random walks. Experimental results show that our approach significantly outperforms the state of the art on a range of large-scale real-world datasets.

We present NavWalker, a flexible random walk-based approach for learning the representations of vertices in an information network. The proposed method enables us to incorporate different walk strategies into the sampling process of random walks, in order to further boost the network embedding techniques. Specifically, we formulate the proposed method by integrating the adjacency matrix of a network with a pre-defined information augmentation matrix. In contrast to SkipGram-based network embedding methods such as DeepWalk and Node2vec, which use only local network information to learn the representations, our method is flexible to further incorporate global or other auxiliary network information to guide the sampling process. Experiments on six real-world datasets demonstrate the advantages of the flexibility and its superior performance as compared to other state-of-the-art network embedding algorithms for the tasks of classification and recommendation.

This paper attempts to conduct analysis for one certain type of user reviews; that is, the reviews on a super-entity (e.g., restaurant) involve descriptions for many sub-entities (e.g., dishes). To deal with such analysis, we propose a text embedding framework for ranking sub-entities from user reviews of a given super-entity. Experiments on two real-world datasets show that our method outperforms three baselines by a statistically significant amount. Intriguing cases from the experiments are discussed in the paper.

This paper proposes an item concept embedding (ICE) framework to model item concepts via textual information. Specifically, in the proposed framework there are two stages: graph construction and embedding learning. In the first stage, we propose a generalized network construction method to build a network involving heterogeneous nodes and a mixture of both homogeneous and heterogeneous relations. The second stage leverages the concept of neighborhood proximity to learn the embeddings of both items and words. With the proposed carefully designed ICE networks, the resulting embedding facilitates both homogeneous and heterogeneous retrieval, including item-to-item and word-to-item retrieval. Moreover, as a distributed embedding approach, the proposed ICE approach not only generates related retrieval results but also delivers more diverse results than traditional keyword-matching-based approaches. As our experiments on two real-world datasets show, ICE encodes useful textual information and thus outperforms traditional methods in various item classification and retrieval tasks.

In this demonstration, we present FIN10K, a web-based information system that facilitates the analysis of textual information in financial reports. The proposed system has three main components: (1) a 10-K Corpus, including an inverted index of financial reports on Form 10-K, several numerical finance measures, and pre-trained word embeddings; (2) an information retrieval system; and (3) two data visualizations of the analyzed results. The system can be of great help in revealing valuable insights within large amounts of textual information. The system is now online available at http: //clip.csie.org/10K/.

This paper provides a deterministic online algorithm and a randomized online algorithm to search for suitable parameter values in Monte Carlo simulation for derivative pricing which are needed to achieve desired precisions. This paper also gives the competitive ratios of the two algorithms and proves the optimality of the algorithms. Experimental results on the performance of the algorithms are presented and analyzed as well.

This paper proposes to apply the contin-uous vector representations of words for discovering keywords from a financial sen-timent lexicon. In order to capture more keywords, we also incorporate syntactic information into the Continuous Bag-of-Words (CBOW) model. Experimental re-sults on a task of financial risk prediction using the discovered keywords demonstrate that the proposed approach is good at pre-dicting financial risk. 1

With the rapid growth of financial markets, many complex derivatives have been structured to meet specific financial goals. But most complex derivatives have no analytical formulas for their prices, e.g., when more than one market variable is factored. As a result, they must be priced by numerical methods such as lattice. A derivative is called multivariate if its value depends on more than one market variable. A lattice for a multivariate derivative is called a multivariate lattice. This paper proposes a flexible multi-phase method to build a multivariate lattice for pricing derivatives accurately. First, the original, correlated processes are transformed into uncorrelated ones by the orthogonalization method. A multivariate lattice is then constructed for the transformed, uncorrelated processes. To sharply reduce the nonlinearity error of many numerical pricing methods, our lattice has the flexibility to match the so-called “critical locations” - the locations where nonlinearity of the derivative's value function occurs. Numerical results for vulnerable options, insurance contracts guaranteed minimum withdrawal benefit, and defaultable bonds show that our methodology can be applied to the pricing of a wide range of complex financial contracts.