Fast Estimation of True Bounds on Bermudan Option Prices under Jump-diffusion Processes

Fast pricing of American-style options has been a difficult problem since it was first introduced to financial markets in 1970s, especially when the underlying stocks' prices follow some jump-diffusion processes. In this paper, we propose a new algorithm to generate tight upper bounds on the Bermudan option price without nested simulation, under the jump-diffusion setting. By exploiting the martingale representation theorem for jump processes on the dual martingale, we are able to explore the unique structure of the optimal dual martingale and construct an approximation that preserves the martingale property. The resulting upper bound estimator avoids the nested Monte Carlo simulation suffered by the original primal-dual algorithm, therefore significantly improves the computational efficiency. Theoretical analysis is provided to guarantee the quality of the martingale approximation. Numerical experiments are conducted to verify the efficiency of our proposed algorithm

Benchmarking Large Language Models on CMExam -- A Comprehensive Chinese Medical Exam Dataset

Recent advancements in large language models (LLMs) have transformed the field of question answering (QA). However, evaluating LLMs in the medical field is challenging due to the lack of standardized and comprehensive datasets. To address this gap, we introduce CMExam, sourced from the Chinese National Medical Licensing Examination. CMExam consists of 60K+ multiple-choice questions for standardized and objective evaluations, as well as solution explanations for model reasoning evaluation in an open-ended manner. For in-depth analyses of LLMs, we invited medical professionals to label five additional question-wise annotations, including disease groups, clinical departments, medical disciplines, areas of competency, and question difficulty levels. Alongside the dataset, we further conducted thorough experiments with representative LLMs and QA algorithms on CMExam. The results show that GPT-4 had the best accuracy of 61.6% and a weighted F1 score of 0.617. These results highlight a great disparity when compared to human accuracy, which stood at 71.6%. For explanation tasks, while LLMs could generate relevant reasoning and demonstrate improved performance after finetuning, they fall short of a desired standard, indicating ample room for improvement. To the best of our knowledge, CMExam is the first Chinese medical exam dataset to provide comprehensive medical annotations. The experiments and findings of LLM evaluation also provide valuable insights into the challenges and potential solutions in developing Chinese medical QA systems and LLM evaluation pipelines. The dataset and relevant code are available at https://github.com/williamliujl/CMExam

Degradation of HK2 by chaperone-mediated autophagy promotes metabolic catastrophe and cell death

Hexokinase II (HK2), a key enzyme involved in glucose metabolism, is regulated by growth factor signaling and is required for initiation and maintenance of tumors. Here we show that metabolic stress triggered by perturbation of receptor tyrosine kinase FLT3 in non–acute myeloid leukemia cells sensitizes cancer cells to autophagy inhibition and leads to excessive activation of chaperone-mediated autophagy (CMA). Our data demonstrate that FLT3 is an important sensor of cellular nutritional state and elucidate the role and molecular mechanism of CMA in metabolic regulation and mediating cancer cell death. Importantly, our proteome analysis revealed that HK2 is a CMA substrate and that its degradation by CMA is regulated by glucose availability. We reveal a new mechanism by which excessive activation of CMA may be exploited pharmacologically to eliminate cancer cells by inhibiting both FLT3 and autophagy. Our study delineates a novel pharmacological strategy to promote the degradation of HK2 in cancer cells

Beclin1 Controls the Levels of p53 by Regulating the Deubiquitination Activity of USP10 and USP13

Autophagy is an important intracellular catabolic mechanism that mediates the degradation of cytoplasmic proteins and organelles. We report a potent small molecule inhibitor of autophagy named “spautin-1” for specific and potent autophagy inhibitor-1. Spautin-1 promotes the degradation of Vps34 PI3 kinase complexes by inhibiting two ubiquitin-specific peptidases, USP10 and USP13, that target the Beclin1 subunit of Vps34 complexes. Beclin1 is a tumor suppressor and frequently monoallelically lost in human cancers. Interestingly, Beclin1 also controls the protein stabilities of USP10 and USP13 by regulating their deubiquitinating activities. Since USP10 mediates the deubiquitination of p53, regulating deubiquitination activity of USP10 and USP13 by Beclin1 provides a mechanism for Beclin1 to control the levels of p53. Our study provides a molecular mechanism involving protein deubiquitination that connects two important tumor suppressors, p53 and Beclin1, and a potent small molecule inhibitor of autophagy as a possible lead compound for developing anticancer drugs

EAPP: Gatekeeper at the crossroad of apoptosis and p21-mediated cell-cycle arrest

We previously identified and characterized E2F-associated phospho-protein (EAPP), a nuclear phosphoprotein that interacts with the activating members of the E2F transcription factor family. EAPP levels are frequently elevated in transformed human cells. To examine the biological relevance of EAPP, we studied its properties in stressed and unstressed cells. Overexpression of EAPP in U2OS cells increased the fraction of G1 cells and lead to heightened resistance against DNA damage- or E2F1-induced apoptosis in a p21-dependent manner. EAPP itself becomes upregulated in confluent cells and after DNA damage and stimulates the expression of p21 independently of p53. It binds to the p21 promoter and seems to be required for the assembly of the transcription initiation complex. RNAi-mediated knockdown of EAPP expression brought about increased sensitivity towards DNA damage and resulted in apoptosis even in the absence of stress. Our results indicate that the level of EAPP is critical for cellular homeostasis. Too much of it results in G1 arrest and resistance to apoptosis, which, paradoxically, might favor cellular transformation. Too little EAPP seems to retard the expression not only of the p21 gene, but also of a number of other genes and ultimately results in apoptosis

Comparative Developmental Expression Profiling of Two C. elegans Isolates

Gene expression is known to change during development and to vary among genetically diverse strains. Previous studies of temporal patterns of gene expression during C. elegans development were incomplete, and little is known about how these patterns change as a function of genetic background. We used microarrays that comprehensively cover known and predicted worm genes to compare the landscape of genetic variation over developmental time between two isolates of C. elegans. We show that most genes vary in expression during development from egg to young adult, many genes vary in expression between the two isolates, and a subset of these genes exhibit isolate-specific changes during some developmental stages. This subset is strongly enriched for genes with roles in innate immunity. We identify several novel motifs that appear to play a role in regulating gene expression during development, and we propose functional annotations for many previously unannotated genes. These results improve our understanding of gene expression and function during worm development and lay the foundation for linkage studies of the genetic basis of developmental variation in gene expression in this important model organism

Multiple molecular interactions redundantly contribute to RB-mediated cell cycle control

BACKGROUND: The G1-S phase transition is critical to maintaining proliferative control and preventing carcinogenesis. The retinoblastoma tumor suppressor is a key regulator of this step in the cell cycle. RESULTS: Here we use a structure–function approach to evaluate the contributions of multiple protein interaction surfaces on pRB towards cell cycle regulation. SAOS2 cell cycle arrest assays showed that disruption of three separate binding surfaces were necessary to inhibit pRB-mediated cell cycle control. Surprisingly, mutation of some interaction surfaces had no effect on their own. Rather, they only contributed to cell cycle arrest in the absence of other pRB dependent arrest functions. Specifically, our data shows that pRB–E2F interactions are competitive with pRB–CDH1 interactions, implying that interchangeable growth arrest functions underlie pRB’s ability to block proliferation. Additionally, disruption of similar cell cycle control mechanisms in genetically modified mutant mice results in ectopic DNA synthesis in the liver. CONCLUSIONS: Our work demonstrates that pRB utilizes a network of mechanisms to prevent cell cycle entry. This has important implications for the use of new CDK4/6 inhibitors that aim to activate this proliferative control network

Efficient computation in stochastic optimization and simulation: Dynamic programs, risk quantification, and risk optimization

Stochastic optimization and simulation are two of the most fundamental research areas in Operations Research. In this thesis, we develop efficient computational approaches for three important topics in the realm of stochastic optimization and simulation. First, for general dynamic programs, we propose a regression approach to solve the information relaxation dual problems by exploring the structure of the function space of dual penalties. Compared with most of the existing approaches, the proposed one is more efficient since it circumvents the issue of nested simulation in approximating the so-called optimal dual penalty. The resulted approximations maintain to be feasible dual penalties, and thus yield valid dual bounds on the optimal value function. We further apply the proposed framework to a high-dimensional dynamic trading problem to demonstrate its effectiveness and efficiency in solving the duals of complex dynamic programs. Second, for general stochastic simulation, we study the risk quantification of mean response under input uncertainty, which, to the best of our knowledge, has been rarely systematically studied in the literature. We develop nested Monte Carlo estimators for risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) of mean response under input certainty. We show that they are strongly consistent and asymptotically normally distributed, and thus yield asymptotically valid confidence intervals. We further study the associated budget allocation problem for efficient simulation of the proposed nested risk estimators. Last, for general loss distributions, we study the extension of the recently proposed model-based approach, namely, the gradient-based adaptive stochastic search (GASS), to the optimization of risk measures such as VaR and CVaR. This problem is usually difficult, because 1) the loss function might lack structural properties such as convexity or differentiability since it is often generated via black-box simulation of a stochastic system; 2) evaluation of VaR or CVaR for a general loss distribution often requires rare-event simulation, which is computationally expensive. Instead of optimizing VaR or CVaR at target risk level directly, we incorporate an adaptive adjustment scheme on the risk level, by initializing the algorithm at a small risk level and adaptively increasing it until the simultaneous achievement of target risk level and convergence of the algorithm. This enables us to adaptively reduce the number of samples needed to estimate the risk measures at each iteration, and thus improving the overall efficiency.Ph.D