Continuous-Time Markowitz's Model with Transaction Costs

A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem,inherently in a finite time horizon. With a series of transformations, the problem is turned into a so-called double obstacle problem, a well studied problem in physics and partial differential equation literature, featuring two time-varying free boundaries. The two boundaries, which define the buy, sell, and no-trade regions, are proved to be smooth in time. This in turn characterizes the optimal strategy, via a Skorokhod problem, as one that tries to keep a certain adjusted bond-stock position within the no-trade region. Several features of the optimal strategy are revealed that are remarkably different from its no-transaction-cost counterpart. It is shown that there exists a critical length in time, which is dependent on the stock excess return as well as the transaction fees but independent of the investment target and the stock volatility, so that an expected terminal return may not be achievable if the planning horizon is shorter than that critical length (while in the absence of transaction costs any expected return can be reached in an arbitrary period of time). It is further demonstrated that anyone following the optimal strategy should not buy the stock beyond the point when the time to maturity is shorter than the aforementioned critical length. Moreover, the investor would be less likely to buy the stock and more likely to sell the stock when the maturity date is getting closer. These features, while consistent with the widely accepted investment wisdom, suggest that the planning horizon is an integral part of the investment opportunities.Comment: 30 pages, 1 figur

Anti-PD-1 immunotherapy combined with stereotactic body radiation therapy and GM-CSF for the treatment of advanced malignant PEComa: A case report

BackgroundPerivascular epithelioid cell neoplasm (PEComa) is a rare mesenchymal tumour. Due to its low incidence, a standard treatment regimen for PEComa has not yet been established. Radiotherapy has a synergistic effect with PD-1 inhibitors and GM-CSF. We treated advanced malignant PEComa with a triple regimen of PD-1 inhibitor, SBRT and GM-CSF to provide better therapeutic effect.Case presentationA 63-year-old woman was diagnosed with malignant PEComa after presenting with postmenopausal vaginal bleeding. Despite two surgeries, the neoplasm eventually metastasized throughout the body. We formulated triple therapy with SBRT, a PD-1 inhibitor, and GM-CSF for the patient. The patient’s local symptoms were controlled at the radiotherapy site, and the lesions at the unirradiated sites were also relieved.ConclusionsFor the first time, a triple regimen of PD-1 inhibitor, SBRT and GM-CSF was used in the treatment of malignant PEComa and achieved good efficacy. Considering the lack of prospective clinical studies in PEComa, we believe that this triple therapy is a good-quality regimen for advanced malignant PEComa

AgentVerse: Facilitating Multi-Agent Collaboration and Exploring Emergent Behaviors in Agents

Autonomous agents empowered by Large Language Models (LLMs) have undergone significant improvements, enabling them to generalize across a broad spectrum of tasks. However, in real-world scenarios, cooperation among individuals is often required to enhance the efficiency and effectiveness of task accomplishment. Hence, inspired by human group dynamics, we propose a multi-agent framework \framework that can collaboratively and dynamically adjust its composition as a greater-than-the-sum-of-its-parts system. Our experiments demonstrate that \framework framework can effectively deploy multi-agent groups that outperform a single agent. Furthermore, we delve into the emergence of social behaviors among individual agents within a group during collaborative task accomplishment. In view of these behaviors, we discuss some possible strategies to leverage positive ones and mitigate negative ones for improving the collaborative potential of multi-agent groups. Our codes for \framework will soon be released at \url{https://github.com/OpenBMB/AgentVerse}.Comment: Work in progres

Discovery of six high-redshift quasars with the Lijiang 2.4m telescope and the Multiple Mirror Telescope

Quasars with redshifts greater than 4 are rare, and can be used to probe the structure and evolution of the early universe. Here we report the discovery of six new quasars with $i$-band magnitudes brighter than 19.5 and redshifts between 2.4 and 4.6 from the YFOSC spectroscopy of the Lijiang 2.4m telescope in February, 2012. These quasars are in the list of $z>3.6$ quasar candidates selected by using our proposed $J-K/i-Y$ criterion and the photometric redshift estimations from the SDSS optical and UKIDSS near-IR photometric data. Nine candidates were observed by YFOSC, and five among six new quasars were identified as $z>3.6$ quasars. One of the other three objects was identified as a star and the other two were unidentified due to the lower signal-to-noise ratio of their spectra. This is the first time that $z>4$ quasars have been discovered using a telescope in China. Thanks to the Chinese Telescope Access Program (TAP), the redshift of 4.6 for one of these quasars was confirmed by the Multiple Mirror Telescope (MMT) Red Channel spectroscopy. The continuum and emission line properties of these six quasars, as well as their central black hole masses and Eddington ratios, were obtained.Comment: 7 pages, 2 figures, published in Research in Astronomy and Astrophysics (RAA) as a lette

Raw Garlic Consumption and Risk of Liver Cancer: A Population-Based Case-Control Study in Eastern China.

Although the major risk factors for liver cancer have been established, preventive factors for liver cancer have not been fully explored. We evaluated the association between raw garlic consumption and liver cancer in a large population-based case-control study in Eastern China. The study was conducted in Jiangsu, China, from 2003 to 2010. A total of 2011 incident liver cancer cases and 7933 randomly selected population-controls were interviewed. Epidemiological data including raw garlic intake and other exposures were collected, and serum markers of hepatitis B virus (HBV) and hepatitis C virus (HCV) infection were assayed. Overall, eating raw garlic twice or more per week was inversely associated with liver cancer, with an adjusted odds ratio (aOR) of 0.77 (95% confidence interval (CI): 0.62-0.96) compared to those ingesting no raw garlic or less than twice per week. In stratified analyses, high intake of raw garlic was inversely associated with liver cancer among Hepatitis B surface antigen (HBsAg) negative individuals, frequent alcohol drinkers, those having history of eating mold-contaminated food or drinking raw water, and those without family history of liver cancer. Marginal interactions on an additive scale were observed between low raw garlic intake and HBsAg positivity (attributable proportion due to interaction (AP) = 0.31, 95% CI: -0.01-0.62) and heavy alcohol drinking (AP = 0.28, 95% CI: 0.00-0.57). Raw garlic consumption is inversely associated with liver cancer. Such an association shed some light on the potential etiologic role of garlic intake on liver cancer, which in turn might provide a possible dietary intervention to reduce liver cancer in Chinese population