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In this paper, we consider a stock that follows a geometric Brownian motion (GBM) and a riskless asset continuously compounded at a constant rate. We assume that the stock can go bankrupt, i.e. lose all of its value, at some exogenous random time (independent of the stock price) modeled as the first arrival time of a homogeneous Poisson process. For this setup, we study Merton’s optimal portfolio problem consisting in maximizing the expected isoelastic utility of the total wealth at a given finite maturity time. We obtain an analytical solution using coupled Hamilton–Jacobi–Bellman (HJB) equations. The optimal strategy bans borrowing and never allocates more wealth into the stock than the classical Merton ratio recommends. For nonlogarithmic isoelastic utilities, the optimal weights are nonmyopic. This is an example where a realistic problem, being merely a slight modification of the usual GBM model, leads to nonmyopic weights. For logarithmic utility, we additionally present an alternative derivation using a stochastic integral and verify that the weights obtained are identical to our first approach. We also present an example for our strategy applied to a stock with nonzero bankruptcy probability. 

Abstract Optimal decision-making requires consideration of internal and external contexts. Biased decision-making is a transdiagnostic symptom of neuropsychiatric disorders. We created a computational model demonstrating how the striosome compartment of the striatum constructs a context-dependent mathematical space for decision-making computations, and how the matrix compartment uses this space to define action value. The model explains multiple experimental results and unifies other theories like reward prediction error, roles of the direct versus indirect pathways, and roles of the striosome versus matrix, under one framework. We also found, through new analyses, that striosome and matrix neurons increase their synchrony during difficult tasks, caused by a necessary increase in dimensionality of the space. The model makes testable predictions about individual differences in disorder susceptibility, decision-making symptoms shared among neuropsychiatric disorders, and differences in neuropsychiatric disorder symptom presentation. The model provides evidence for the central role that striosomes play in neuroeconomic and disorder-affected decision-making. 

The multivariate Vasicek model is commonly used to capture mean-reverting dynamics typical for short rates, asset price stochastic log-volatilities, etc. Reparametrizing the discretized problem as a VAR(1) model, the parameters are oftentimes estimated using the multivariate least squares (MLS) method, which can be susceptible to outliers. To account for potential model violations, a maximum trimmed likelihood estimation (MTLE) approach is utilized to derive a system of nonlinear estimating equations, and an iterative procedure is developed to solve the latter. In addition to robustness, our new technique allows for reliable recovery of the long-term mean, unlike existing methodologies. A set of simulation studies across multiple dimensions, sample sizes and robustness configurations are performed. MTLE outcomes are compared to those of multivariate least trimmed squares (MLTS), MLE and MLS. Empirical results suggest that MTLE not only maintains good relative efficiency for uncontaminated data but significantly improves overall estimation quality in the presence of data irregularities. Additionally, real data examples containing daily log-volatilities of six common assets (commodities and currencies) and US/Euro short rates are also analyzed. The results indicate that MTLE provides an attractive instrument for interest rate forecasting, stochastic volatility modeling, risk management and other applications requiring statistical robustness in complex economic and financial environments. 

Optimal decision-making requires consideration of internal and external contexts. Biased decision-making is a transdiagnostic symptom of neu- ropsychiatric disorders. We created a computational model demonstrating how the striosome compartment of the striatum constructs a context- dependent mathematical space for decision-making computations, and how the matrix compartment uses this space to define action value. The model explains multiple experimental results and unifies other theories like reward prediction error, roles of the direct versus indirect pathways, and roles of the striosome versus matrix, under one framework. We also found, through new analyses, that striosome and matrix neurons increase their synchrony during difficult tasks, caused by a necessary increase in dimensionality of the space. The model makes testable predictions about individual differences in disorder susceptibility, decision-making symptoms shared among neuropsychiatric disorders, and differences in neuropsychiatric disorder symptom presenta- tion. The model provides evidence for the central role that striosomes play in neuroeconomic and disorder-affected decision-making. 

The class activation map (CAM) represents the neural-network-derived region of interest, which can help clarify the mechanism of the convolutional neural network’s determination of any class of interest. In medical imaging, it can help medical practitioners diagnose diseases like COVID-19 or pneumonia by highlighting the suspicious regions in Computational Tomography (CT) or chest X-ray (CXR) film. Many contemporary deep learning techniques only focus on COVID-19 classification tasks using CXRs, while few attempt to make it explainable with a saliency map. To fill this research gap, we first propose a VGG-16-architecture-based deep learning approach in combination with image enhancement, segmentation-based region of interest (ROI) cropping, and data augmentation steps to enhance classification accuracy. Later, a multi-layer Gradient CAM (ML-Grad-CAM) algorithm is integrated to generate a class-specific saliency map for improved visualization in CXR images. We also define and calculate a Severity Assessment Index (SAI) from the saliency map to quantitatively measure infection severity. The trained model achieved an accuracy score of 96.44% for the three-class CXR classification task, i.e., COVID-19, pneumonia, and normal (healthy patients), outperforming many existing techniques in the literature. The saliency maps generated from the proposed ML-GRAD-CAM algorithm are compared with the original Gran-CAM algorithm. 

We develop a new globally convergent optimization method for solving a constrained minimization problem underlying the minimum density power divergence estimator for univariate Gaussian data in the presence of outliers. Our hybrid procedure combines classical Newton’s method with a gradient descent iteration equipped with a step control mechanism based on Armijo’s rule to ensure global convergence. Extensive simulations comparing the resulting estimation procedure with the more prominent robust competitor, Minimum Covariance Determinant (MCD) estimator, across a wide range of breakdown point values suggest improved efficiency of our method. Application to estimation and inference for a real-world dataset is also given. 

Abstract Climate emulators are a powerful instrument for climate modeling, especially in terms of reducing the computational load for simulating spatiotemporal processes associated with climate systems. The most important type of emulators are statistical emulators trained on the output of an ensemble of simulations from various climate models. However, such emulators oftentimes fail to capture the “physics” of a system that can be detrimental for unveiling critical processes that lead to climate tipping points. Historically, statistical mechanics emerged as a tool to resolve the constraints on physics using statistics. We discuss how climate emulators rooted in statistical mechanics and machine learning can give rise to new climate models that are more reliable and require less observational and computational resources. Our goal is to stimulate discussion on how statistical climate emulators can further be improved with the help of statistical mechanics which, in turn, may reignite the interest of statistical community in statistical mechanics of complex systems.