Search

In this paper, we address the identification and estimation of insurance models where insurees have private information about their risk and risk aversion. The model includes random damages and allows for several claims, while insurers choose from a finite number of coverages. We show that the joint distribution of risk and risk aversion is nonparametrically identified despite bunching due to multidimensional types and a finite number of coverages. Our identification strategy exploits the observed number of claims as well as an exclusion restriction, and a full support assumption. Furthermore, our results apply to any form of competition. We propose a novel estimation procedure combining nonparametric estimators and GMM estimation that we illustrate in a Monte Carlo study.

Each homeomorphic parametrization of a Jordan curve via the unit circle extends to a homeomorphism of the entire plane. It is a natural question to ask if such a homeomorphism can be chosen so as to have some Sobolev regularity. This prompts the simplified question: for a homeomorphic embedding of the unit circle into the plane, when can we find a homeomorphism from the unit disk that has the same boundary values and integrable first-order distributional derivatives? We give the optimal geometric criterion for the interior Jordan domain so that there exists a Sobolev homeomorphic extension for any homeomorphic parametrization of the Jordan curve. The problem is partially motivated by trying to understand which boundary values can correspond to deformations of finite energy., Comment: 16 pages, 8 figures

The magnetic field inside the sunspot umbra, as observed by the Full-disk MagnetoGraph (FMG) onboard the Advanced Space based Solar Observatory (ASO-S), was found to be experiencing a weakening. To address this issue, we employed a method developed by Xu et al. (2021) to correct the weakening in the data of 20 active regions observed by FMG during the period spanning December 29, 2022, to July 23, 2023. Research has revealed that the onset of magnetic field weakening occurs at a minimum magnetic field strength of 705 G, with the peak strength reaching up to 1931 G. We computed the change ratio (R1) of the unsigned magnetic flux within the sunspot umbra, considering measurements both before and after correction. The change ratio (R1) spans from 26% to 124%, indicating a significant increase in the unsigned magnetic flux within sunspot umbrae observed by FMG after correction. To illustrate this, we selected four active regions for comparison with data from the Helioseismic and Magnetic Imager (HMI). After correction, it is found that the unsigned magnetic flux in sunspot umbrae measured by FMG aligns more closely with that of HMI. This supports the effectiveness of the corrective method for FMG, despite imperfections, particularly at the umbra-penumbra boundary., Comment: 12 pages, 5 figures

Filament eruptions often result in flares and coronal mass ejections (CMEs). Most studies attribute the filament eruptions to their instabilities or magnetic reconnection. In this study, we report a unique observation of a filament eruption whose initiation process has not been reported before. This large-scale filament, with a length of about 360 Mm crossing an active region, is forced to erupted by two small-scale erupting filaments pushing out from below. This process of multi-filament eruption results in an M6.4 flare in the active region NOAA 13229 on 25th February 2023. The whole process can be divided into three stages: the eruptions of two active-region filaments F1 and F2; the interactions between the erupting F1, F2, and the large-scale filament F3; and the eruption of F3. Though this multi-filament eruption occurs near the northwest limb of the solar disk, it produces a strong halo CME that causes a significant geomagnetic disturbance. Our observations present a new filament eruption mechanism, in which the initial kinetic energy of the eruption is obtained from and transported to by other erupting structures. This event provides us a unique insight into the dynamics of multi-filament eruptions and their corresponding effects on the interplanetary space., Comment: 16 pages, 10 figures. Accepted for publication in Solar Physics

Observations of magnetic helicity transportation through the solar photosphere reflect the interaction of turbulent plasma movements and magnetic fields in the solar dynamo process. In this chapter, we have reviewed the research process of magnetic helicity inferred from the observed solar magnetic fields in the photosphere and also the solar morphological configurations with solar cycles. After introducing some achievements in the study of magnetic helicity, some key points would like to be summarized. The magnetic (current) helicity in the solar surface layer presents a statistical distribution similar to that of the sunspot butterfly diagram, but its maximum value is delayed from the extreme value of the sunspot butterfly diagram and corresponds in the phase with the statistical eruption of solar flares. During the spatial transport of magnetic (current) helicity from the interior of the sun into the interplanetary space at the time-space scale of the solar cycle, it shows the statistical distribution and the fluctuation with the hemispheric sign rule. These show that the current helicity and magnetic helicity transport calculation methods are complementary to each other. We also notice that the study of the inherent relationship between magnetic helicity and the solar cycle still depends on the observed accuracy of the solar magnetic field., Comment: 48 page,17 figures

The over-the-counter (OTC) market is characterized by a unique feature that allows market makers to adjust bid-ask spreads based on order size. However, this flexibility introduces complexity, transforming the market-making problem into a high-dimensional stochastic control problem that presents significant challenges. To address this, this paper proposes an innovative solution utilizing reinforcement learning techniques to tackle the OTC market-making problem. By assuming a linear inverse relationship between market order arrival intensity and bid-ask spreads, we demonstrate the optimal policy for bid-ask spreads follows a Gaussian distribution. We apply two reinforcement learning algorithms to conduct a numerical analysis, revealing the resulting return distribution and bid-ask spreads under different time and inventory levels.

Market making of options with different maturities and strikes is a challenging problem due to its high dimensional nature. In this paper, we propose a novel approach that combines a stochastic policy and reinforcement learning-inspired techniques to determine the optimal policy for posting bid-ask spreads for an options market maker who trades options with different maturities and strikes. When the arrival of market orders is linearly inverse to the spreads, the optimal policy is normally distributed.

Machine learning (ML) solutions to indoor localization problems have become popular in recent years due to high positioning accuracy and low cost of implementation. This paper proposes a novel local nonparametric approach for solving localizations from high-dimensional Received Signal Strength Indicator (RSSI) values. Our approach consists of a sequence of classification algorithms that sequentially narrows down the possible space for location solutions into smaller neighborhoods. The idea of this sequential classification method is similar to the decision tree algorithm, but a key difference is our splitting of the dataset at each node is not based on features of input (i.e. RSSI values), but some discrete-valued variables generated from the output variable (i.e. the 3D real-world coordinates). The strength of our localization solution can be tuned to problem specifics by the appropriate choice of how to sequentially partition the the space of location into smaller neighborhoods. Using the publicly available indoor localization dataset UJIIndoorLoc, we evaluate our proposed method vs. the global ML algorithms for the dataset. The primary contribution of this paper is to introduce a novel local ML solution for indoor localization problems., Comment: To be published in IEEE SoutheastCon 2023 conference proceedings

In this paper, we solve the Dirichlet problem for Sobolev maps between singular metric spaces that extends the corresponding result of Guo and Wenger [Comm. Anal. Geom. 2020]. The main new ingredient in our proofs is a suitable extension of the theory of trace for metric valued Sobolev maps developed by Korevaar and Schoen [Comm. Anal. Geom. 1993]. We also develop a theory of trace in the borderline case, which investigates a sharp condition to characterize the existence of traces.

Let $\mathbb{X}$ be a Jordan domain satisfying hyperbolic growth conditions. Assume that $\varphi$ is a homeomorphism from the boundary $\partial \mathbb{X}$ of $\mathbb{X}$ onto the unit circle. Denote by $h$ the harmonic diffeomorphic extension of $\varphi $ from $\mathbb{X}$ onto the unit disk. We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of $h.$ These generalize the Sobolev regularity of $h$ by Koski-Onninen [21, Theorem 3.1].

longitudinal magnetic field often suffers the saturation effect in strong magnetic field region when the measurement performs in a single-wavelength point and linear calibration is adopted. In this study, we develop a method that can judge the threshold of saturation in Stokes $V/I$ observed by the Solar Magnetic Field Telescope (SMFT) and correct for it automatically. The procedure is that first perform the second-order polynomial fit to the Stokes $V/I$ \textit{vs} $I/I_{m}$ ($I_{m}$ is the maximum value of Stokes $I$) curve to estimate the threshold of saturation, then reconstruct Stokes $V/I$ in strong field region to correct for saturation. The algorithm is proved to be effective by comparing with the magnetograms obtained by the Helioseismic and Magnetic Imager (HMI). The accurate rate of detection and correction for saturation is $\sim$99.4\% and $\sim$88\% respectively among 175 active regions. The advantages and disadvantages of the algorithm are discussed., Comment: 13 pages, 8 figures, accepted by RAA

Multi-wavelength observations of prominence eruptions provide an opportunity to uncover the physical mechanism of the triggering and the evolution process of the eruption. In this paper, we investigated an erupting prominence on October 14, 2012, recorded in H{\alpha}, EUV, and X-ray wavelengths. The process of the eruption gives evidences on the existence of a helical magnetic structure and showing the twist being converting to writhe. The estimated twist is ~6{\pi} (3 turns), exceeding the threshold of the kink instability. The rising plasma then reached a high speed, estimated at 228 km s-1, followed by a sudden rapid acceleration at 2715 m s-2, and synchronous with a solar are. Co-spatial cusp shaped structures were observed in both AIA 131{\AA} and 94{\AA} images, signifying the location of the magnetic reconnection. The erupted flux rope finally undergone a deceleration with a maximum value of 391 m s-2, which is even larger than the free-fall acceleration on the Sun (273 m s-2) , suggesting that the eruption finally failed, possibly due to an inward magnetic tension force., Comment: 17 pages, 12 figures, accepted by ApJ

In this notes, we survey the recent developments on theory of generalized quasidisks. Based on the more or less standard techniques used earlier, we also provide some minor improvements on the recorded results. A few nature questions were posed., Comment: 14 pages; Survey article

The conformal mapping $f(z)=(z+1)^2 $ from $\mathbb{D}$ onto the standard cardioid has a homeomorphic extension of finite distortion to entire $\mathbb{R}^2 .$ We study the optimal regularity of such extensions, in terms of the integrability degree of the distortion and of the derivatives, and these for the inverse. We generalize all outcomes to the case of conformal mappings from $\mathbb{D}$ onto cardioid-type domains.

Let $\Omega \subset \mbr^2$ be an internal chord-arc domain and $\varphi : \mbs^1 \rightarrow \partial \Omega$ be a homeomorphism. Then there is a diffeomorphic extension $h : \mbd \rightarrow \Omega$ of $\varphi .$ We study the relationship between weighted integrability of the derivatives of $h$ and double integrals of $\varphi$ and of $\varphi^{-1} .$

The weak-field approximation implying linear relationship between Stokes $V/I$ and longitudinal magnetic field, $B_{\Vert}$, often suffers from saturation observed in strong magnetic field regions such as sunspot umbra. In this work, we intend to improve the magnetic field observations carried out by the \textit{Solar Magnetic Field Telescope} (SMFT) at Huairou Solar Observing Station, China. We propose using non-linear relationship between Stokes $V/I$ and $B_{\Vert}$ to derive the magnetic field. To determine the form of the relationship, we perform a cross-calibration of the observed SMFT data and magnetograms provided by the \textit{Helioseismic and Magnetic Imager} on board the \textit{Solar Dynamics Observatory}. The algorithm of the magnetic field derivation is described in details. We show that using non-linear relationship between Stokes $V/I$ and $B_{\Vert}$ allows us to eliminate magnetic field saturation inside sunspot umbra. The proposed technique enables one to enhance the reliability of the SMFT magnetic field data obtained even long before the space-based instrumentation era, since 1987., Comment: 16 pages, 9 figures, published by Solar Physics

Let $\Omega$ be an internal chord-arc Jordan domain and $\varphi:\mathbb S\rightarrow\partial\Omega$ be a homeomorphism. We show that $\varphi$ has finite dyadic energy if and only if $\varphi$ has a diffeomorphic extension $h: \mathbb D\rightarrow \Omega$ which has finite energy., Comment: 19 pages, 1 figure

Unobserved heterogeneous treatment effects have been emphasized in the recent policy evaluation literature (see e.g., Heckman and Vytlacil, 2005). This paper proposes a nonparametric test for unobserved heterogeneous treatment effects in a treatment effect model with a binary treatment assignment, allowing for individuals' self-selection to the treatment. Under the standard local average treatment effects assumptions, i.e., the no defiers condition, we derive testable model restrictions for the hypothesis of unobserved heterogeneous treatment effects. Also, we show that if the treatment outcomes satisfy a monotonicity assumption, these model restrictions are also sufficient. Then, we propose a modified Kolmogorov-Smirnov-type test which is consistent and simple to implement. Monte Carlo simulations show that our test performs well in finite samples. For illustration, we apply our test to study heterogeneous treatment effects of the Job Training Partnership Act on earnings and the impacts of fertility on family income, where the null hypothesis of homogeneous treatment effects gets rejected in the second case but fails to be rejected in the first application., Comment: arXiv admin note: text overlap with arXiv:1611.06304

The empirical literature on program evaluation limits its scope almost exclusively to models where treatment effects are homogenous for observationally identical individuals. This paper considers a treatment effect model in which treatment effects may be heterogeneous, even among observationally identical individuals. Specifically, extending the classical instrumental variables (IV) model with an endogenous binary treatment and a binary instrument, we allow the heteroskedasticity of the error disturbance to also depend upon the treatment variable so that treatment has both mean and variance effects on the outcome. In this endogenous heteroskedasticity IV (EHIV) model with heterogeneous individual treatment effects, the standard IV estimator can be inconsistent and lead to incorrect inference. After showing identification of the mean and variance treatment effects in a nonparametric version of the EHIV model, we provide closed-form estimators for the linear EHIV for the mean and variance treatment effects and the individual treatment effects (ITE). Asymptotic properties of the estimators are provided. A Monte Carlo simulation investigates the performance of the proposed approach, and an empirical application regarding the effects of fertility on female labor supply is considered., Comment: 43 pages, 7 figures

We analyse the spatial distribution of current helicity in solar active regions. A comparison of current helicity maps derived from three different instruments (Helioseismic and Magnetc Imager on board the Solar Dynamics Observatory, SDO/HMI, Spectro-Polarimeter on board the Hinode, and Solar Magnetic Field Telescope at the Huairou Solar Observing Station, China, HSOS/SMFT) is carried out. The comparison showed an excellent correlation between the maps derived from the spaceborne instruments and moderate correlation between the maps derived from SDO/HMI and HSOS/SMFT vector magnetograms. The results suggest that the obtained maps characterize real spatial distribution of current helicity over an active region. To analyse intermittency of current helicity, we traditionally use the high-order structure functions and flatness function approach. The slope of a flatness function within some range of scales - the flatness exponent - is a measure of the degree of intermittency. SDO/HMI vector magnetograms for 3 ARs (NOAA 11158, 12494, and 12673) were used to calculate the flatness exponent time variations. All three ARs exhibited emergence of a new magnetic flux during the observational interval. The flatness exponent indicated the increase of intermittency 12-20 hours before the emergence of a new flux. We suppose that this behaviour can indicate subphotospheric fragmentation or distortion of the pre-existed electric current system by emerging magnetic flux., Comment: accepted by MNRAS

Research on peer effects in sociology has been focused for long on social influence power to investigate the social foundations for social interactions. This paper extends Xu(2011)'s large--network--based game model by allowing for social-influence-dependent peer effects. In a large network, we use the Katz--Bonacich centrality to measure individuals' social influences. To solve the computational burden when the data come from the equilibrium of a large network, we extend Aguirregabiria and Mira (2007)'s nested pseudo likelihood estimation (NPLE) approach to our large network game model. Using the Add Health dataset, we investigate peer effects on conducting dangerous behaviors of high school students. Our results show that peer effects are statistically significant and positive. Moreover, a student benefits more (statistically significant at the 5% level) from her conformity, or equivalently, pays more for her disobedience, in terms of peer pressures, if friends have higher social-influence status., Comment: Econometric Society Summer Meeting 2014, Texas Econometrics Camp 2014

Unobserved heterogeneous treatment effects have been emphasized in recent policy evaluation literature. In this paper, we extend Lu and White (2014)'s testing method for unobserved heterogeneous treatment effects by developing nonparametric tests under the standard exogenous instrumental variable assumption and allowing for endogenous treatment. Specifically, we propose Kolmogorov--Smirnov--type statistics that are consistent and simple to implement. To illustrate, we apply the proposed test method with two empirical applications: treatment effects of job training program on earnings as well as the impact of fertility on family income. The null hypotheses, i.e., lack of unobserved heterogeneous treatment effects, cannot be rejected at a 10% significance level in the former case, but should be rejected at all usual significance levels in the latter., Comment: 41 pages