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In this paper, we consider a general partially observed diffusion model with periodic coefficients and with non-degenerate diffusion component. The coefficients of such a model depend on an unknown (static and deterministic) parameter which needs to be estimated based on the observed component of the diffusion process. We show that, given enough regularity of the diffusion coefficients, a maximum likelihood estimator of the unknown parameter converges to the true parameter value as the sample size grows to infinity.

The Stefan problem with surface tension is well known to exhibit discontinuities in the associated moving aggregate (i.e., in the domain occupied by the solid), whose structure has only been understood under translational or radial symmetry so far. In this paper, we derive an auxiliary partial differential equation of second-order hyperbolic type, referred to as the cascade equation, that captures said discontinuities in the absence of any symmetry assumptions. Specializing to the one-phase setting, we introduce a novel (global) notion of weak solution to the cascade equation, which is defined as a limit of mean-field game equilibria. For the spatial dimension two, we show the existence of such a weak solution and prove a natural perimeter estimate on the associated moving aggregate., Comment: 41 pages

In this paper we show how the relaxation techniques can be used to establish the existence of an optimal contract in presence of information asymmetry. The method we illustrate was initially motivated by the problem of designing optimal brokerage fees, but it does apply to other optimal contract problems, in which (i) the agent controls linearly the drift of a diffusion process, (ii) the direct dependence of the principal's and the agent's objectives on the strategy of the agent is of a special form, and (iii) the space of admissible contracts is compact. This method is then applied to establish existence of an optimal brokerage fee in a market model with a private trading signal observed by the broker's client but not by the broker.

We study the Stefan problem with surface tension and radially symmetric initial data. In this context, the notion of a so-called physical solution, which exists globally despite the inherent blow-ups of the melting rate, has been recently introduced in [NS23]. The paper at hand is devoted to the proof that the physical solution is unique, the first such result when the free boundary is not flat, or when two phases are present. The main argument relies on a detailed analysis of the hitting probabilities for a three-dimensional Brownian motion, as well as on a novel convexity property of the free boundary obtained by comparison techniques. In the course of the proof, we establish a wide variety of regularity estimates for the free boundary and for the temperature function, of interest in their own right., Comment: 50 pages, 1 figure

Summary: In functional imaging studies, accurately synchronizing the time course of experimental manipulations and stimulus presentations with resulting imaging data is crucial for analysis. Current software tools lack such functionality, requiring manual processing of the experimental and imaging data, which is error-prone and potentially non-reproducible. We present VoDEx, an open-source Python library that streamlines the data management and analysis of functional imaging data. VoDEx synchronizes the experimental timeline and events (eg. presented stimuli, recorded behavior) with imaging data. VoDEx provides tools for logging and storing the timeline annotation, and enables retrieval of imaging data based on specific time-based and manipulation-based experimental conditions. Availability and Implementation: VoDEx is an open-source Python library and can be installed via the "pip install" command. It is released under a BSD license, and its source code is publicly accessible on GitHub https://github.com/LemonJust/vodex. A graphical interface is available as a napari-vodex plugin, which can be installed through the napari plugins menu or using "pip install." The source code for the napari plugin is available on GitHub https://github.com/LemonJust/napari-vodex.

In this work, the influence of Au plasmonics on photocurrent generation in the visible wavelength range in integrated thiol-linked CdSe quantum dot/Au nanogap structures is demonstrated. The plasmonic absorption is sensed utilizing photoacoustic (PA) detection technique. The laser diode is modulated to generate the PA excitation that oscillates the air-filled cell. When light absorption increases, an enhanced acoustic signal is captured by a microphone. The observed enhancement in the PA response is related to plasmonic absorption by the Au layers and the response is further enhanced by about 20% due to CdSe QDs. In our structure, the surface plasmon resonance (SPR) wavelength is approximately 500 nm. The SPR is utilized for generating photocurrents in CdSe quantum dots. Due to energy transfer from the dot to closely spaced Au surface through thiol links, a smooth transmission channel of electrons is established that forms a detectable photocurrent, which can be tuned by a bias voltage. These plasmonic nanogap structures can enable higher sensitivity in photovoltaics, photodetection and sensing.

In this work, we approximate the surface photovoltage (SPV) transients in nm-sized ZnO films by the equivalent RC circuit model. The SPV rises in time in time for about 90 mcs after the exciting light pulse at 275 nm is off at different pulse widths ranging from 1.2 to 12 mcs. The key to this observation is a considerable amount of defects in the films, which form a trap capacitance in the equivalent circuit. The photogeneration of nonequilibrium electrons and holes near the film surface is described by charging of a capacitance by the current source whereas the rate of their spatial separation is determined by a resistance. This resistance reflects an obstacle in the carrier movement while another capacitance determines the charge separation distance. The electron-hole recombination is account for a second resistance introduced into the equivalent circuit. The resulting modeled SPV transient allows to reproduce the observed experimental curve rather well., Comment: 4 pages, 5 figures

This paper constructs optimal brokerage contracts for multiple (heterogeneous) clients trading a single asset whose price follows the Almgren-Chriss model. The distinctive features of this work are as follows: (i) the reservation values of the clients are determined endogenously, and (ii) the broker is allowed to not offer a contract to some of the potential clients, thus choosing her portfolio of clients strategically. We find a computationally tractable characterization of the optimal portfolios of clients (up to a digital optimization problem, which can be solved efficiently if the number of potential clients is small) and conduct numerical experiments which illustrate how these portfolios, as well as the equilibrium profits of all market participants, depend on the price impact coefficients.

We consider the Stefan problem with surface tension, also known as the Stefan-Gibbs-Thomson problem, in an ambient space of arbitrary dimension. Assuming the radial symmetry of the initial data we introduce a novel "probabilistic" notion of solution, which can accommodate the discontinuities in time (of the radius) of the evolving aggregate. Our main result establishes the global existence of a probabilistic solution satisfying the natural upper bound on the sizes of the discontinuities. Moreover, we prove that the upper bound is sharp in dimensions d>2, in the sense that none of the discontinuities in the solution can be decreased in magnitude. The detailed analysis of the discontinuities, via appropriate stochastic representations, differentiates this work from the previous literature on weak solutions to the Stefan problem with surface tension., Comment: 30 pages, 1 figure

This paper presents a tractable sufficient condition for the consistency of maximum likelihood estimators (MLEs) in partially observed diffusion models, stated in terms of stationary distribution of the associated fully observed diffusion, under the assumption that the set of unknown parameter values is finite. This sufficient condition is then verified in the context of a latent price model of market microstructure, yielding consistency of maximum likelihood estimators of the unknown parameters in this model. Finally, we compute the latter estimators using historical financial data taken from the NASDAQ exchange.

We consider (a variant of) the external multi-particle diffusion-limited aggregation (MDLA) process of Rosenstock and Marquardt on the plane. Based on the recent findings of [11], [10] in one space dimension it is natural to conjecture that the scaling limit of the growing aggregate in such a model is given by the growing solid phase in a suitable "probabilistic" formulation of the single-phase supercooled Stefan problem for the heat equation. To address this conjecture, we extend the probabilistic formulation from [10] to multiple space dimensions. We then show that the equation that characterizes the growth rate of the solid phase in the supercooled Stefan problem is satisfied by the scaling limit of the external MDLA process with an inequality, which can be strict in general. In the course of the proof, we establish two additional results interesting in their own right: (i) the stability of a "crossing property" of planar Brownian motion and (ii) a rigorous connection between the probabilistic solutions to the supercooled Stefan problem and its classical and weak solutions., Comment: 41 pages, 2 figures

This paper establishes the well-posedness of reflected backward stochastic differential equations in the non-convex domains that satisfy a weaker version of the star-shaped property. The main results are established (i) in a Markovian framework with H\"older-continuous generator and terminal condition and (ii) in a general setting under a smallness assumption on the input data. We also investigate the connections between this well-posedness result and the theory of martingales on manifolds.

The performance of light-field microscopy is improved by selectively illuminating the relevant subvolume of the specimen with a second objective lens [1-3]. Here we advance this approach to a single-objective geometry, using an oblique one-photon illumination path or two-photon illumination to accomplish selective-volume excitation. The elimination of the second orthogonally oriented objective to selectively excite the volume of interest simplifies specimen mounting; yet, this single-objective approach still reduces out-of-volume background, resulting in improvements in image contrast, effective resolution, and volume reconstruction quality. We validate our new approach through imaging live developing zebrafish, demonstrating the technology's ability to capture imaging data from large volumes synchronously with high contrast, while remaining compatible with standard microscope sample mounting., Comment: Sara Madaan and Kevin Keomanee-Dizon contributed equally to this work; 4 pages, 3 figures; supplementary material included

This article provides a simple explanation of the asymptotic concavity of the price impact of a meta-order via the microstructural properties of the market. This explanation is made more precise by a model in which the local relationship between the order flow and the fundamental price (i.e. the local price impact) is linear, with a constant slope, which makes the model dynamically consistent. Nevertheless, the expected impact on midprice from a large sequence of co-directional trades is nonlinear and asymptotically concave. The main practical conclusion of the proposed explanation is that, throughout a meta-order, the volumes at the best bid and ask prices change (on average) in favor of the executor. This conclusion, in turn, relies on two more concrete predictions, one of which can be tested, at least for large-tick stocks, using publicly available market data.

In this paper, we construct the utility-based optimal hedging strategy for a European-type option in the Almgren-Chriss model with temporary price impact. The main mathematical challenge of this work stems from the degeneracy of the second order terms and the quadratic growth of the first order terms in the associated HJB equation, which makes it difficult to establish sufficient regularity of the value function needed to construct the optimal strategy in a feedback form. By combining the analytic and probabilistic tools for describing the value function and the optimal strategy, we establish the feedback representation of the latter. We use this representation to derive an explicit asymptotic expansion of the utility indifference price of the option, which allows us to quantify the price impact in options' market via the price impact coefficient in the underlying market.

We consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension. A probabilistic reformulation of the problem allows to define global solutions, even in the presence of blow-ups of the freezing rate. We provide a complete description of such solutions, by relating the temperature distribution in the liquid to the regularity of the ice growth process. The latter is shown to transition between (i) continuous differentiability, (ii) Holder continuity, and (iii) discontinuity. In particular, in the second regime we rediscover the square root behavior of the growth process pointed out by Stefan in his seminal paper [Ste89] from 1889 for the ordinary Stefan problem. In our second main theorem, we establish the uniqueness of the global solutions, a first result of this kind in the context of growth processes with singular self-excitation when blow-ups are present., Comment: 41 pages

Building on the line of work [DIRT15a], [DIRT15b], [NS17a], [DT17], [HLS18], [HS18] we continue the study of particle systems with singular interaction through hitting times. In contrast to the previous research, we (i) consider very general driving processes and interaction functions, (ii) allow for inhomogeneous connection structures, and (iii) analyze a game in which the particles determine their connections strategically. Hereby, we uncover two completely new phenomena. First, we characterize the "times of fragility" of such systems (e.g., the times when a macroscopic part of the population defaults or gets infected simultaneously, or when the neuron cells "synchronize") explicitly in terms of the dynamics of the driving processes, the current distribution of the particles' values, and the topology of the underlying network (represented by its Perron-Frobenius eigenvalue). Second, we use such systems to describe a dynamic credit-network game and show that, in equilibrium, the system regularizes: i.e., the times of fragility never occur, as the particles avoid them by adjusting their connections strategically. Two auxiliary mathematical results, useful in their own right, are uncovered during our investigation: a generalization of Schauder's fixed-point theorem for the Skorokhod space with the M1 topology, and the application of the max-plus algebra to the equilibrium version of the network flow problem., Comment: 37 pages

In this paper, we construct a solution to the optimal contract problem for delegated portfolio management of the fist-best (risk-sharing) type. The novelty of our result is (i) in the robustness of the optimal contract with respect to perturbations of the wealth process (interpreted as capital injections), and (ii) in the more general form of principals objective function, which is allowed to depend directly on the agents strategy, as opposed to being a function of the generated wealth only. In particular, the latter feature allows us to incorporate endogenous trading constraints in the contract. We reduce the optimal contract problem to the following inverse problem: for a given portfolio (defined in a feedback form, as a random field), construct a stochastic utility whose optimal portfolio coincides with the given one. We characterize the solution to this problem through a Stochastic Partial Differential Equation (SPDE), prove its well-posedness, and compute the solution explicitly in the Black-Scholes model.

In this paper, we present a family of a control-stopping games which arise naturally in equilibrium-based models of market microstructure, as well as in other models with strategic buyers and sellers. A distinctive feature of this family of games is the fact that the agents do not have any exogenously given fundamental value for the asset, and they deduce the value of their position from the bid and ask prices posted by other agents (i.e. they are pure speculators). As a result, in such a game, the reward function of each agent, at the time of stopping, depends directly on the controls of other players. The equilibrium problem leads naturally to a system of coupled control-stopping problems (or, equivalently, Reflected Backward Stochastic Differential Equations (RBSDEs)), in which the individual reward functions (or, reflecting barriers) depend on the value functions (or, solution components) of other agents. The resulting system, in general, presents multiple mathematical challenges due to the non-standard form of coupling (or, reflection). In the present case, this system is also complicated by the fact that the continuous controls of the agents, describing their posted bid and ask prices, are constrained to take values in a discrete grid. The latter feature reflects the presence of a positive tick size in the market, and it creates additional discontinuities in the agents reward functions (or, reflecting barriers). Herein, we prove the existence of a solution to the associated system in a special Markovian framework, provide numerical examples, and discuss the potential applications.

We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses to other banks, possibly triggering a cascade of defaults. The strength of this interaction is determined by the level of the so-called non-core exposure. We show that, when the size of the system becomes large, the cumulative loss process of a bank resulting from the defaults of other banks exhibits discontinuities. These discontinuities are naturally interpreted as systemic events, and we characterize them explicitly in terms of the level of non-core exposure and the fraction of banks that are "about to default". The main mathematical challenges of our work stem from the very singular nature of the interaction between the particles, which is inherited by the limiting system. A similar particle system is analyzed in [DIRT15a] and [DIRT15b], and we build on and extend their results. In particular, we characterize the large-population limit of the system and analyze the jump times, the regularity between jumps, and the local uniqueness of the limiting process., Comment: 33 pages

In this paper, we present a method for constructing a (static) portfolio of co-maturing European options whose price sign is determined by the skewness level of the associated implied volatility. This property holds regardless of the validity of a specific model - i.e. the method is robust. The strategy is given explicitly and depends only on beliefs about the future values of implied skewness, which is an observable market indicator. As such, our method allows to use the existing statistical tools to formulate the beliefs, providing a practical interpretation of the more abstract mathematical setting, in which the belies are understood as a family of probability measures. One of the applications of our results is a method for trading views on the future changes in implied skew, largely independently of other market factors. Another application provides a concrete improvement of the existing model-independent super- and sub- replication strategies for barrier options, which exploits a given set of beliefs on the implied skew. Our theoretical results are tested empirically, using the historical prices of SP500 options.

The three dimensional vibrations in a periodically poled ZX-cut Lithium Niobate thin bar with 0.3-mm long domains are considered. The acoustical vibrations may be excited by the 1) longitudinal acousto-electric current when a radio frequency voltage is parallel to the x-axis, and 2) transverse electric field when a radio frequency voltage is parallel to the z-axis. The computations by the Final Element Method reveal all the three displacements along the x, y, and z crystallographic axes. The amplitudes may be different for two types of vibration excitations. The positions of peaks in admittance versus frequency correlate with the frequencies of maximum acoustic amplitudes. The superlattice with 0.3-mm long domains along the x-axis is fabricated in the z-cut 0.5-mm-thick wafer. The experimental data on the radio frequency admittance versus frequency is in agreement with the corresponding theoretical computations., Comment: 10 pages, 6 figures, 171 Meeting of the Acoustical Society of America

We report the observations of nonstructural acousto-injection luminescence (NAIL) from tantalized LiNbO3 wafers. The samples under study are the X cut or Y cut wafers with the silver paste electrodes on opposite surfaces. The thickness is 1 to 2 mm and other linear dimensions are in the range of 2 to 25 mm. Experiments are done at room temperature in the MHz-frequency range. Mainly the fundamental shear ultrasound modes are excited in the samples. Experimentally are measured the spectra of NAIL, photo-luminescence spectra, acousto-electric properties, X Ray diffraction under NAIL. The NAIL and other effects appear above certain threshold amplitude of the acoustical strain that is about 10E-5. The involvement of the microstructural non-uniformity in the effects observed is experimentally identified by the photo-luminescence of point defects taken from different micro-regions of the samples. The data are explained in terms of the considerable acoustic stresses and piezoelectric fields that are capable injecting charge carriers from the metal contacts into a crystal., Comment: 12 pages, 7 figures, 171 Meeting of the American Acoustical Society (May,2016)

In this work, we present a continuous-time large-population game for modeling market microstructure betweentwo consecutive trades. The proposed modeling framework is inspired by our previous work [23]. In this framework, the Limit Order Book (LOB) arises as an outcome of an equilibrium between multiple agents who have different beliefs about the future demand for the asset. The agents' beliefs may change according to the information they observe, triggering changes in their behavior. We present an example illustrating how the proposed models can be used to quantify the consequences of changes in relevant information signals. If these signals, themselves, depend on the LOB, then, our approach allows one to model the "indirect" market impact (as opposed to the "direct" impact that a market order makes on the LOB, by eliminating certain limit orders). On the mathematical side, we formulate the proposed modeling framework as a continuum-player control-stopping game. We manage to split the equilibrium problem into two parts. The first one is described by a two-dimensional system of Reflected Backward Stochastic Differential Equations (RBSDEs), whose solution components reflect against each other. The second one leads to an infinite-dimensional fixed-point problem for a discontinuous mapping. Both problems are non-standard, and we prove the existence of their solutions in the paper.