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As an image-making tool for scientists studying the transient, instantaneous photography has long been seen as opening up a visual realm previously inaccessible to the inferior testimony of the human eye. But when photographic pioneer Henry Fox Talbot took the first photograph of a moving object by the light of an electric spark in 1851, he was guided by existing visual practices designed to create instantaneous vision in the eye itself. Exploring the background behind the peculiar subject of his experiment – a mechanically spinning disc – reveals a hidden prehistory of spark-illuminated photography: physicists’ pre-photographic techniques for stopping time. [Copyright &y& Elsevier]

Motivated by problems in behavioural finance, we provide two explicit constructions of a randomized stopping time which embeds a given centred distribution μ on integers into a simple symmetric random walk in a uniformly integrable manner. Our first construction has a simple Markovian structure: at each step, we stop if an independent coin with a state-dependent bias returns tails. Our second construction is a discrete analogue of the celebrated Azéma–Yor solution and requires independent coin tosses only when excursions away from maximum breach predefined levels. Further, this construction maximizes the distribution of the stopped running maximum among all uniformly integrable embeddings of μ. [ABSTRACT FROM AUTHOR]

Most results regarding Skorokhod embedding problems SEP so far rely on the assumption that the corresponding stopped process is uniformly integrable, which is equivalent to the convex ordering condition U μ ≤ U ν when the underlying process is a local martingale. In this paper, we study the existence, construction of Root's solutions to SEP, in the absence of this convex ordering condition. We replace the uniform integrability condition by the minimality condition (Monroe, 1972), as the criterion of "good" solutions. A sufficient and necessary condition (in terms of local time) for minimality is given. We also discuss the optimality of such minimal solutions. These results extend the generality of the results given by Cox and Wang (2013) and Gassiat et al. (2015). At last, we extend all the results above to multi-marginal embedding problems based on the work of Cox et al. (2018). [ABSTRACT FROM AUTHOR]

Let X be a progressively measurable, almost surely right-continuous stochastic process such that X τ ∈ L 1 and E [ X τ ] = E [ X 0 ] for each finite stopping time τ . In 2006, Cherny showed that X is then a uniformly integrable martingale provided that X is additionally nonnegative. Cherny then posed the question whether this implication also holds even if X is not necessarily nonnegative. We provide an example that illustrates that this implication is wrong, in general. If, however, an additional integrability assumption is made on the limit inferior of | X | then the implication holds. Finally, we argue that this integrability assumption holds if the stopping times are allowed to be randomized in a suitable sense. [ABSTRACT FROM AUTHOR]

Abstract We work in the setting of the progressive enlargement G of a reference filtration F through the observation of a random time τ. We study an integral representation property for some classes of G -martingales stopped at τ. In the first part, we focus on the case where F is a Poisson filtration and we establish a predictable representation property with respect to three G -martingales. In the second part, we relax the assumption that F is a Poisson filtration and we assume that τ is an F -pseudo-stopping time. We establish integral representations with respect to some G -martingales built from F -martingales and, under additional hypotheses, we obtain a predictable representation property with respect to two G -martingales. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study a kind of financial product, stock loans, in which there is a capped limit for the stock price when it exceeds a predetermined barrier. Loans with two types of cap are analyzed: constant caps and caps with a constant growth rate. We build the pricing models of the contracts by analyzing the form of the optimal stopping time and derive the formulas of the value functions. We present the numerical results and make an analysis of fair values of related parameters. A comparison between capped stock loans and uncapped ones is also given. We find that capped loans have their own advantages such as more flexibility and lower cost. [Copyright &y& Elsevier]

This paper extends results of Mortimer and Williams (1991) about changes of probability measure up to a random time under the assumptions that all martingales are continuous and that the random time avoids stopping times. We consider locally absolutely continuous measure changes up to a random time, changes of probability measure up to and after an honest time, and changes of probability measure up to a pseudo-stopping time. Moreover, we apply our results to construct a change of probability measure that is equivalent to the enlargement formula and to build, for a certain class of pseudo-stopping times, a class of measure changes that preserve the pseudo-stopping time property. Furthermore, we study for a price process modeled by a continuous semimartingale the stability of the No Free Lunch with Vanishing Risk (NFLVR) property up to a random time, that avoids stopping times, in the progressively enlarged filtration and provide sufficient conditions for this stability in terms of the Azéma supermartingale. [ABSTRACT FROM AUTHOR]

In this study, asbestos-free automotive brake pads produced from palm kernel fibers with epoxy-resin binder was evaluated. Resins varied in formulations and properties such as friction coefficient, wear rate, hardness test, porosity, noise level, temperature, specific gravity, stopping time, moisture effects, surface roughness, oil and water absorptions rates, and microstructure examination were investigated. Other basic engineering properties of mechanical overload, thermal deformation fading behaviour shear strength, cracking resistance, over-heat recovery, and effect on rotor disc, caliper pressure, pad grip effect and pad dusting effect were also investigated. The results obtained indicated that the wear rate, coefficient of friction, noise level, temperature, and stopping time of the produced brake pads increased as the speed increases. The results also show that porosity, hardness, moisture content, specific gravity, surface roughness, and oil and water absorption rates remained constant with increase in speed. The result of microstructure examination revealed that worm surfaces were characterized by abrasion wear where the asperities were ploughed thereby exposing the white region of palm kernel fibers, thus increasing the smoothness of the friction materials. Sample S 6 with composition of 40% epoxy-resin, 10% palm wastes, 6% Al 2 O 3 , 29% graphite, and 15% calcium carbonate gave better properties. The result indicated that palm kernel fibers can be effectively used as a replacement for asbestos in brake pad production. [ABSTRACT FROM AUTHOR]

The problem of stopping a Brownian bridge with an unknown pinning point to maximise the expected value at the stopping time is studied. A few general properties, such as continuity and various bounds of the value function, are established. However, structural properties of the optimal stopping region are shown to crucially depend on the prior, and we provide a general condition for a one-sided stopping region. Moreover, a detailed analysis is conducted in the cases of the two-point and the mixed Gaussian priors, revealing a rich structure present in the problem. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the solvability of a class of multi-dimensional forward–backward stochastic differential equations (FBSDEs) with oblique reflection and unbounded stopping time. Under some mild assumptions on the coefficients in such FBSDE, the existence result of adapted solutions is done via a penalization method. The uniqueness is obtained by a verification theorem similarly to the one used by Hu and Tang (2010) [7]. Finally, we establish the connection with the corresponding optimal switching problem. This latter is solved by using the previous results on FBSDEs. [Copyright &y& Elsevier]

This paper completes the studies undertaken in Aksamit et al. (2017, 2018) [ [1,2] ] and Choulli and Deng (2017) [ [8] ], where we quantify the impact of a random time on the no-unbounded-profit-with-bounded-risk concept (called NUPBR hereafter) for quasi-left-continuous models and discrete-time market models respectively. Herein, we focus on NUPBR for semimartingale models that live on thin predictable sets only and when the extra information about the random time is added progressively over time. This leads to the probabilistic setting of two filtrations where one filtration contains the other and makes the random time a stopping time. For this framework, we explain how far NUPBR is affected when one stops the model by an arbitrary random time, or when one incorporates in a progressive way an honest time into the model. Furthermore, we show how to construct explicitly some local martingale deflators in the largest filtration for a particular class of models. As a consequence, by combining the current results on the thin case and those of Aksamit et al. (2017, 2018) [ [1,2] ], we elaborate universal results for general semimartingale models. [ABSTRACT FROM AUTHOR]

Abstract: Under the framework of -expectation and -Brownian motion, we introduce Itô’s integral for stochastic processes without assuming quasi-continuity. Then we can obtain Itô’s integral on stopping time interval. This new formulation permits us to obtain Itô’s formula for a general -function, which essentially generalizes the previous results of Peng (2006, 2008, 2009, 2010, 2010)  as well as those of Gao (2009)  and Zhang et al. (2010) . [Copyright &y& Elsevier]

Abstract: Users in Service-oriented architecture (SOA) seek the best Quality of service (QoS) by service selection from the candidates responding in succession. In case the QoS changes dynamically, choosing one service and stop the searching is problematic for a service user who makes the choice online. Lack of accurate knowledge of service distribution, the user is unable to make a good decision. The Local Martingale Difference (LMD) approach is developed in this paper to help users to achieve optimal results, in the sense of probability. The stopping time is proved to be bounded to ensure the existence of an optimal solution first. Then, a global estimation over the time horizon is transformed to a local determination based on current martingale difference to make the algorithm feasible. Independent of any predetermined threshold or manual intervention, LMD enables users to stop around the optimal time, based on the information collected during the stochastic process. Verified to be efficient by comparison with three traditional methods, LMD is adaptable in vast applications with dynamic QoS. [Copyright &y& Elsevier]

Abstract This study describes a modified partial differential equation (PDE)-based algorithm for contrast enhancement of hazy images. The formulation is supported by similarities between haze and low light conditions. The proposed approach employs multi-scale, local-global enhancement of inverted log reflectance and illumination components. These multiple processes are combined in a suitable PDE framework for improved effectiveness. Furthermore, the de-hazing process is automated via gradient-based optimization, eliminating the manual determination of PDE stopping time. Solutions are also devised for visual halo effect, over-enhancement and colour distortion. Based on subjective and quantitative analysis, the proposed technique consistently outperforms several de-hazing algorithms from the literature. [ABSTRACT FROM AUTHOR]

Abstract: We develop an explicit non-randomized solution to the Skorokhod embedding problem in an abstract setup of signed functionals of excursions of Markov processes. Our setting allows us to solve the Skorokhod embedding problem, in particular, for the age process of excursions of a Markov process, for diffusions and their signed age processes, for Azéma’s martingale and for Bessel processes of dimension smaller than 2. This work is a continuation and an important generalization of Obłój and Yor [J. Obłój, M. Yor, An explicit Skorokhod embedding for the age of Brownian excursions and Azéma martingale, Stochastic Process. Appl. 110 (1) (2004) 83–110]. Our methodology is based on excursion theory and the solution to the Skorokhod embedding problem is described in terms of the Itô measure of the functional. We also derive an embedding for positive functionals and we correct a mistake in the formula of Obłój and Yor [J. Obłój, M. Yor, An explicit Skorokhod embedding for the age of Brownian excursions and Azéma martingale, Stochastic Process. Appl. 110 (1) (2004) 83–110] for measures with atoms. [Copyright &y& Elsevier]

Suppose you have one unit of stock, currently worth 1, which you must sell before time T . The Optional Sampling Theorem tells us that whatever stopping time we choose to sell, the expected discounted value we get when we sell will be 1. Suppose however that we are able to see a units of time into the future, and base our stopping rule on that; we should be able to do better than expected value 1. But how much better can we do? And how would we exploit the additional information? The optimal solution to this problem will never be found, but in this paper we establish remarkably close bounds on the value of the problem, and we derive a fairly simple exercise rule that manages to extract most of the value of foresight. [ABSTRACT FROM AUTHOR]

Abstract: To reduce the harmful emissions from automobiles and massive surges in fuel prices, automotive electric vehicles are an effective alternate solution. In this paper, a cascaded bi-directional DC/DC buck-boost converter with dual control strategy during regenerative braking is used for a two-wheeler application. The dual control strategy with the cascaded converter is used to increase the average power stored during the braking period and to reduce the vehicle’s stopping time. The converter with the proposed control strategy used in this work has made it possible to charge the battery even when the back emf of the machine is less than the battery voltage. A fuzzy logic control strategy is used to consider the non-linear factors like SOC, speed of the vehicle and the required brake force. This is done in order to make the system more reliable and realistic. The complete model is simulated in MATLAB/Simulink. By implementing the dual control strategy, the average power stored by the battery is increased by 2.5 times and the vehicle comes to halt faster in comparison with the existing control strategy. The versatility of the strategy is shown by examining three different scenarios during the regenerative braking process. To support the above claims, simulation results are presented to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Comparatively f ew studies have been carried out on air weapon injuries yet there are significant number of injuries and fatalities caused by these l ow power weapons because of their availability and the public perception that because they need no licence they are assumed to be safe. In this study ballistic gel was tested by Bloom and rupture tests to check on consistency of production. Two series of tests were carried out firing into unclothed gel blocks and blocks loosely covered by different items of clothing to simulate attire (tee shirt, jeans, fleece, and jacket). The damage to the clothing caused by different shaped pellets when fired at different ranges was examined. The apparent hole size was affected by the shape of pellet (round, pointed, flat and hollow point) and whether damage was predominantly caused by pushing yarn to one side or by laceration of the yarn through cutting or tearing. The study also compared penetration into clothed gel and unclothed gel under identical conditions, and loose clothing greatly reduced penetration. With loose clothing at 9.1 m range clothing reduced penetration to 50-70% of the penetration of unclothed gel but at 18.3 m range only 7 out of 36 shots penetrated the gel. This cannot be accounted for by the energy loss at the longer range (3-7% reduction from 9.1 m to 18.3 m range in unclothed gels) and it is suggested that impulse may have a role to play. Shots that did not penetrate the gel were used to estimate the possible stopping time for the pellet (around 75 |xs) and force (1700 N) or stress (100 MPa) required to bring the pellet to a halt. Even with these l ow energy projectiles, cloth fibres were entrained in the gel showing the potential for penetration of the body and subsequent infection. [ABSTRACT FROM AUTHOR]

Rationale and Objectives: To evaluate clinical and imaging features associated with adequacy of the hepatocyte phase (HP) in gadoxetate disodium–enhanced liver magnetic resonance imaging (MRI) in patients without chronic liver disease (CLD). Materials and Methods: This was a retrospective institutional review board–approved study of 97 patients who underwent liver MRI examinations with gadoxetate disodium and had no history of CLD. Available late dynamic and HP sequences (3–20 minutes postinjection) were independently analyzed by four radiologists for perceived image adequacy and level of biliary enhancement. Signal intensity ratios (SIRs) of liver/inferior vena cava (IVC), liver/spleen, and liver/muscle were measured. The Spearman ρ and receiver operating characteristic analyses were performed correlating various factors with HP adequacy. A rule for predicting HP adequacy was also derived and tested to determine whether overall examination time could be shortened. Results: A visually adequate HP was observed in 12% of subjects by 10 minutes, 80% by 15 minutes, and 93% by 20 minutes. An SIRliver/IVC > 1.8 was the imaging feature that had the strongest correlation with an adequate HP (ρ = 0.813, P < .001), and was more predictive of adequacy of the HP than the time postinjection (ρ = 0.5, P < .001). The time at which an adequate HP was first observed did not correlate with any tested demographic or laboratory values. Stopping imaging when an SIRliver/IVC > 1.8 would have successfully reduced mean postcontrast time to 15:39 ± 4:02 from 20:00 (P < .001), although maintaining HP adequacy. Conclusions: Most patients without CLD undergoing gadoxetate-enhanced liver MRI achieve adequate HP at 20 minutes. However, a shorter postcontrast stopping time can be used in most patients. [Copyright &y& Elsevier]

Nationwide unification of carbon emission right market in China has long been proposed yet not achieved. Launching of the nationwide trading center at Shanghai was a recent great step towards this target but the regional pilots covering respective zones are still in operation. With all trading data in those markets from their inceptions, this paper investigates the development status and trend of each submarket, based on which, it is revealed that sudden replacement of regional markets by the unified nationwide trading center is infeasible at the present stage, furthermore, feasibility of market merging is analyzed and optimized route for essential unification is designed. This paper contributes to deconstruct the value of carbon emission right and interprets its properties of option value, the equivalence of which value from the perspective of financial investment and enterprise operations is explored and formally established. Applying the geometric Brownian motion and optimal stopping time to model the carbon asset operation, option value of carbon emission right is estimated and marginal return-ability of its consumption is calculated for each region. Based on the analysis regionally, market merging is simulated and optimized route for nationwide market unification is proposed with policy suggestions. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of the partially observed optimal stopping problem. Then, we propose a numerical method, based on the quantization of the discrete-time filter process and the inter-jump times, to approximate the value function and to compute an -optimal stopping time. We prove the convergence of the algorithms and bound the rates of convergence. [Copyright &y& Elsevier]

Abstract: We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings for Lévy processes obtained essentially via the Wiener–Hopf factorization. The main ingredient in our approach is the representation of the -excessive functions as expected suprema. A variety of examples is given. [Copyright &y& Elsevier]

Abstract: The converse comparison theorem has received much attention in the theory of backward stochastic differential equations (BSDEs). However, no such theorem has been proved for anticipated BSDEs. In this paper, we derive a converse comparison theorem by first giving an existence and uniqueness theorem for adapted solutions of anticipated BSDEs with a stopping time and then related to -expectations induced by anticipated BSDEs. [Copyright &y& Elsevier]

Abstract: The contribution of this paper is to introduce change of measure based techniques for the rare-event analysis of heavy-tailed random walks. Our changes of measures are parameterized by a family of distributions admitting a mixture form. We exploit our methodology to achieve two types of results. First, we construct Monte Carlo estimators that are strongly efficient (i.e. have bounded relative mean squared error as the event of interest becomes rare). These estimators are used to estimate both rare-event probabilities of interest and associated conditional expectations. We emphasize that our techniques allow us to control the expected termination time of the Monte Carlo algorithm even if the conditional expected stopping time (under the original distribution) given the event of interest is infinity–a situation that sometimes occurs in heavy-tailed settings. Second, the mixture family serves as a good Markovian approximation (in total variation) of the conditional distribution of the whole process given the rare event of interest. The convenient form of the mixture family allows us to obtain functional conditional central limit theorems that extend classical results in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, for any submartingale of class defined on a filtered probability space satisfying some technical conditions, we associate a -finite measure on , such that for all , and for all events : where is the last time for which the process hits zero. The existence of has already been proven in several particular cases, some of them are related with Brownian penalization, and others are involved with problems in mathematical finance. More precisely, the existence of in the general case gives an answer to a problem stated by Madan, Roynette and Yor, in a paper about the link between the Black–Scholes formula and the last passage times of some particular submartingales. Moreover, the equality defining still holds if the fixed time is replaced by any bounded stopping time. This generalization can be considered as an extension of Doob’s optional stopping theorem. [Copyright &y& Elsevier]

Abstract: We consider the following on-line decision problem. The vertices of a realization of the random graph are being observed one by one by a selector. At time , the selector examines the th vertex and knows the graph induced by the vertices that have already been examined. The selector’s aim is to choose the currently examined vertex maximizing the probability that this vertex has full degree, i.e. it is connected to all other vertices in the graph. An optimal algorithm for such a choice (in other words, optimal stopping time) is given. We show that it is of a threshold type and we find the threshold and its asymptotic estimation. [Copyright &y& Elsevier]

Abstract: A dispensing system is used in a materials-mixing plant to provide accurate blend ratios in producing the desired end-use product. The AIS-based (Artificial Immune Systems) fine tuning of dispensing parameters is proposed by optimizing the components of dispensing time and stopping time delay to obtain constant and accurate reading from the precision balance scale. Based on the new dispensing sequence, experimental tests had been carried out using different materials with varying viscosities. The results indicate that the combination of both PWM and AIS techniques would minimize overshoot while exhibiting lower steady-state error and faster response time. These are important in order to overcome the limitations of the conventional volumetric dispensing and manual parameter tuning presently applied in the dispensing system used in the coatings industry. [Copyright &y& Elsevier]

Abstract: A simple parameterisation is introduced which represents the insurance market’s response to an insurer adopting a pricing strategy determined via optimal control theory. Claims are modelled using a lognormally distributed mean claim size rate, and the market average premium is determined via the expected value principle. If the insurer maximises its expected wealth then the resulting Bellman equation has a moving boundary in state space that determines when it is optimal to stop selling insurance. This stochastic optimisation problem is simplified by the introduction of a stopping time that prevents an insurer leaving and then re-entering the insurance market. Three finite difference schemes are used to verify the existence of a solution to the resulting Bellman equation when there is market reaction. All of the schemes use a front-fixing transformation. If the market reacts, then it is found that the optimal strategy is altered, in that premiums are raised if the strategy is of loss-leading type and lowered if it is optimal for the insurer to set a relatively high premium and sell little insurance. [Copyright &y& Elsevier]

Abstract: In this article, we consider the properties of hitting times for -martingales and the stopped processes. We prove that the stopped processes for -martingales are still -martingales and that the hitting times for a class of -martingales including one-dimensional -Brownian motion are quasi-continuous. As an application, we improve the -martingale representation theorems of . [Copyright &y& Elsevier]

Abstract: Models of random spatial permutations arise in the study of Bose-Einstein condensation. Namely, permutations of sites occur with probabilities depending on lengths of permutation jumps, as well as on interactions between jumps. Below a critical temperature, one observes the onset of long permutation cycles in spite of short individual jump lengths. We have devised several Markov chain Monte Carlo algorithms for sampling from this probability distribution. In this note, we present one particularly promising technique: a worm algorithm. It admits an elegant correctness theory. However, it suffers from a stopping-time problem: the CPU time needed to complete a sweep is strongly quadratic in the number of lattice points N. [ABSTRACT FROM AUTHOR]

Abstract: We consider the following online decision problem. The vertices of a directed path are being observed one by one in some random order by a selector. At time the selector examines the th vertex and knows the graph induced by the vertices that have already been examined. The selector’s aim is to choose the currently examined vertex maximizing the probability that it belongs to some prescribed subset of vertices. The optimal stopping time for a subset consisting of the two top vertices is given. For the path of cardinality the numerical approximation of the probability of the right choice according to the optimal algorithm is given. [Copyright &y& Elsevier]

Abstract: Introducing a surrender option in unit-linked life insurance contracts leads to a dependence between the surrender time and the financial market. [J. Barbarin, Risk minimizing strategies for life insurance contracts with surrender option, Tech. rep., University of Louvain-La-Neuve, 2007] used a lot of concepts from credit risk to describe the surrender time in order to hedge such types of contracts. The basic assumption made by Barbarin is that the surrender time is not a stopping time with respect to the financial market. The goal of this article is to make the hedging strategies more explicit by introducing concrete processes for the risky asset and by restricting the hazard process to an absolutely continuous process. First, we assume that the risky asset follows a geometric Brownian motion. This extends the theory of [T. Møller, Risk-minimizing hedging strategies for insurance payment processes, Finance and Stochastics 5 (2001) 419–446], in that the random times of payment are not independent of the financial market. Second, the risky asset follows a Lévy process. For both cases, we assume the payment process contains a continuous payment stream until surrender or maturity and a payment at surrender or at maturity, whichever comes first. [Copyright &y& Elsevier]