Nanocrystalline molybdenum oxide (α-MoO3) thin films with iso-oriented crystalline layers were synthesised by the anodisation of Mo foils. Upon band-gap excitation using light illumination, α-MoO3 generates excited electrons for reductive reactions and stores some of the excited electrons in its layered crystalline structure via alkali cation intercalation. These stored electrons can be subsequently discharged from α-MoO3 to allow reductive reactions to continue to occur under non-illuminated conditions. The modulation of water concentrations in the organic/aqueous anodisation electrolytes readily produces α-MoO3 crystals with high degree of (kk0) crystallographic orientation. Moreover, these (kk0)-oriented MoO3 crystals exhibit well-developed {hk0} and {0k0} crystal facets. In this paper, we show the benefits of producing α-MoO3 thin films with defined crystal facets and an iso-oriented layered structure for in situ storing of excited charges. α-MoO3 crystals with dominant (kk0) planes can achieve fast charging and a strong balance between charge release for immediate exploitation under illuminated conditions and charge storage for subsequent utilisation in dark. In comparison, α-MoO3 crystals with dominant (0k0) planes show a preference for excited charge storage.

Abstract. Optimal control problems of switching type with linear state dynamics are ubiquitous in applications of stochastic optimization. For high-dimensional problems of this type, solutions which utilize some convexity related properties are useful. For such problems, we present novel algorithmic solutions which require minimal assumptions while demonstrating remarkable computational efficiency. Furthermore, we devise procedures of the primal-dual kind to assess the distance to optimality of these approximate solutions.Key words. optimal control, American options, pathwise stochastic control, duality DOI. 10.1137/S0040585X97T9879101. Introduction. When making decisions under uncertainty, the major difficulty is to determine how to update estimates and decisions in order to achieve optimality over a given time period. These kinds of questions are often framed within the realm of Markov decision theory, which can be viewed as discrete-time optimal stochastic control.The theoretical underpinnings of Markov decision theory are now well understood. Rigorous mathematical treatments are available in textbook form (see [2], [4], [12], and [23]). However, practical applications remain persistently challenging despite the rich arsenal of theoretical tools that are currently available. In this context, approximate dynamic programming (see [22]) grew from attempts to provide simultaneously practically implementable heuristics and theoretical insights as to why they perform well in practice.In order to control a large system, a practical approach to dealing with the high dimensionality of the state space is to first achieve a finite discretization of it. Alternatively, one can rely on an efficient approximation of functions on this space. In this spirit, function-based methods suggest approximating value functions on the state space. One such method is the least squares Monte Carlo approach, which suggests an approximation by a suitably parameterized set of basis functions. As these parameters are computed by performing successive regressions, this method is placed within the regression-based method family.Following [7], [28], [29], the contribution [18] became the source of subsequent research focused on its theoretical justification. Convergence issues are addressed in [8] and later generalized in [27], [9], and [10], and extensions to multiple exercise rights were considered in [6] and studied in [3], where the connection to statistical learning theory and the theory of empirical processes is emphasized. For an overview of the applications of Monte Carlo methods in financial engineering, we refer the interested reader to Glasserman's book [13] and to the literature cited therein. Beyond financial applications, function approximation methods have also been used to capture local behavior of value functions, and advanced regression methods; e.g., kernel methods [20],

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Для задач оптимального управления переключающегося типа с линейной динамикой состояния представлен новый алгоритмический метод построения решения, который требует минимальных предположений, связанных с выпуклостью, демонстрируя при этом отличную вычислительную эффективность, в том числе, на задачах большой размерности. Кроме того, разработаны прямые двойственные процедуры для оценки расстояния от построенных приближенных решений до оптимальных. Ключевые слова и фразы: оптимальное управление, американские опционы, потраекторное управление, дуальность.

Optimal control problems of stochastic switching type appear frequently when making decisions under uncertainty and are notoriously challenging from a computational viewpoint. Although numerous approaches have been suggested in the literature to tackle them, typical real-world applications are inherently high dimensional and usually drive common algorithms to their computational limits. Furthermore, even when numerical approximations of the optimal strategy are obtained, practitioners must apply time-consuming and unreliable Monte Carlo simulations to assess their quality. In this paper, we show how one can overcome both difficulties for a specific class of discrete-time stochastic control problems. A simple and efficient algorithm which yields approximate numerical solutions is presented and methods to perform diagnostics are provided.