Computation of efficient solutions of discretely distributed stochastic optimization problems

In engineering and economics often a certain vectorx of inputs or decisions must be chosen, subject to some constraints, such that the expected costs (or loss) arising from the deviation between the outputA() x of a stochastic linear systemxA()x and a desired stochastic target vectorb() are minimal. Hence, one has the following stochastic linear optimization problem minimizeF(x)=Eu(A()x b()) s.t.xD, (1) whereu is a convex loss function on ^m , (A(), b()) is a random (m,n + 1)-matrix, E denotes the expectation operator andD is a convex subset of ⁿ . Concrete problems of this type are e.g. stochastic linear programs with recourse, error minimization and optimal design problems, acid rain abatement methods, problems in scenario analysis and non-least square regression analysis.Solving (1), the loss functionu should be exactly known. However, in practice mostly there is some uncertainty in assigning appropriate penalty costs to the deviation between the outputA ()x and the targetb(). For finding in this situation solutions hedging against uncertainty a set of so-called efficient points of (1) is defined and a numerical procedure for determining these compromise solutions is derived. Several applications are discussed.     

A chlorinated non-fullerene acceptor for efficient polymer solar cells

Improving the performance and reducing the manufacturing costs are the main directions for the development of organic solar cells in the future. Here, the strategy that uses chemical structure modification to optimize the photoelectric properties is reported. A new narrow bandgap (1.30 eV) chlorinated non-fullerene electron acceptor (Y15), based on benzo[d][1,2,3] triazole with two 3-undecyl-thieno[2′,3′:4,5] thieno[3,2-b] pyrrole fused -7-heterocyclic ring, with absorption edge extending to the near-infrared (NIR) region, namely A-DA'D-A type structure, is designed and synthesized. Its electrochemical and optoelectronic properties are systematically investigated. Benefitting from its NIR light harvesting, the fabricated photovoltaic devices based on Y15 deliver a high power conversion efficiency (PCE) of 14.13%, when blending with a wide bandgap polymer donor PM6. Our results show that the A-DA'D-A type molecular design and application of near-infrared electron acceptors have the potential to further improve the PCE of polymer solar cells (PSCs).     

Martingales, detrending data, and the efficient market hypothesis

We discuss martingales, detrending data, and the efficient market hypothesis (EMH) for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that martingale stochastic processes generate uncorrelated, generally non-stationary increments. Generally, a test for a martingale is therefore a test for uncorrelated increments. A detrended process with an x-dependent drift coefficient is generally not a martingale, and so we extend our analysis to include the class of (x,t)-dependent drift coefficients of interest in finance. We explain why martingales look Markovian at the level of both simple averages and 2-point correlations. And while a Markovian market has no memory to exploit and presumably cannot be beaten systematically, it has never been shown that martingale memory cannot be exploited in 3-point or higher correlations to beat the market. We generalize our Markov scaling solutions presented earlier, and also generalize the martingale formulation of the EMH to include (x,t)-dependent drift in log returns. We also use the analysis of this paper to correct a misstatement of the ‘fair game’ condition in terms of serial correlations in Fama's paper on the EMH. We end with a discussion of Levy's characterization of Brownian motion and prove that an arbitrary martingale is topologically inequivalent to a Wiener process.     

Estimating the efficient price from the order flow: A Brownian Cox process approach

At the ultra high frequency level, the notion of price of an asset is very ambiguous. Indeed, many different prices can be defined (last traded price, best bid price, mid price, etc.). Thus, in practice, market participants face the problem of choosing a price when implementing their strategies. In this work, we propose a notion of efficient price which seems relevant in practice. Furthermore, we provide a statistical methodology enabling to estimate this price from the order flow.     

Theories of rings with divisibility

We consider several different theories of commutative rings with a new predicate symbol | together with the additional axiom a|b ? ?c (a . c = b) and show that none of these has a model companion.     

Efficient pricing of commodity options with early-exercise under the Ornstein-Uhlenbeck process

We analyze the efficiency properties of a numerical pricing method based on Fourier-cosine expansions for early-exercise options. We focus on variants of Schwartz? model based on a mean reverting Ornstein-Uhlenbeck process, which is commonly used for modeling commodity prices. This process however does not possess favorable properties for the option pricing method of interest. We therefore propose an approximation of its characteristic function, so that the Fast Fourier Transform can be applied for highest efficiency.     

ON THE PROJECTION OF THE EFFICIENT SET AND POTENTIAL APPLICATIONS

Abstract

We study the efficient set X _E for a multiple objective linear program by using its projection into the linear space L spanned by the independent criteria. We show that in the orthogonally complementary space of L, the efficient points form a polyhedron, while in L an efficiency-equivalent polyhedron for the projection P(X _E ) of X _E can be constructed by algorithms of outer and inner approximation types. These algorithms can be also used for generating all extreme points of P(X _E ). Application to optimization over the efficient set for a multiple objective linear program is considered.     

Safety and waste considerations in donated blood screening

We study an important problem faced by Blood Centers, of selecting screening tests for donated blood to reduce the risk of “transfusion-transmitted infectious diseases” (TTIs), including the human immunodeficiency virus (HIV), hepatitis viruses, human T-cell lymphotropic virus, syphilis, West Nile Virus, and Chagas’ Disease. This decision has a significant impact on health care quality in both developed and developing countries. The budget-constrained decision-maker needs to construct a portfolio of screening tests, from a set of available tests, each with given efficacy (sensitivity and specificity) and cost, to administer to each unit of donated blood so as to minimize the “risk” of a TTI for blood classified as “infection-free.” While doing this, it is critical, for a viable blood system, that the decision-maker does not falsely (i.e., through screening error) discard too much of the infection-free blood (“waste”). We construct mathematical models of this decision problem, considering the various objective functions (minimization of the TTI risk or the weighted TTI risk) and various constraints (on budget and wasted blood) relevant in practice. Our work generates insights on the test selection problem. We show, for example, that a reduction in risk does not necessarily come at the expense of an increase in waste. This underscores the importance of considering these different metrics in decision-making through an optimization-based model. Our work also highlights the importance of generating region-specific testing schemes that explicitly take into account the regional prevalence and co-infection rates, along with the impacts of the infections on the society and individuals.     

Organization and efficiency in the international insurance industry: A cross-frontier analysis

This paper employs cross-frontier analysis, an innovative tool based on data envelopment analysis, to provide new insight into the relationship between organization and efficiency in international insurance markets. We are the first to empirically test the expense preference hypothesis and the efficient structure hypothesis in a large cross-country study. For this purpose, we consider 23,807 firm-years for 21 countries from northern America and the European Union—a dataset not previously analyzed in this context. We find evidence for the efficient structure hypothesis in selected market segments, but we find no evidence for the expense preference hypothesis. Our results provide insight into the competitiveness of stock and mutual insurers from different countries. At the country level, the results can be used to compare different insurance markets. Our findings are especially interesting for the strategic management of insurance companies as well as for regulators and boards of national insurance associations.     

Efficient computation for dynamic responses of systems with time-varying characteristics

Based on Neumman series and epsilon-algorithm, an efficient computation for dynamic responses of systems with arbitrary time-varying characteristics is investigated. Avoiding the calculation for the inverses of the equivalent stiffness matrices in each time step, the computation effort of the proposed method is reduced compared with the full analysis of Newmark method. The validity and applications of the proposed method are illustrated by a 4-DOF spring-mass system with periodical time-varying stiffness properties and a truss structure with arbitrary time-varying lumped mass. It shows that good approximate results can be obtained by the proposed method compared with the responses obtained by the full analysis of Newmark method.