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In this paper we study the possibilities of sharing profit in combinatorial procurement auctions and exchanges. Bundles of heterogeneous items are offered by the sellers, and the buyers can then place bundle bids on sets of these items. That way, both sellers and buyers can express synergies between items and avoid the well-known risk of exposure (see, e.g., [3]). The reassignment of items to participants is known as the Winner Determination Problem (WDP). We propose solving the WDP by using a Set Covering formulation, because profits are potentially higher than with the usual Set Partitioning formulation, and subsidies are unnecessary. The achieved benefit is then to be distributed amongst the participants of the auction, a process which is known as profit sharing. The literature on profit sharing provides various desirable criteria. We focus on three main properties we would like to guarantee: Budget balance, meaning that no more money is distributed than profit was generated, individual rationality, which guarantees to each player that participation does not lead to a loss, and the core property, which provides every subcoalition with enough money to keep them from separating. We characterize all profit sharing schemes that satisfy these three conditions by a monetary flow network and state necessary conditions on the solution of the WDP for the existence of such a profit sharing. Finally, we establish a connection to the famous VCG payment scheme [2, 8, 19], and the Shapley Value [17].

We introduce a refined tree method to compute option prices using the stochastic volatility model of Heston. In a first step, we model the stock and variance process as two separate trees and with transition probabilities obtained by matching tree moments up to order two against the Heston model ones. The correlation between the driving Brownian motions in the Heston model is then incorporated by the node-wise adjustment of the probabilities. This adjustment, leaving the marginals fixed, optimizes the match between tree and model correlation. In some nodes, we are even able to further match moments of higher order. Numerically this gives convergence orders faster than 1/N, where N is the number of dis- cretization steps. Accuracy of our method is checked for European option prices against a semi closed-form, and our prices for both European and American options are compared to alternative approaches.

In this paper we deal with dierent statistical modeling of real world accident data in order to quantify the eectiveness of a safety function or a safety conguration (meaning a specic combination of safety functions) in vehicles. It is shown that the eectiveness can be estimated along the so-called relative risk, even if the eectiveness does depend on a confounding variable which may be categorical or continuous. For doing so a concrete statistical modeling is not necessary, that is the resulting estimate is of nonparametric nature. In a second step the quite usual and from a statistical point of view classical logistic regression modeling is investigated. Main emphasis has been laid on the understanding of the model and the interpretation of the occurring parameters. It is shown that the eectiveness of the safety function also can be detected via such a logistic approach and that relevant confounding variables can and should be taken into account. The interpretation of the parameters related to the confounder and the quantication of the in uence of the confounder is shown to be rather problematic. All the theoretical results are illuminated by numerical data examples.

This report describes the calibration and completion of the volatility cube in the SABR model. The description is based on a project done for Assenagon GmbH in Munich. However, we use fictitious market data which resembles realistic market data. The problem posed by our client is formulated in section 1. Here we also motivate why this is a relevant problem. The SABR model is briefly reviewed in section 2. Section 3 discusses the calibration and completion of the volatility cube. An example is presented in section 4. We conclude by suggesting possible future research in section 5.

In this article, a new model predictive control approach to nonlinear stochastic systems will be presented. The new approach is based on particle filters, which are usually used for estimating states or parameters. Here, two particle filters will be combined, the first one giving an estimate for the actual state based on the actual output of the system; the second one gives an estimate of a control input for the system. This is basically done by adopting the basic model predictive control strategies for the second particle filter. Later in this paper, this new approach is applied to a CSTR (continuous stirred-tank reactor) example and to the inverted pendulum.

The modelling of hedge funds poses a difficult problem since the available reported data sets are often small and incomplete. We propose a switching regression model for hedge funds, in which the coefficients are able to switch between different regimes. The coefficients are governed by a Markov chain in discrete time. The different states of the Markov chain represent different states of the economy, which influence the performance of the independent variables. Hedge fund indices are chosen as regressors. The parameter estimation for the switching parameter as well as for the switching error term is done through a filtering technique for hidden Markov models developed by Elliott (1994). Recursive parameter estimates are calculated through a filter-based EM-algorithm, which uses the hidden information of the underlying Markov chain. Our switching regression model is applied on hedge fund series and hedge fund indices from the HFR database.

In this paper a three dimensional stochastic model for the lay-down of fibers on a moving conveyor belt in the production process of nonwoven materials is derived. The model is based on stochastic diferential equations describing the resulting position of the fiber on the belt under the influence of turbulent air ows. The model presented here is an extension of an existing surrogate model, see [6, 3].

The optimal design of rotational production processes for glass wool manufacturing poses severe computational challenges to mathematicians, natural scientists and engineers. In this paper we focus exclusively on the spinning regime where thousands of viscous thermal glass jets are formed by fast air streams. Homogeneity and slenderness of the spun fibers are the quality features of the final fabric. Their prediction requires the computation of the fuidber-interactions which involves the solving of a complex three-dimensional multiphase problem with appropriate interface conditions. But this is practically impossible due to the needed high resolution and adaptive grid refinement. Therefore, we propose an asymptotic coupling concept. Treating the glass jets as viscous thermal Cosserat rods, we tackle the multiscale problem by help of momentum (drag) and heat exchange models that are derived on basis of slender-body theory and homogenization. A weak iterative coupling algorithm that is based on the combination of commercial software and self-implemented code for ow and rod solvers, respectively, makes then the simulation of the industrial process possible. For the boundary value problem of the rod we particularly suggest an adapted collocation-continuation method. Consequently, this work establishes a promising basis for future optimization strategies.

The scope of this paper is to enhance the model for the own-company stockholder (given in Desmettre, Gould and Szimayer (2010)), who can voluntarily performance-link his personal wealth to his management success by acquiring stocks in the own-company whose value he can directly influence via spending work effort. The executive is thereby characterized by a parameter of risk aversion and the two work effectiveness parameters inverse work productivity and disutility stress. We extend the model to a constant absolute risk aversion framework using an exponential utility/disutility set-up. A closed-form solution is given for the optimal work effort an executive will apply and we derive the optimal investment strategies of the executive. Furthermore, we determine an up-front fair cash compensation applying an indifference utility rationale. Our study shows to a large extent that the results previously obtained are robust under the choice of the utility/disutility set-up.

We will present a rigorous derivation of the equations and interface conditions for ion, charge and heat transport in Li-ion insertion batteries. The derivation is based exclusively on universally accepted principles of nonequilibrium thermodynamics and the assumption of a one step intercalation reaction at the interface of electrolyte and active particles. Without loss of generality the transport in the active particle is assumed to be isotropic. The electrolyte is described as a fully dissociated salt in a neutral solvent. The presented theory is valid for transport on a spatial scale for which local charge neutrality holds i.e. beyond the scale of the diffuse double layer. Charge neutrality is explicitely used to determine the correct set of thermodynamically independent variables. The theory guarantees strictly positive entropy production. The various contributions to the Peltier coeficients for the interface between the active particles and the electrolyte as well as the contributions to the heat of mixing are obtained as a result of the theory.

Simulation of multibody systems (mbs) is an inherent part in developing and design of complex mechanical systems. Moreover, simulation during operation gained in importance in the recent years, e.g. for HIL-, MIL- or monitoring applications. In this paper we discuss the numerical simulation of multibody systems on different platforms. The main section of this paper deals with the simulation of an established truck model [9] on different platforms, one microcontroller and two real-time processor boards. Additional to numerical C-code the latter platforms provide the possibility to build the model with a commercial mbs tool, which is also investigated. A survey of different ways of generating code and equations of mbs models is given and discussed concerning handling, possible limitations as well as performance. The presented benchmarks are processed under terms of on-board real time applications. A further important restriction, caused by the real-time requirement, is a fixed integration step size. Whence, carefully chosen numerical integration algorithms are necessary, especially in the case of closed loops in the model. We investigate linearly-implicit time integration methods with fixed step size, so-called Rosenbrock methods, and compare them with respect to their accuracy and performance on the tested processors.

This work deals with the modeling and simulation of slender viscous jets exposed to gravity and rotation, as they occur in rotational spinning processes. In terms of slender-body theory we show the asymptotic reduction of a viscous Cosserat rod to a string system for vanishing slenderness parameter. We propose two string models, i.e. inertial and viscous-inertial string models, that differ in the closure conditions and hence yield a boundary value problem and an interface problem, respectively. We investigate the existence regimes of the string models in the four-parametric space of Froude, Rossby, Reynolds numbers and jet length. The convergence regimes where the respective string solution is the asymptotic limit to the rod turn out to be disjoint and to cover nearly the whole parameter space. We explore the transition hyperplane and derive analytically low and high Reynolds number limits. Numerical studies of the stationary jet behavior for different parameter ranges complete the work.

Numerical modeling of electrochemical process in Li-Ion battery is an emerging topic of great practical interest. In this work we present a Finite Volume discretization of electrochemical diffusive processes occurring during the operation of Li-Ion batteries. The system of equations is a nonlinear, time-dependent diffusive system, coupling the Li concentration and the electric potential. The system is formulated at length-scale at which two different types of domains are distinguished, one for the electrolyte and one for the active solid particles in the electrode. The domains can be of highly irregular shape, with electrolyte occupying the pore space of a porous electrode. The material parameters in each domain differ by several orders of magnitude and can be non-linear functions of Li ions concentration and/or the electrical potential. Moreover, special interface conditions are imposed at the boundary separating the electrolyte from the active solid particles. The field variables are discontinuous across such an interface and the coupling is highly non- linear, rendering direct iteration methods ineffective for such problems. We formulate a Newton iteration for an purely implicit Finite Volume discretization of the coupled system. A series of numerical examples are presented for different type of electrolyte/electrode configurations and material parameters. The convergence of the Newton method is characterized both as function of nonlinear material parameters as well as the nonlinearity in the interface conditions.

Modeling of species and charge transport in Li-Ion Batteries based on non-equilibrium thermodynamics
(2010)

In order to improve the design of Li ion batteries the complex interplay of various physical phenomena in the active particles of the electrodes and in the electrolyte has to be balanced. The separate transport phenomena in the electrolyte and in the active particle as well as their coupling due to the electrochemical reactions at the interfaces between the electrode particles and the electrolyte will inuence the performance and the lifetime of a battery. Any modeling of the complex phenomena during the usage of a battery has therefore to be based on sound physical and chemical principles in order to allow for reliable predictions for the response of the battery to changing load conditions. We will present a modeling approach for the transport processes in the electrolyte and the electrodesbased on non-equilibrium thermodynamics and transport theory. The assumption of local charge neutrality, which is known to be valid in concentrated electrolytes, is explicitly used to identify the independent thermodynamic variables and uxes. The theory guarantees strictly positive entropy production. Dierences to other theories will be discussed.

This paper discusses a numerical subgrid resolution approach for solving the Stokes-Brinkman system of equations, which is describing coupled ow in plain and in highly porous media. Various scientic and industrial problems are described by this system, and often the geometry and/or the permeability vary on several scales. A particular target is the process of oil ltration. In many complicated lters, the lter medium or the lter element geometry are too ne to be resolved by a feasible computational grid. The subgrid approach presented in the paper is aimed at describing how these ne details are accounted for by solving auxiliary problems in appropriately chosen grid cells on a relatively coarse computational grid. This is done via a systematic and a careful procedure of modifying and updating the coecients of the Stokes-Brinkman system in chosen cells. This numerical subgrid approach is motivated from one side from homogenization theory, from which we borrow the formulations for the so called cell problem, and from the other side from the numerical upscaling approaches, such as Multiscale Finite Volume, Multiscale Finite Element, etc. Results on the algorithm's eciency, both in terms of computational time and memory usage, are presented. Comparison with solutions on full ne grid (when possible) are presented in order to evaluate the accuracy. Advantages and limitations of the considered subgrid approach are discussed.

We consider a highly-qualified individual with respect to her choice between two distinct career paths. She can choose between a mid-level management position in a large company and an executive position within a smaller listed company with the possibility to directly affect the company’s share price. She invests in the financial market includ- ing the share of the smaller listed company. The utility maximizing strategy from consumption, investment, and work effort is derived in closed form for logarithmic utility. The power utility case is discussed as well. Conditions for the individual to pursue her career with the smaller listed company are obtained. The participation constraint is formulated in terms of the salary differential between the two posi- tions. The smaller listed company can offer less salary. The salary shortfall is offset by the possibility to benefit from her work effort by acquiring own-company shares. This gives insight into aspects of optimal contract design. Our framework is applicable to the pharma- ceutical and financial industry, and the IT sector.

We present a two-scale finite element method for solving Brinkman’s and Darcy’s equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes’ equations byWang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy’s equations. In order to reduce the “resonance error” and to ensure convergence to the global fine solution the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems.

This work deals with the optimal control of a free surface Stokes flow which responds to an applied outer pressure. Typical applications are fiber spinning or thin film manufacturing. We present and discuss two adjoint-based optimization approaches that differ in the treatment of the free boundary as either state or control variable. In both cases the free boundary is modeled as the graph of a function. The PDE-constrained optimization problems are numerically solved by the BFGS method, where the gradient of the reduced cost function is expressed in terms of adjoint variables. Numerical results for both strategies are finally compared with respect to accuracy and efficiency.

We present some optimality results for robust Kalman filtering. To this end, we introduce the general setup of state space models which will not be limited to a Euclidean or time-discrete framework. We pose the problem of state reconstruction and repeat the classical existing algorithms in this context. We then extend the ideal-model setup allowing for outliers which in this context may be system-endogenous or -exogenous, inducing the somewhat conflicting goals of tracking and attenuation. In quite a general framework, we solve corresponding minimax MSE-problems for both types of outliers separately, resulting in saddle-points consisting of an optimally-robust procedure and a corresponding least favorable outlier situation. Still insisting on recursivity, we obtain an operational solution, the rLS filter and variants of it. Exactly robust-optimal filters would need knowledge of certain hard-to-compute conditional means in the ideal model; things would be much easier if these conditional means were linear. Hence, it is important to quantify the deviation of the exact conditional mean from linearity. We obtain a somewhat surprising characterization of linearity for the conditional expectation in this setting. Combining both optimal filter types (for system-endogenous and -exogenous situation) we come up with a delayed hybrid filter which is able to treat both types of outliers simultaneously. Keywords: robustness, Kalman Filter, innovation outlier, additive outlier

A number of water flow problems in porous media are modelled by Richards’ equation [1]. There exist a lot of different applications of this model. We are concerned with the simulation of the pressing section of a paper machine. This part of the industrial process provides the dewatering of the paper layer by the use of clothings, i.e. press felts, which absorb the water during pressing [2]. A system of nips are formed in the simplest case by rolls, which increase sheet dryness by pressing against each other (see Figure 1). A lot of theoretical studies were done for Richards’ equation (see [3], [4] and references therein). Most articles consider the case of x-independent coefficients. This simplifies the system considerably since, after Kirchhoff’s transformation of the problem, the elliptic operator becomes linear. In our case this condition is not satisfied and we have to consider nonlinear operator of second order. Moreover, all these articles are concerned with the nonstationary problem, while we are interested in the stationary case. Due to complexity of the physical process our problem has a specific feature. An additional convective term appears in our model because the porous media moves with the constant velocity through the pressing rolls. This term is zero in immobile porous media. We are not aware of papers, which deal with such kind of modified steady Richards’ problem. The goal of this paper is to obtain the stability results, to show the existence of a solution to the discrete problem, to prove the convergence of the approximate solution to the weak solution of the modified steady Richards’ equation, which describes the transport processes in the pressing section. In Section 2 we present the model which we consider. In Section 3 a numerical scheme obtained by the finite volume method is given. The main part of this paper is theoretical studies, which are given in Section 4. Section 5 presents a numerical experiment. The conclusion of this work is given in Section 6.