Using acoustic emission methods to monitor cement composites during setting and hardening

Cement-based composites belong among the basic building materials used in civil engineering. Their properties are given not only by their composition but also by their behaviour after mixing as well as by the methods of curing. Monitoring the processes and phenomena during the early stages of setting is vital for determining the resulting properties and durability. The acoustic emission method is a unique non-destructive method that can detect structural changes as a cement-based composite is setting. It can also detect the onset and growth of cracks during the service life of a cement-based composite since the moment it has been mixed. The paper discusses the use of the acoustic emission method with focus on the early stage of the lifespan of a cement-based composite including the measures necessary for its use and description of the parameters of acoustic emission signals

Neparametrické modely finančních časových řad

In this diploma thesis we study basic models of time series, both parametric and nonparametric, and their basic properties. In the first part several conditional homoscedastic models are examined and the basic estimation methods are explained. Afterwards, we continue with conditional heteroscedastic models. We explain the reasons why are these models suitable to analyze financial time series. We state and prove the conditions for the strict stationarity of GARCH and calculate the mean square error (MSE) of prediction in GARCH(1,1). Eventually, the robustness of the least absolute deviation (LAD) method for GARCH is discussed and supported by numerical results. At the end of this thesis we discuss methods for nonparametric GARCH(1,1) estimation.Department of Probability and Mathematical StatisticsKatedra pravděpodobnosti a matematické statistikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Essays on risk exchanges within a collective

This thesis considers a group of investors who have joined their endowments and formed a collective. The collective is assumed to construct an internal (intra-group) market where its members can exchange assets (trade) under conditions that can be different to those that prevail outside of the collective. Two chapters of this thesis focus on the intra-group trades that are both financially fair and Pareto efficient. There are formulated conditions under which there exists a unique set of financially fair and Pareto efficient intra-group trades (redistribution). The results of these chapters were published in Journal of Mathematical Economics and in Insurance: Mathematics and Economics. The last chapter considers a collective in a setting where there are bid-ask spreads on an extra-group market and the collective is free to use its intra-group market. In this setting, we define an equilibrium similar to the competitive equilibria, and we investigate under which bid-ask spreads is the intra-group market superuous or, to the contrary, when the intra-group market can accommodate all equilibrium trades. The chapter also proposes a measure of tendency to trade internally” and offers a link with the term “group heterogeneity”

Nonparametric models of financial time series

In this diploma thesis we study basic models of time series, both parametric and nonparametric, and their basic properties. In the first part several conditional homoscedastic models are examined and the basic estimation methods are explained. Afterwards, we continue with conditional heteroscedastic models. We explain the reasons why are these models suitable to analyze financial time series. We state and prove the conditions for the strict stationarity of GARCH and calculate the mean square error (MSE) of prediction in GARCH(1,1). Eventually, the robustness of the least absolute deviation (LAD) method for GARCH is discussed and supported by numerical results. At the end of this thesis we discuss methods for nonparametric GARCH(1,1) estimation

Markov Chains and Categorial Data

Katedra pravděpodobnosti a matematické statistikyDepartment of Probability and Mathematical StatisticsMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Intra-group Risk Sharing Under Financial Fairness

We examine intra-group risk sharing under the assumption that prices are given exogenously. Two situations are considered: one in which the entities that constitute the group choose to trade only among each other, and one in which the entities have limited access to the external market. In the first situation we prove that, if agents are expected utility maximizers, there is a unique risk-sharing rule that preserves value according to the exogenous rule and that is Pareto optimal among feasible allocations. This provides an extension of a result by Balasko (1979). In the second situation we give necessary and sufficient conditions for the internal market to be completable in the sense that all agents can reach all positions, subject only to the budget constraint, by combining their own partial access to the external market with internal trades under the given pricing rule

The composite iteration algorithm for finding efficient and financially fair risk-sharing rules

We consider the problem of finding an efficient and fair ex-ante rule for division of an uncertain monetary outcome among a finite number of von Neumann–Morgenstern agents. Efficiency is understood here, as usual, in the sense of Pareto efficiency subject to the feasibility constraint. Fairness is defined as financial fairness with respect to a predetermined pricing functional. We show that efficient and financially fair allocation rules are in one-to-one correspondence with positive eigenvectors of a nonlinear homogeneous and monotone mapping associated to the risk sharing problem. We establish relevant properties of this mapping. On the basis of this, we obtain a proof of existence and uniqueness of solutions via nonlinear Perron–Frobenius theory, as well as a proof of global convergence of the natural iterative algorithm. We argue that this algorithm is computationally attractive, and discuss its rate of convergence

Intra-group Risk Sharing Under Financial Fairness

We examine intra-group risk sharing under the assumption that prices are given exogenously. Two situations are considered: one in which the entities that constitute the group choose to trade only among each other, and one in which the entities have limited access to the external market. In the first situation we prove that, if agents are expected utility maximizers, there is a unique risk-sharing rule that preserves value according to the exogenous rule and that is Pareto optimal among feasible allocations. This provides an extension of a result by Balasko (1979). In the second situation we give necessary and sufficient conditions for the internal market to be completable in the sense that all agents can reach all positions, subject only to the budget constraint, by combining their own partial access to the external market with internal trades under the given pricing rule