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  • Gustavsson, Thomas, 1951- (författare)
  • No Arbitrage Pricing and the Term Structure of Interest Rates
  • 1992
  • Licentiatavhandling (övrigt vetenskapligt)abstract
    • This dissertation provides an introduction to the concept of no arbitrage pricing and probability measures. In complete markets prices are arbitrage-free if and only if there exists an equivalent probability measure under which all asset prices are martingales. This is only a slight generalization of the classical fair game hypothesis. The most important limitation of this approach is the requirement of free and public information. Also in order to apply the martingale representation theorem we have to limit our attention to stochastic processes that are generated by Wiener or Poisson processes. While this excludes branching it does include diusion processes with stochastic variances.The result is a non-linear arbitrage pricing theory for nancial assets in general and for bonds in particular. Discounting of future cash ows is performed with zero coupon bonds as well as with short term interest rates (roll-over). In the presence of bonds discounting is an ambiguous operation unless an explicit intertemporal numeraire is dened. However, with the proper denitions we can dispense with the traditional expectations hypothesis about the term structure of interest rates. Arbitrage-free bond prices can be found simply from the fact that these are assets with a nite life and a xed redemption value. 
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  • Jeppsson, Ulf (författare)
  • On the Verifiability of the Activated Sludge System Dynamics
  • 1993
  • Licentiatavhandling (övrigt vetenskapligt)abstract
    • Wastewater treatment processes are inherently dynamic because of variations in the influent flow rate, concentration, and composition. The adaptive behaviour of the microorganisms further emphasizes this fact. Mathematical models and computer simulations are essential to describe, predict, and control the complicated interactions of the processes. Any attempt to model all details of the various reaction mechanisms are, however, destined to fail due to lacking knowledge and the extreme complexity required for such models. A reduced order dynamic model for an activated sludge process performing carbonaceous removal, nitrification, and denitrification is presented herein. The identifiability of the model is investigated using both off-line and on-line methods and its dynamic behaviour is verified against simulations of a recognized model - the IAWPRC Activated Sludge Model No. 1. The required data for the identification algorithms is based on directly measurable real time data. The simplified model may serve as a tool for predicting the dynamic behaviour of an activated sludge process since the parameters under varying operating conditions can be tracked on-line. The model is aimed for operation and control purposes as an integral part of a hierarchical control structure.
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  • Landelius, Tomas (författare)
  • Behavior Representation by Growing a Learning Tree
  • 1993
  • Licentiatavhandling (övrigt vetenskapligt)abstract
    • The work presented in this thesis is based on the basic idea of learning by reinforcement, within the theory of behaviorism. The reason for this choice is the generality of such an approach, especially that the reinforcement learning paradigm allows systems to be designed which can improve their behavior beyond that of their teacher. The role of the teacher is to define the reinforcement function, which acts as a description of the problem the machine is to solve.Learning is considered to be a bootstrapping procedure. Fragmented past experience, of what to do when performing well, is used for response generation. The new response, in its turn, adds more information to the system about the environment. Gained knowledge is represented by a behavior probability density function. This density function is approximated with a number of normal distributions which are stored in the nodes of a binary tree. The tree structure is grown by applying a recursive algorithm to the stored stimuli-response combinations, called decisions. By considering both the response and the stimulus, the system is able to bring meaning to structures in the input signal. The recursive algorithm is first applied to the whole set of stored decisions. A mean decision vector and a covariance matrix are calculated and stored in the root node. The decision space is then partitioned into two halves across the direction of maximal data variation. This procedure is now repeated recursively for each of the two halves of the decision space, forming a binary tree with mean vectors and covariance matrices in its nodes.The tree is the system's guide to response generation. Given a stimulus, the system searches for responses likely to result in highly reinforced decisions. This is accomplished by treating the sum of the normal distributions in the leaves as distribution describing the behavior of the system. The sum of normal distributions, with the current stimulus held fixed, is finally used for random generation of the response.This procedure makes it possible for the system to have several equally plausible responses to one stimulus. Not applying maximum likelihood principles will make the system more explorative and reduce its risk of being trapped in local minima.The performance and complexity of the learning tree is investigated and compared to some well known alternative methods. Presented are also some simple, yet principally important, experiments verifying the behavior of the proposed algorithm.
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  • Lindfors, Thomas (författare)
  • Underlagstak
  • 1994
  • Licentiatavhandling (övrigt vetenskapligt)
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