Faculty of Science School of Statistics and Actuarial science 9802374m nhuang@glenrandmib.co.za / The purpose of this research report is to review the embedded value concept and to examine its practical use in South Africa. Important recent developments relating to the embedded value concept are discussed and compared with the existing embedded value concept. These developments include fair value accounting, market-consistent embedded value and the European Embedded Value Principle. In the second part of the report, the disclosure of the embedded value information of four major South African life assurance companies is examined. It was found that the market capitalisations of these companies were smaller than their embedded values for most of the period under the investigation. Reasons for this phenomenon are considered and tested against the data available. It was found that the risk discount rates used by some life assurance companies in calculating their embedded values may be too low. It appears that a ‘herding’ tendency exists among South African life assurance companies when selecting risk discount rates for the embedded value calculation. It is suggested that a more market consistent approach for the embedded value calculation and a better disclosure for the embedded value reporting should be considered by life assurance companies in South Africa. This should improve investors’ understanding and confidence in the embedded value disclosed, which in turn should help narrow or eliminate the discount of the market capitalisation to the embedded value observed in the market.

In preparation for, and for decision support during, CBRN (chemical, biological, radiological and nuclear) emergencies it is essential to know how such an event would turn out, so that one can prepare a possible evacuation. Afterwards it might be good to know how to backtrack and see what caused the emergency, and in the case of e.g. a gas leak, where did it begin? The Swedish Defence Research Agency (FOI) develops models for such scenarios. In this thesis FOI's model, "The Nordic Urban Dispersion model" (NUD), has been studied. The system of equations set up by this model was originally solved using Intel's PARDISO solver, which is a direct solver. An evaluation on how an iterative multigrid method would work to solve the system has been done in this thesis. The wind model is a mass-consistent model which sets up a diagnostic initial wind field. The final wind field is later minimized under the constraint of the continuity equation. The minimization problem is solved using Lagrange multipliers and the system turns into a Poisson-like problem. The iterative algebraic multigrid solver (AMG) which has been evaluated had difficulties solving the problem of an asymmetric system matrix generated by NUD. The AMG solver was then tried on a symmetric discrete Poisson problem instead, and the solution turns out to be the same as for the PARDISO solver. A comparison was made between the AMG and PARDISO solver, and for the discrete Poisson case the AMG solver turned out on top for both larger system size and less computational time. To try out the solvers for the original NUD case a modification of the boundary conditions was made to make the system matrix symmetric. This modification turns the problem into a mathematical problem rather than a physical one, as the wind fields generated are not physically correct. For this modified case both the solvers get the same solution in essentially the same computational time. A method of how to in the future solve the original (asymmetric) problem, by modifying the discretization of the boundary conditions, has been discussed.

Στην εργασία αυτή παρουσιάζουμε μια καινούργια προσέγγιση και διερεύνηση της μεθοδολογίας μέσου αυτό-συνεπούς πεδίου για την μελέτη πολυμερικών συστημάτων κοντά σε επιφάνειες. Η καινούργια μεθοδολογία εισάγει πάνω στο πλέγμα τμηματικές πολυμερικές διαμορφώσεις που αναπτύσσονται σε σχεδόν «συνεχή» χώρο. Τροποποιείται ο παραδοσιακός υπολογισμός της ενέργειας αλληλεπίδρασης ενώ προσδιορίζεται με μεγαλύτερη σαφήνεια η ύπαρξη περιοχής «ισχυρής επιμήκυνσης της αλυσίδας» όπου σύμφωνα και με τις αναλυτικές θεωρίες μέσου αυτό-συνεπούς πεδίου, απουσιάζει το στρώμα μείωσης συγκέντρωσης κοντά στην επιφάνεια. Η ύπαρξη αυτού του στρώματος για μικρότερες πυκνότητες πρόσδεσης αποτελεί ιδιαίτερο χαρακτηριστικό που διακρίνει τις ψήκτρες σε δυο υποπεριοχές (μεσαίας και υψηλής πυκνότητας πρόσδεσης). Η μέθοδος επεκτάθηκε για την μελέτη μακρομορίων σε σχήμα αστεριού. Σε πολύ καλή συμφωνία με το πείραμα παρατηρήσαμε ότι με αύξηση του αριθμού των κλάδων μειώνεται δραστικά η προσρόφηση αυτών των μακρομορίων. Για περιπτώσεις συνύπαρξης στο ίδιο διάλυμα αστεριών με διαφορετικό βαθμό διακλάδωσης παρατηρήθηκε ότι οι λιγότερο διακλαδισμένες αλυσίδες τείνουν να αναπτυχθούν κάτω από τη «ομπρέλα» των πιο διακλαδισμένων. Επίσης μελετήθηκαν πολυμερικά συστήματα μεταβλητής πυκνότητας (χρησιμοποιώντας την καταστατική εξίσωση των Sanchez-Lacombe) για τα οποία υπολογίσουμε τις επιπτώσεις της πίεσης και της θερμοκρασίας στην πυκνότητα στην περίπτωση τήγματος. Διαπιστώσαμε ότι το διάγραμμα τάσης παραμόρφωσης υποδεικνύει μεγαλύτερη αντοχή για γραμμικές αλυσίδες όταν γίνει σύγκριση με αστερόμορφες ίδιου μοριακού βάρους. Αυτό αποδίδεται στην διαφορετική πυκνότητα και μορφολογία των μακρομοριακών διαπλοκών στην περιοχή αλληλοεπικάλυψης προσροφημένων και ελεύθερων αλυσίδων. Στην περίπτωση που η διαδικασία εφελκυσμού είναι αντιστρεπτή τα δείγματα αστερόμορφων μακρομορίων παρουσιάζουν μεγαλύτερη αντοχή λόγω της ικανότητας τους να προσροφόνται ταυτόχρονα και στις δύο επιφάνειες. Η επίδραση της εξωτερικής πίεσης δίνει μη αναμενόμενη συμπεριφορά μόνο σε εξαιρετικά μεγάλες πιέσεις. / -

We develop a self-consistent field theory of polymer dynamics, based on a functional integral approach, which is analogous to the existing equilibrium self-consistent field theory for polymers. We apply a saddle-point approximation to the exact dynamical theory, which generates a set of mean-field equations for the time-dependent density and mean force field. We also develop a method of treating the single-chain dynamics exactly, subject to this mean-field, resulting in a functional Fokker-Planck equation that must be solved along with the mean-field equations in a self-consistent manner. To test the self-consistency, we apply the theory to the simple but non-trivial case of np Brownian particles in one dimension interacting via a short-range repulsion in a harmonic external potential. Results for the non-interacting case agree with the literature. The interacting case demonstrates physically sensible interaction-dependent dynamics, such as an increased broadening of the density field when the repulsion is increased. We also examine the dynamics of a binary system with two distinct particle species. We calculate the center-of-mass trajectories for colliding distributions of species A and B, and observe that when the difference of repulsion strengths between like and unlike species chi is greater than a threshold value (between chi = 0.3 and chi = 0.4), the two species do not mix (indicating the onset of phase segregation).

A common strategy employed to destroy harmful bacteria is to disrupt the bacterial membrane through the action of pore-forming anti-microbial peptides. The manner in which the peptides arrange themselves spatially to form a pore in the membrane, which is important for understanding both the mechanism of pore formation and pore function, is a topic of current debate. We contrast the response of a model membrane bilayer to the presence of solid, cylindrical nanoparticle insertions, when the bilayer is composed of persistent worm-like chains and when it is composed of flexible Gaussian chains. We use self-consistent field theory, with the appropriate single-chain propagator, to describe the amphiphilic star-like triblock copolymers composing the membrane and the solvent. The nanoparticle surfaces are designed to have patches that prefer either the solvent or the tail groups of the copolymers, and the nanoparticles are fixed in space. Using this model with polymers in the lamellar phase, we investigate the question of pore-formation, nanoparticle insertion and hydrophobic mismatch in lipid bilayers and the effect that chain rigidity has on these particular interactions. We find that the main effect of increased chain rigidity is that it increases the free energy scaling and the significance of the energy barriers associated with these pore-forming processes. These results demonstrate the importance of using a more realistic persistent chain when modelling pore formation. / NSERC, CFI, SHARCNET

In this article we investigate the question whether the highly demanding informative requirements of rational expectations models are necessary to derive equilibria within capital market models. In the analysis agents are only provided with publicly available information such as prices and dividends. Nevertheless, we require that agents should behave like econometricians. Additionally, we skip the assumption of rational expectations models that agents know the implied law of motion of the system. By these assumptions, the stock market can be considered as a Sorger-Hommes consistent expectations model. In this article, we show the existence of consistent expectations equilibria with myopic agents, where the only CEE is the rational expectations equilibrium. In the simulation part we demonstrate how the steady state CEE can be derived by means of sample autocorrelation learning. Thus, we are able to derive a stock market equilibrium with less demanding requirements, where this equilibrium is equal to the rational expectations equilibrium. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

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Techn. Universiẗat, Diss., 2004--Kaiserslautern.

University, Diss., 2005--Frankfurt (Main). / Zsfassung in dt. Sprache.