Ambiguity on the insurer's side: the demand for insurance

Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., [23]). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then there exist optimal monotonic indemnity schedules. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., [25]). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow [5] on the optimality of the deductible indemnity schedule.

Stability of Random Sums and Extremes

This study is about the stability of random sums and extremes.The difficulty in finding exact sampling distributions resulted in considerable problems of computing probabilities concerning the sums that involve a large number of terms.Functions of sample observations that are natural interest other than the sum,are the extremes,that is , the minimum and the maximum of the observations.Extreme value distributions also arise in problems like the study of size effect on material strengths,the reliability of parallel and series systems made up of large number of components,record values and assessing the levels of air pollution.It may be noticed that the theories of sums and extremes are mutually connected.For instance,in the search for asymptotic normality of sums ,it is assumed that at least the variance of the population is finite.In such cases the contributions of the extremes to the sum of independent and identically distributed(i.i.d) r.vs is negligible.

Consequence modelling,vulnerability assessment and fuzzy fault tree analysis of hazardous storages in an industrial area

The hazards associated with major accident hazard (MAH) industries are fire, explosion and toxic gas releases. Of these, toxic gas release is the worst as it has the potential to cause extensive fatalities. Qualitative and quantitative hazard analyses are essential for the identitication and quantification of the hazards associated with chemical industries. This research work presents the results of a consequence analysis carried out to assess the damage potential of the hazardous material storages in an industrial area of central Kerala, India. A survey carried out in the major accident hazard (MAH) units in the industrial belt revealed that the major hazardous chemicals stored by the various industrial units are ammonia, chlorine, benzene, naphtha, cyclohexane, cyclohexanone and LPG. The damage potential of the above chemicals is assessed using consequence modelling. Modelling of pool fires for naphtha, cyclohexane, cyclohexanone, benzene and ammonia are carried out using TNO model. Vapor cloud explosion (VCE) modelling of LPG, cyclohexane and benzene are carried out using TNT equivalent model. Boiling liquid expanding vapor explosion (BLEVE) modelling of LPG is also carried out. Dispersion modelling of toxic chemicals like chlorine, ammonia and benzene is carried out using the ALOHA air quality model. Threat zones for different hazardous storages are estimated based on the consequence modelling. The distance covered by the threat zone was found to be maximum for chlorine release from a chlor-alkali industry located in the area. The results of consequence modelling are useful for the estimation of individual risk and societal risk in the above industrial area.Vulnerability assessment is carried out using probit functions for toxic, thermal and pressure loads. Individual and societal risks are also estimated at different locations. Mapping of threat zones due to different incident outcome cases from different MAH industries is done with the help of Are GIS.Fault Tree Analysis (FTA) is an established technique for hazard evaluation. This technique has the advantage of being both qualitative and quantitative, if the probabilities and frequencies of the basic events are known. However it is often difficult to estimate precisely the failure probability of the components due to insufficient data or vague characteristics of the basic event. It has been reported that availability of the failure probability data pertaining to local conditions is surprisingly limited in India. This thesis outlines the generation of failure probability values of the basic events that lead to the release of chlorine from the storage and filling facility of a major chlor-alkali industry located in the area using expert elicitation and proven fuzzy logic. Sensitivity analysis has been done to evaluate the percentage contribution of each basic event that could lead to chlorine release. Two dimensional fuzzy fault tree analysis (TDFFTA) has been proposed for balancing the hesitation factor invo1ved in expert elicitation .

Stochastic processes and their applications time dependent solutions for some queueing and inventory models

The objective of this thesis is to study the time dependent behaviour of some complex queueing and inventory models. It contains a detailed analysis of the basic stochastic processes underlying these models. In the theory of queues, analysis of time dependent behaviour is an area.very little developed compared to steady state theory. Tine dependence seems certainly worth studying from an application point of view but unfortunately, the analytic difficulties are considerable. Glosod form solutions are complicated even for such simple models as M/M /1. Outside M/>M/1, time dependent solutions have been found only in special cases and involve most often double transforms which provide very little insight into the behaviour of the queueing systems themselves. In inventory theory also There is not much results available giving the time dependent solution of the system size probabilities. Our emphasis is on explicit results free from all types of transforms and the method used may be of special interest to a wide variety of problems having regenerative structure.

Stochastic processes and their applications semi-markov analysis of some inventory and queuing problems

This thesis analyses certain problems in Inventories and Queues. There are many situations in real-life where we encounter models as described in this thesis. It analyses in depth various models which can be applied to production, storag¢, telephone traffic, road traffic, economics, business administration, serving of customers, operations of particle counters and others. Certain models described here is not a complete representation of the true situation in all its complexity, but a simplified version amenable to analysis. While discussing the models, we show how a dependence structure can be suitably introduced in some problems of Inventories and Queues. Continuous review, single commodity inventory systems with Markov dependence structure introduced in the demand quantities, replenishment quantities and reordering levels are considered separately. Lead time is assumed to be zero in these models. An inventory model involving random lead time is also considered (Chapter-4). Further finite capacity single server queueing systems with single/bulk arrival, single/bulk services are also discussed. In some models the server is assumed to go on vacation (Chapters 7 and 8). In chapters 5 and 6 a sort of dependence is introduced in the service pattern in some queuing models.

Synthesis and Photoluminescence Properties of Novel Red Phosphors for White Light Emitting Diode Applications

Several series of Eu3+ based red emitting phosphor materials were synthesized using solid state reaction route and their properties were characterized. The present studies primarily investigated the photoluminescence properties of Eu3+ in a family of closely related host structure with a general formula Ln3MO7. The results presented in the previous chapters throws light to a basic understanding of the structure, phase formation and the photoluminescence properties of these compounds and their co-relations. The variation in the Eu3+ luminescence properties with different M cations was studied in Gd3-xMO7 (M = Nb, Sb, Ta) system.More ordering in the host lattice and more uniform distribution of Eu3+ ions resulting in the increased emission properties were observed in tantalate system.Influence of various lanthanide ion (Lu, Y, Gd, La) substitutions on the Eu3+ photoluminescence properties in Ln3MO7 host structures was also studied. The difference in emission profiles with different Ln ions demonstrated the influence of long range ordering, coordination of cations and ligand polarizability in the emission probabilities, intensity and quantum efficiency of these phosphor materials. Better luminescence of almost equally competing intensities from all the 4f transitions of Eu3+ was noticed for La3TaO7 system. Photoluminescence properties were further improved in La3TaO7 : Eu3+ phosphors by the incorporation of Ba2+ ions in La3+ site. New red phosphor materials Gd2-xGaTaO7 : xEu3+ exhibiting intense red emissions under UV excitation were prepared. Optimum doping level of Eu3+ in these different host lattices were experimentally determined. Some of the prepared samples exhibited higher emission intensities than the standard Y2O3 : Eu3+ red phosphors. In the present studies, Eu3+ acts as a structural probe determining the coordination and symmetry of the atoms in the host lattice. Results from the photoluminescence studies combined with the powder XRD and Raman spectroscopy investigations helped in the determination of the correct crystal structures and phase formation of the prepared compounds. Thus the controversy regarding the space groups of these compounds could be solved to a great extent. The variation in the space groups with different cation substitutions were discussed. There was only limited understanding regarding the various influential parameters of the photoluminescence properties of phosphor materials. From the given studies, the dependence of photoluminescence properties on the crystal structure and ordering of the host lattice, site symmetries, polarizability of the ions, distortions around the activator ion, uniformity in the activator distribution, concentration of the activator ion etc. were explained. Although the presented work does not directly evidence any application, the materials developed in the studies can be used for lighting applications together with other components for LED lighting. All the prepared samples were well excitable under near UV radiation. La3TaO7 : 0.15Eu3+ phosphor with high efficiency and intense orange red emissions can be used as a potential red component for the realization of white light with better color rendering properties. Gd2GaTaO7 : Eu3+, Bi2+ red phosphors give good color purity matching to NTSC standards of red. Some of these compounds exhibited higher emission intensities than the standard Y2O3 : Eu3+ red phosphors. However thermal stability and electrical output using these compounds should be studied further before applications. Based on the studies in the closely related Ln3MO7 structures, some ideas on selecting better host lattice for improved luminescence properties could be drawn. Analyzing the CTB position and the number of emission splits, a general understanding on the doping sites can be obtained. These results could be helpful for phosphor designs in other host systems also, for enhanced emission intensity and efficiency.

Aspekte des Prozesses der N-Freisetzung aus Humus-Vorratsabbau

In der vorliegenden Arbeit werden die Auswirkungen von Umweltveränderungen in einem N-gesättigten Buchenwaldökosystem über Basalt (Braunerde) untersucht. Unter veränderten Umweltbedingungen sind hier vor allem Bestandesdachauflösung, immissions- oder waldbaulich bedingt, und Klimaveränderung zu verstehen, die eine Erwärmung des Oberbodens zur Folge haben. Die Änderungen der Umweltbedingungen werden in diesem Versuchsansatz durch einen waldbaulichen Eingriff simuliert, durch den eine Bestandeslücke entsteht, die in einer Erwärmung des Bodens resultieren und damit den Wasser- und Elementhaushalt insgesamt beeinflussen. Es wird deutlich, dass die in der vorliegenden Arbeit untersuchten Flächen als N-gesättigt bezeichnet werden können, da die N-Verluste aus dem System die Größe der Einträge überschreiten. In der Folge ist es zu einer Entkopplung des Stoffhaushalts und damit zu erhöhter N-Mobilisierung gekommen. Diese konnte vor allem im hydrologischen Jahr 1996 dokumentiert werden; der Überschuss-N-Output liegt auf der Auflichtungsfläche bei bis zu 50 kg N/(ha*a)! Die beobachteten hohen N-Austräge erfolgten trotz eines ebenfalls beobachteten Anwachsens des mikrobiellen Stickstoff-Pools und des Aufwachsens einer krautigen und strauchigen Vegetation auf der Auflichtungsfläche. Im Jahresgang konnten auf der Auflichtungsfläche in 0 - 30 cm Bodentiefe maximale Änderungen im Nmic-Vorrat von 130 kg N/(ha*a) beobachtet werden. Das im Frühjahr beginnende quantitative Anwachsen des mikrobiellen Stickstoff-Pools mit dem Jahresgang zeigt vor allem dessen Temperaturabhängigkeit auf. Die am Ende der Vegetationsperiode deutlich ansteigenden Austragsraten zeigen jedoch an, dass der freigesetzte Stickstoff auch von den Mikroorganismen nicht dauerhaft im System gehalten werden kann, da mit fallender Temperatur auch die Mikroorganismen absterben und der in ihrer Biomasse gespeicherte Stickstoff freigesetzt wird. Aufwachsende Vegetation auf der Auflichtungsfläche konnte einen Großteil des Netto-Stickstoff-Jahreseintrages aufnehmen. Da die "Netto-Jahres-Mineralisation" 1996 leicht über der Wurzelaufnahme liegt, verbleibt ein Rest, der nicht von der aufwachsenden krautigen Vegetation der Auflichtungsfläche aufgenommen werden kann. Ergebnis ist damit, dass die auf Lochhieben aufwachsende krautige und strauchige Vegetation eine temperaturbedingte Stickstoffmobilisierung nur teilweise kompensieren kann. Allein aufwachsende verholzende Vegetation kann Stickstoff langfristig im System binden.

Profile simulations of gas chopping etching processes : model development and comparison with experiments

The progress in microsystem technology or nano technology places extended requirements to the fabrication processes. The trend is moving towards structuring within the nanometer scale on the one hand, and towards fabrication of structures with high aspect ratio (ratio of vertical vs. lateral dimensions) and large depths in the 100 µm scale on the other hand. Current procedures for the microstructuring of silicon are wet chemical etching and dry or plasma etching. A modern plasma etching technique for the structuring of silicon is the so-called "gas chopping" etching technique (also called "time-multiplexed etching"). In this etching technique, passivation cycles, which prevent lateral underetching of sidewalls, and etching cycles, which etch preferably in the vertical direction because of the sidewall passivation, are constantly alternated during the complete etching process. To do this, a CHF3/CH4 plasma, which generates CF monomeres is employed during the passivation cycle, and a SF6/Ar, which generates fluorine radicals and ions plasma is employed during the etching cycle. Depending on the requirements on the etched profile, the durations of the individual passivation and etching cycles are in the range of a few seconds up to several minutes. The profiles achieved with this etching process crucially depend on the flow of reactants, i.e. CF monomeres during the passivation cycle, and ions and fluorine radicals during the etching cycle, to the bottom of the profile, especially for profiles with high aspect ratio. With regard to the predictability of the etching processes, knowledge of the fundamental effects taking place during a gas chopping etching process, and their impact onto the resulting profile is required. For this purpose in the context of this work, a model for the description of the profile evolution of such etching processes is proposed, which considers the reactions (etching or deposition) at the sample surface on a phenomenological basis. Furthermore, the reactant transport inside the etching trench is modelled, based on angular distribution functions and on absorption probabilities at the sidewalls and bottom of the trench. A comparison of the simulated profiles with corresponding experimental profiles reveals that the proposed model reproduces the experimental profiles, if the angular distribution functions and absorption probabilities employed in the model is in agreement with data found in the literature. Therefor the model developed in the context of this work is an adequate description of the effects taking place during a gas chopping plasma etching process.

Digitales stochastisches Magnetfeld-Sensorarray

Digitales stochastisches Magnetfeld-Sensorarray Stefan Rohrer Im Rahmen eines mehrjährigen Forschungsprojektes, gefördert von der Deutschen Forschungsgesellschaft (DFG), wurden am Institut für Mikroelektronik (IPM) der Universität Kassel digitale Magnetfeldsensoren mit einer Breite bis zu 1 µm entwickelt. Die vorliegende Dissertation stellt ein aus diesem Forschungsprojekt entstandenes Magnetfeld-Sensorarray vor, das speziell dazu entworfen wurde, um digitale Magnetfelder schnell und auf minimaler Fläche mit einer guten räumlichen und zeitlichen Auflösung zu detektieren. Der noch in einem 1,0µm-CMOS-Prozess gefertigte Test-Chip arbeitet bis zu einer Taktfrequenz von 27 MHz bei einem Sensorabstand von 6,75 µm. Damit ist er das derzeit kleinste und schnellste digitale Magnetfeld-Sensorarray in einem Standard-CMOS-Prozess. Konvertiert auf eine 0,09µm-Technologie können Frequenzen bis 1 GHz erreicht werden bei einem Sensorabstand von unter 1 µm. In der Dissertation werden die wichtigsten Ergebnisse des Projekts detailliert beschrieben. Basis des Sensors ist eine rückgekoppelte Inverter-Anordnung. Als magnetfeldsensitives Element dient ein auf dem Hall-Effekt basierender Doppel-Drain-MAGFET, der das Verhalten der Kippschaltung beeinflusst. Aus den digitalen Ausgangsdaten kann die Stärke und die Polarität des Magnetfelds bestimmt werden. Die Gesamtanordnung bildet einen stochastischen Magnetfeld-Sensor. In der Arbeit wird ein Modell für das Kippverhalten der rückgekoppelten Inverter präsentiert. Die Rauscheinflüsse des Sensors werden analysiert und in einem stochastischen Differentialgleichungssystem modelliert. Die Lösung der stochastischen Differentialgleichung zeigt die Entwicklung der Wahrscheinlichkeitsverteilung des Ausgangssignals über die Zeit und welche Einflussfaktoren die Fehlerwahrscheinlichkeit des Sensors beeinflussen. Sie gibt Hinweise darauf, welche Parameter für das Design und Layout eines stochastischen Sensors zu einem optimalen Ergebnis führen. Die auf den theoretischen Berechnungen basierenden Schaltungen und Layout-Komponenten eines digitalen stochastischen Sensors werden in der Arbeit vorgestellt. Aufgrund der technologisch bedingten Prozesstoleranzen ist für jeden Detektor eine eigene kompensierende Kalibrierung erforderlich. Unterschiedliche Realisierungen dafür werden präsentiert und bewertet. Zur genaueren Modellierung wird ein SPICE-Modell aufgestellt und damit für das Kippverhalten des Sensors eine stochastische Differentialgleichung mit SPICE-bestimmten Koeffizienten hergeleitet. Gegenüber den Standard-Magnetfeldsensoren bietet die stochastische digitale Auswertung den Vorteil einer flexiblen Messung. Man kann wählen zwischen schnellen Messungen bei reduzierter Genauigkeit und einer hohen lokalen Auflösung oder einer hohen Genauigkeit bei der Auswertung langsam veränderlicher Magnetfelder im Bereich von unter 1 mT. Die Arbeit präsentiert die Messergebnisse des Testchips. Die gemessene Empfindlichkeit und die Fehlerwahrscheinlichkeit sowie die optimalen Arbeitspunkte und die Kennliniencharakteristik werden dargestellt. Die relative Empfindlichkeit der MAGFETs beträgt 0,0075/T. Die damit erzielbaren Fehlerwahrscheinlichkeiten werden in der Arbeit aufgelistet. Verglichen mit dem theoretischen Modell zeigt das gemessene Kippverhalten der stochastischen Sensoren eine gute Übereinstimmung. Verschiedene Messungen von analogen und digitalen Magnetfeldern bestätigen die Anwendbarkeit des Sensors für schnelle Magnetfeldmessungen bis 27 MHz auch bei kleinen Magnetfeldern unter 1 mT. Die Messungen der Sensorcharakteristik in Abhängigkeit von der Temperatur zeigen, dass die Empfindlichkeit bei sehr tiefen Temperaturen deutlich steigt aufgrund der Abnahme des Rauschens. Eine Zusammenfassung und ein ausführliches Literaturverzeichnis geben einen Überblick über den Stand der Technik.

Double photoionization of argon into the {3s3p^5} {^1P}- and {^3P}-states

Double photoionization of argon was studied by photon induced fluorescence spectroscopy (PIFS). Cross sections for the double photoionization into the {3s3p^5} {^1P}, {^3P} states of Ar^{+ +} are presented for exciting photon energies between threshold and 120 eV. In the threshold range the energy dependencies of these cross sections were determined for the first time. Singlet and triplet states are populated with comparable probabilities at equal excess energies, in contrast to predictions of the extended Wannier theory. At hv = 100eV the spin-or-bit splitting of the 3s3p^5 ^3P state was resolved, and a cross section for the production of Ar^{+ +} {3s^0}{3p^6 } {^1S_0} was determined for the first time.

Double-autoionization decay of resonantly excited single-electron states

Perturbation theory in the lowest non-vanishing order in interelectron interaction has been applied to the theoretical investigation of double-ionization decays of resonantly excited single-electron states. The formulae for the transition probabilities were derived in the LS coupling scheme, and the orbital angular momentum and spin selection rules were obtained. In addition to the formulae, which are exact in this order, three approximate expressions, which correspond to illustrative model mechanisms of the transition, were derived as limiting cases of the exact ones. Numerical results were obtained for the decay of the resonantly excited Kr 1 3d^{-1}5p[^1P] state which demonstrated quite clearly the important role of the interelectron interaction in double-ionization processes. On the other hand, the results obtained show that low-energy electrons can appear in the photoelectron spectrum below the ionization threshold of the 3d shell. As a function of the photon frequency, the yield of these low-energy electrons is strongly amplified by the resonant transition of the 3d electron to 5p (or to other discrete levels), acting as an intermediate state, when the photon frequency approaches that of the transition.

Application of inclusive probability theory to heavy ion-atom collisions

Using the independent particle model as our basis we present a scheme to reduce the complexity and computational effort to calculate inclusive probabilities in many-electron collision system. As an example we present an application to K - K charge transfer in collisions of 2.6 MeV Ne{^9+} on Ne. We are able to give impact parameter-dependent probabilities for many-particle states which could lead to KLL-Auger electrons after collision and we compare with experimental values.

Inclusive probability calculations for the K-vacancy transfer in collisions of S{^15+} on Ar

Using the single-particle amplitudes from a 20-level coupled-channel calculation with ab initio relativistic self consistent LCAO-MO Dirac-Fock-Slater energy eigenvalues and matrix elements we calculate within the frame of the inclusive probability formalism impact-parameter-dependent K-hole transfer probabilities. As an example we show results for the heavy asymmetric collision system S{^15+} on Ar for impact energies from 4.7 to 16 MeV. The inclusive probability formalism which reinstates the many-particle aspect of the collision system permits a qualitative and quantitative agreement with the experiment which is not achieved by the single-particle picture.

Equilibrium K-shell excitation of highly ionized neon

Augerelectron emission from foil-excited Ne-ions (6 to 10 MeV beam energy) has been measured. The beam-foil time-of-flight technique has been applied to study electronic transitions of metastable states (delayed spectra) and to determine their lifetimes. To achieve a line identification for the complex structure observed in the prompt spectrum, the spectrum is separated into its isoelectronic parts by an Augerelectron-ion coincidence correlating the emitted electrons and the emitting projectiles of well defined final charge states q_f. Well resolved spectra were obtained and the lines could be identified using intermediate coupling Dirac-Fock multiconfiguration calculations. From the total KLL-Augerelectron transition probabilities observed in the electronion coincidence experiment for Ne (10 MeV) the amount of projectiles with one K-hole just behind a C-target can be estimated. For foil-excited Ne-projectiles in contrast to single collision results the comparison of transition intensities for individual lines with calculated transition probabilities yields a statistical population of Li- and Be-like configurations.

Simulative Risikoanalyse von Biomethanprojekten

Im Zuge der Novellierung der Gasnetzzugangsverordnung sowie des Erneuerbare-Energien-Gesetzes entwickelte sich die Einspeisung von Biomethan in das Erdgasnetz als alternative Investitionsmöglichkeit der Erneuerbare-Energien-Branche. Als problematisch erweist sich dabei die Identifikation und Strukturierung einzelner Risikofaktoren zu einem Risikobereich, sowie die anschließende Quantifizierung dieser Risikofaktoren innerhalb eines Risikoportfolios. Darüber hinaus besteht die Schwierigkeit, diese Risikofaktoren in einem cashflowbasierten und den Ansprüchen der Investoren gewachsenem Risikomodell abzubilden. Zusätzlich müssen dabei Wechselwirkungen zwischen einzelnen Risikofaktoren berücksichtigt werden. Aus diesem Grund verfolgt die Dissertation das Ziel, die Risikosituation eines Biomethanprojektes anhand aggregierter und isolierter Risikosimulationen zu analysieren. Im Rahmen einer Diskussion werden Strategien und Instrumente zur Risikosteuerung angesprochen sowie die Implementierungsfähigkeit des Risikomodells in das Risikomanagementsystem von Investoren. Die Risikomaße zur Beschreibung der Risikoauswirkung betrachten die Shortfälle einer Verteilung. Dabei beziehen sich diese auf die geplanten Ausschüttungen sowie interne Verzinsungsansprüche der Investoren und die von Kreditinstituten geforderte minimale Schuldendienstdeckungsrate. Im Hinblick auf die Risikotragfähigkeit werden liquiditätsorientierte Kennzahlen hinzugezogen. Investoren interessieren sich vor dem Hintergrund einer gezielten Risikosteuerung hauptsächlich für den gefahrvollsten Risikobereich und innerhalb dessen für den Risikofaktor, der die größten Risikoauswirkungen hervorruft. Zudem spielt der Zeitpunkt maximaler Risikoauswirkung eine große Rolle. Als Kernaussage dieser Arbeit wird festgestellt, dass in den meisten Fällen die Aussagefähigkeit aggregierter Risikosimulationen durch Überlagerungseffekte negativ beeinträchtigt wird. Erst durch isoliert durchgeführte Risikoanalysen können diese Effekte eliminiert werden. Besonders auffällig gestalten sich dabei die Ergebnisse der isoliert durchgeführten Risikoanalyse des Risikobereichs »Politik«. So verursacht dieser im Vergleich zu den übrigen Risikobereichen, wie »Infrastruktur«, »Rohstoffe«, »Absatzmarkt« und »Finanzmarkt«, die geringsten Wahrscheinlichkeiten avisierte Planwerte der Investoren zu unterschreiten. Kommt es jedoch zu einer solchen Planwert-Unterschreitung, nehmen die damit verbundenen Risikoauswirkungen eine überraschende Position im Risikoranking der Investoren ein. Hinsichtlich der Aussagefähigkeit des Risikomodells wird deutlich, dass spezifische Risikosichtweisen der Investoren ausschlaggebend dafür sind, welche Strategien und Instrumente zur Risikosenkung umgesetzt werden. Darüber hinaus wird festgestellt, dass die Grenzen des Risikomodells in der Validität der Expertenmeinungen und dem Auffinden einer Optimallösung zu suchen sind.