Three essays in financial economics: asset pricing, optimal portfolio selection and financial integration

Executive Summary The unifying theme of this thesis is the pursuit of a satisfactory ways to quantify the riskureward trade-off in financial economics. First in the context of a general asset pricing model, then across models and finally across country borders. The guiding principle in that pursuit was to seek innovative solutions by combining ideas from different fields in economics and broad scientific research. For example, in the first part of this thesis we sought a fruitful application of strong existence results in utility theory to topics in asset pricing. In the second part we implement an idea from the field of fuzzy set theory to the optimal portfolio selection problem, while the third part of this thesis is to the best of our knowledge, the first empirical application of some general results in asset pricing in incomplete markets to the important topic of measurement of financial integration. While the first two parts of this thesis effectively combine well-known ways to quantify the risk-reward trade-offs the third one can be viewed as an empirical verification of the usefulness of the so-called "good deal bounds" theory in designing risk-sensitive pricing bounds. Chapter 1 develops a discrete-time asset pricing model, based on a novel ordinally equivalent representation of recursive utility. To the best of our knowledge, we are the first to use a member of a novel class of recursive utility generators to construct a representative agent model to address some long-lasting issues in asset pricing. Applying strong representation results allows us to show that the model features countercyclical risk premia, for both consumption and financial risk, together with low and procyclical risk free rate. As the recursive utility used nests as a special case the well-known time-state separable utility, all results nest the corresponding ones from the standard model and thus shed light on its well-known shortcomings. The empirical investigation to support these theoretical results, however, showed that as long as one resorts to econometric methods based on approximating conditional moments with unconditional ones, it is not possible to distinguish the model we propose from the standard one. Chapter 2 is a join work with Sergei Sontchik. There we provide theoretical and empirical motivation for aggregation of performance measures. The main idea is that as it makes sense to apply several performance measures ex-post, it also makes sense to base optimal portfolio selection on ex-ante maximization of as many possible performance measures as desired. We thus offer a concrete algorithm for optimal portfolio selection via ex-ante optimization over different horizons of several risk-return trade-offs simultaneously. An empirical application of that algorithm, using seven popular performance measures, suggests that realized returns feature better distributional characteristics relative to those of realized returns from portfolio strategies optimal with respect to single performance measures. When comparing the distributions of realized returns we used two partial risk-reward orderings first and second order stochastic dominance. We first used the Kolmogorov Smirnov test to determine if the two distributions are indeed different, which combined with a visual inspection allowed us to demonstrate that the way we propose to aggregate performance measures leads to portfolio realized returns that first order stochastically dominate the ones that result from optimization only with respect to, for example, Treynor ratio and Jensen's alpha. We checked for second order stochastic dominance via point wise comparison of the so-called absolute Lorenz curve, or the sequence of expected shortfalls for a range of quantiles. As soon as the plot of the absolute Lorenz curve for the aggregated performance measures was above the one corresponding to each individual measure, we were tempted to conclude that the algorithm we propose leads to portfolio returns distribution that second order stochastically dominates virtually all performance measures considered. Chapter 3 proposes a measure of financial integration, based on recent advances in asset pricing in incomplete markets. Given a base market (a set of traded assets) and an index of another market, we propose to measure financial integration through time by the size of the spread between the pricing bounds of the market index, relative to the base market. The bigger the spread around country index A, viewed from market B, the less integrated markets A and B are. We investigate the presence of structural breaks in the size of the spread for EMU member country indices before and after the introduction of the Euro. We find evidence that both the level and the volatility of our financial integration measure increased after the introduction of the Euro. That counterintuitive result suggests the presence of an inherent weakness in the attempt to measure financial integration independently of economic fundamentals. Nevertheless, the results about the bounds on the risk free rate appear plausible from the view point of existing economic theory about the impact of integration on interest rates.

Modelling diffusion of innovations in a social network

A simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information, agents decide whether to upgrade their level or not, balancing their possible benefit with the upgrading cost. A critical point where technological avalanches display a power-law behavior is also found. This critical point is characterized by a macroscopic observable that turns out to optimize technological growth in the stationary state. Analytical results supporting our findings are found for the globally coupled case.

Nonlinear chemoconvection in the Methylene-blue-glucose system

Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue¿glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.

Can we identify Walrasian allocations?

[eng] We consider a discrete time, pure exchange infinite horizon economy with two or more consumers and at least one concumption good per period. Within the framework of decentralized mechanisms, we show that for a given consumption trade at any period of time, say at time one, the consumers will need, in general, an infinite dimensional (informational) space to identigy such a trade as an intemporal Walrasian one. However, we show and characterize a set of enviroments where the Walrasian trades at each period of time can be achieved as the equilibrium trades of a sequence of decentralized competitive mechanisms, using only both current prices and quantities to coordinate decisions.

Hierarchical modeling gave plausible estimates of associations between metabolic syndrome and components of antiretroviral therapy.

OBJECTIVE: Hierarchical modeling has been proposed as a solution to the multiple exposure problem. We estimate associations between metabolic syndrome and different components of antiretroviral therapy using both conventional and hierarchical models. STUDY DESIGN AND SETTING: We use discrete time survival analysis to estimate the association between metabolic syndrome and cumulative exposure to 16 antiretrovirals from four drug classes. We fit a hierarchical model where the drug class provides a prior model of the association between metabolic syndrome and exposure to each antiretroviral. RESULTS: One thousand two hundred and eighteen patients were followed for a median of 27 months, with 242 cases of metabolic syndrome (20%) at a rate of 7.5 cases per 100 patient years. Metabolic syndrome was more likely to develop in patients exposed to stavudine, but was less likely to develop in those exposed to atazanavir. The estimate for exposure to atazanavir increased from hazard ratio of 0.06 per 6 months' use in the conventional model to 0.37 in the hierarchical model (or from 0.57 to 0.81 when using spline-based covariate adjustment). CONCLUSION: These results are consistent with trials that show the disadvantage of stavudine and advantage of atazanavir relative to other drugs in their respective classes. The hierarchical model gave more plausible results than the equivalent conventional model.

Conditional maximum likelihood timing recovery: estimators and bounds

This paper is concerned with the derivation of new estimators and performance bounds for the problem of timing estimation of (linearly) digitally modulated signals. The conditional maximum likelihood (CML) method is adopted, in contrast to the classical low-SNR unconditional ML (UML) formulationthat is systematically applied in the literature for the derivationof non-data-aided (NDA) timing-error-detectors (TEDs). A new CML TED is derived and proved to be self-noise free, in contrast to the conventional low-SNR-UML TED. In addition, the paper provides a derivation of the conditional Cramér–Rao Bound (CRB ), which is higher (less optimistic) than the modified CRB (MCRB)[which is only reached by decision-directed (DD) methods]. It is shown that the CRB is a lower bound on the asymptotic statisticalaccuracy of the set of consistent estimators that are quadratic with respect to the received signal. Although the obtained boundis not general, it applies to most NDA synchronizers proposed in the literature. A closed-form expression of the conditional CRBis obtained, and numerical results confirm that the CML TED attains the new bound for moderate to high Eg/No.

Wigner higher-order spectra: definition, properties, computation and application to transient signal analysis

The Wigner higher order moment spectra (WHOS)are defined as extensions of the Wigner-Ville distribution (WD)to higher order moment spectra domains. A general class oftime-frequency higher order moment spectra is also defined interms of arbitrary higher order moments of the signal as generalizations of the Cohen’s general class of time-frequency representations. The properties of the general class of time-frequency higher order moment spectra can be related to theproperties of WHOS which are, in fact, extensions of the properties of the WD. Discrete time and frequency Wigner higherorder moment spectra (DTF-WHOS) distributions are introduced for signal processing applications and are shown to beimplemented with two FFT-based algorithms. One applicationis presented where the Wigner bispectrum (WB), which is aWHOS in the third-order moment domain, is utilized for thedetection of transient signals embedded in noise. The WB iscompared with the WD in terms of simulation examples andanalysis of real sonar data. It is shown that better detectionschemes can be derived, in low signal-to-noise ratio, when theWB is applied.

Ruin problems under IBNR Dynamics

In this paper, we consider a discrete-time risk process allowing for delay in claim settlement, which introduces a certain type of dependence in the process. From martingale theory, an expression for the ultimate ruin probability is obtained, and Lundberg-type inequalities are derived. The impact of delay in claim settlement is then investigated. To this end, a convex order comparison of the aggregate claim amounts is performed with the corresponding non-delayed risk model, and numerical simulations are carried out with Belgian market data.

Converter-flux-based current control of voltage source PWM rectifiers - analysis and implementation

Pulsewidth-modulated (PWM) rectifier technology is increasingly used in industrial applications like variable-speed motor drives, since it offers several desired features such as sinusoidal input currents, controllable power factor, bidirectional power flow and high quality DC output voltage. To achieve these features,however, an effective control system with fast and accurate current and DC voltage responses is required. From various control strategies proposed to meet these control objectives, in most cases the commonly known principle of the synchronous-frame current vector control along with some space-vector PWM scheme have been applied. Recently, however, new control approaches analogous to the well-established direct torque control (DTC) method for electrical machines have also emerged to implement a high-performance PWM rectifier. In this thesis the concepts of classical synchronous-frame current control and DTC-based PWM rectifier control are combined and a new converter-flux-based current control (CFCC) scheme is introduced. To achieve sufficient dynamic performance and to ensure a stable operation, the proposed control system is thoroughly analysed and simple rules for the controller design are suggested. Special attention is paid to the estimationof the converter flux, which is the key element of converter-flux-based control. Discrete-time implementation is also discussed. Line-voltage-sensorless reactive reactive power control methods for the L- and LCL-type line filters are presented. For the L-filter an open-loop control law for the d-axis current referenceis proposed. In the case of the LCL-filter the combined open-loop control and feedback control is proposed. The influence of the erroneous filter parameter estimates on the accuracy of the developed control schemes is also discussed. A newzero vector selection rule for suppressing the zero-sequence current in parallel-connected PWM rectifiers is proposed. With this method a truly standalone and independent control of the converter units is allowed and traditional transformer isolation and synchronised-control-based solutions are avoided. The implementation requires only one additional current sensor. The proposed schemes are evaluated by the simulations and laboratory experiments. A satisfactory performance and good agreement between the theory and practice are demonstrated.

Geometric stopping of a random walk and its applications to valuing equity-linked death benefits

We study discrete-time models in which death benefits can depend on a stock price index, the logarithm of which is modeled as a random walk. Examples of such benefit payments include put and call options, barrier options, and lookback options. Because the distribution of the curtate-future-lifetime can be approximated by a linear combination of geometric distributions, it suffices to consider curtate-future-lifetimes with a geometric distribution. In binomial and trinomial tree models, closed-form expressions for the expectations of the discounted benefit payment are obtained for a series of options. They are based on results concerning geometric stopping of a random walk, in particular also on a version of the Wiener-Hopf factorization.

Unidirectional quantum walks: Evolution and exit times

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the currently widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in place or move in a fixed direction, e.g., rightward or upward. While both formulations are essentially equivalent, the present approach leads us to consider discrete Fourier transforms, which eventually results in obtaining explicit expressions for the wave functions in terms of finite sums and allows the use of efficient algorithms based on the fast Fourier transform. The wave functions here obtained govern the probability of finding the particle at any given location but determine as well the exit-time probability of the walker from a fixed interval, which is also analyzed.

Diskreettiaikainen liukuvan moodin säätö kiinteäoksidipolttokennon DC-tasonnostossa

Huoli ympäristön tilasta ja fossiilisten polttoaineiden hinnan nousu ovat vauhdittaneet tutkimusta uusien energialähteiden löytämiseksi. Polttokennot ovat yksi lupaavimmista tekniikoista etenkin hajautetun energiantuotannon, varavoimalaitosten sekä liikennevälineiden alueella. Polttokenno on tehonlähteenä kuitenkin hyvin epäideaalinen, ja se asettaa tehoelektroniikalle lukuisia erityisvaatimuksia. Polttokennon kytkeminen sähköverkkoon on tavallisesti toteutettu käyttämällä galvaanisesti erottavaa DC/DC hakkuria sekä vaihtosuuntaajaa sarjassa. Polttokennon kulumisen estämiseksi tehoelektroniikalta vaaditaan tarkkaa polttokennon lähtövirran hallintaa. Perinteisesti virran hallinta on toteutettu säätämällä hakkurin tulovirtaa PI (Proportional and Integral) tai PID (Proportional, Integral and Derivative) -säätimellä. Hakkurin epälineaarisuudesta johtuen tällainen ratkaisu ei välttämättä toimi kaukana linearisointipisteestä. Lisäksi perinteiset säätimet ovat herkkiä mallinnusvirheille. Tässä diplomityössä on esitetty polttokennon jännitettä nostavan hakkurin tilayhtälökeskiarvoistusmenetelmään perustuva malli, sekä malliin perustuva diskreettiaikainen integroiva liukuvan moodin säätö. Esitetty säätö on luonteeltaan epälineaarinen ja se soveltuu epälineaaristen ja heikosti tunnettujen järjestelmien säätämiseen.

Method of numerical correction of errors occasioned by delay of records during the monitoring of environmental variables of interest for animal production

Thermal and air conditions inside animal facilities change during the day due to the influence of the external environment. For statistical and geostatistical analyses to be representative, a large number of points spatially distributed in the facility area must be monitored. This work suggests that the time variation of environmental variables of interest for animal production, monitored within animal facility, can be modeled accurately from discrete-time records. The aim of this study was to develop a numerical method to correct the temporal variations of these environmental variables, transforming the data so that such observations are independent of the time spent during the measurement. The proposed method approached values recorded with time delays to those expected at the exact moment of interest, if the data were measured simultaneously at the moment at all points distributed spatially. The correction model for numerical environmental variables was validated for environmental air temperature parameter, and the values corrected by the method did not differ by Tukey's test at 5% significance of real values recorded by data loggers.

The knapsack problem approach in solving partial hedging problems of options

En option är ett finansiellt kontrakt som ger dess innehavare en rättighet (men medför ingen skyldighet) att sälja eller köpa någonting (till exempel en aktie) till eller från säljaren av optionen till ett visst pris vid en bestämd tidpunkt i framtiden. Den som säljer optionen binder sig till att gå med på denna framtida transaktion ifall optionsinnehavaren längre fram bestämmer sig för att inlösa optionen. Säljaren av optionen åtar sig alltså en risk av att den framtida transaktion som optionsinnehavaren kan tvinga honom att göra visar sig vara ofördelaktig för honom. Frågan om hur säljaren kan skydda sig mot denna risk leder till intressanta optimeringsproblem, där målet är att hitta en optimal skyddsstrategi under vissa givna villkor. Sådana optimeringsproblem har studerats mycket inom finansiell matematik. Avhandlingen "The knapsack problem approach in solving partial hedging problems of options" inför en ytterligare synpunkt till denna diskussion: I en relativt enkel (ändlig och komplett) marknadsmodell kan nämligen vissa partiella skyddsproblem beskrivas som så kallade kappsäcksproblem. De sistnämnda är välkända inom en gren av matematik som heter operationsanalys. I avhandlingen visas hur skyddsproblem som tidigare lösts på andra sätt kan alternativt lösas med hjälp av metoder som utvecklats för kappsäcksproblem. Förfarandet tillämpas även på helt nya skyddsproblem i samband med så kallade amerikanska optioner.

BEM/FEM non-linear model applied to transient analysis with viscous damping

In this article a two-dimensional transient boundary element formulation based on the mass matrix approach is discussed. The implicit formulation of the method to deal with elastoplastic analysis is considered, as well as the way to deal with viscous damping effects. The time integration processes are based on the Newmark rhoand Houbolt methods, while the domain integrals for mass, elastoplastic and damping effects are carried out by the well known cell approximation technique. The boundary element algebraic relations are also coupled with finite element frame relations to solve stiffened domains. Some examples to illustrate the accuracy and efficiency of the proposed formulation are also presented.