A filtering approach to tracking volatility from prices observed at random times

This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $S=(S_{t})_{t\geq0}$ is given by $$dS_{t}=r(\theta_{t})S_{t}dt+v(\theta_{t})S_{t}dB_{t},$$ where $B=(B_{t})_{t\geq0}$ is a Brownian motion, $v$ is a positive function, and $\theta=(\theta_{t})_{t\geq0}$ is a c\'{a}dl\'{a}g strong Markov process. The random process $\theta$ is unobservable. We assume also that the asset price $S_{t}$ is observed only at random times $0<\tau_{1}<\tau_{2}<....$ This is an appropriate assumption when modelling high frequency financial data (e.g., tick-by-tick stock prices). In the above setting the problem of estimation of $\theta$ can be approached as a special nonlinear filtering problem with measurements generated by a multivariate point process $(\tau_{k},\log S_{\tau_{k}})$. While quite natural, this problem does not fit into the standard diffusion or simple point process filtering frameworks and requires more technical tools. We derive a closed form optimal recursive Bayesian filter for $\theta_{t}$, based on the observations of $(\tau_{k},\log S_{\tau_{k}})_{k\geq1}$. It turns out that the filter is given by a recursive system that involves only deterministic Kolmogorov-type equations, which should make the numerical implementation relatively easy

Monte Carlo Valuation of Optimal Portfolios in Complete Markets

We introduce a method that relies exclusively on Monte Carlo simulation in order to compute optimal portfolios. Our method is completely general and only requires complete markets and knowledge of the dynamics of the security processes. It is precise and easy to implement. It can be applied regardless or the number of factors and of whether the agent derives utility from intertemporal consumption, terminal wealth or both. We perform some comparative statics and find that portfolios are sensitive to parameter values outside the class of affine models traditionally considered in the literature. The method we suggest can also be applied to the computation of the optimal hedge of a derivative when Monte Carlo simulation is used as a pricing method.

Cross-Border Cooperation Programme As an Impetus for Establishment of New Modes of Governance in Croatia

Generated as a response to the requirements in managing European cross border cooperation programmes, Neighbourhood Programme Slovenia-Hungary-Croatia 2004-2006 (NP) in particular served as an impetus for establishment of new modes of governance in Croatia. Together with Hungary and Slovenia, Croatia participates in this trilateral Programme as an external EU border candidate state. The NP is implemented as a grant scheme in Croatia for the first time requiring many institutional changes for its implementation. On all levels of government, the NP contributed to the establishment of stronger relations among institutions, horizontally and vertically, and a transfer of know-how in preparation and implementation from experienced partners, Slovenia and Hungary. Such a complex programme generated also problems due to weak administrative capacity, different sources of financing and socio-economic discrepancies. On national level, weak capacity of the Croatian Ministry of Foreign Affairs and European Integration (MFAEI) has directly influenced the initiation and implementation of NP and difficulties in the decision-making process occurred. The relationship between MFAEI and the Delegation of the European Commission was unclear and there were difficulties in developing new administrative procedures. Additionally, insufficiently transparent information dissemination mechanisms through different government levels influenced the quality and selection of project proposals in certain counties. Socio-cultural differences in Croatia were insufficiently considered while setting up the coordination system resulting in the extent and quality of submitted proposals and their success in the selection procedure. Some regions showed successful coordination on county level contributing to selection of greater number of proposals from those counties, while in others, there was a lack of capacity in preparing coherent project proposals. In accordance with the presented first Croatian experiences in the trilateral European cross-border programme, the following can be concluded: In terms of socio-developmental impacts, the joint-project proposal preparation process of the cross border partners created intensive inter-institutional cooperation and inter-institutional communication. However, only successful project proposals result in inter-institutional collaboration through joint implementation of projects, which is considered fundamental to the creation of a network society and building of social capital.

Interpersonal Problems and the Therapeutic Alliance in Psychodynamic Psychotherapy

Articlehttp://deepblue.lib.umich.edu/bitstream/2027.42/96966/1/UMURF-Issue03_2006-AJaksa.pd

Interpreting Non-Recognition in De Facto States Engagement: The Case of Abkhazia’s Foreign Relations

This research looks at how Abkhazia’s political elites and foreign policy decision-makers in Russia, the EU, and the US, which engage with Abkhazia, interpret non-recognition and how this interpretation influences the formulation and implementation of their respective foreign policy objectives and strategies. Although there is an emerging literature on engagement this has tended to analyse it as a one-way interaction, while this research represents the first multi-sided account of foreign policy interaction of a de facto state. It focuses on a single case study of Abkhazia between October 1999 and November 2014. Non-recognition has largely been taken a priori as a negative constraining factor. The great majority of scholarship on de facto states takes non-recognition for granted and views it in substantive rather than in relational terms. Focusing on meaning and interpretation of non-recognition by elites in de facto states as well as decision-makers in the patron state and other significant engagers, allows for a better understanding of the interactions between de facto states and other actors in the international community. The research proceeds from a constructivist theoretical framework, claiming that non-recognition is ultimately what states (including de facto states) make of it. To capture both domestic and external dimensions, the concepts of ontological security and geopolitical role, respectively, are introduced. Methodologically, the data was gathered through process tracing and semi-structured elite interviews with policy elites and decision makers in Sukhum/i, Tbilisi, Brussels, Moscow, and Washington D.C. The main finding of this research is that the internal situation in the de facto state and wider geopolitical considerations influence interpretations of non-recognition (by both recognised actors as well as the de facto state itself), which in turn shape interaction between de facto states and other actors

A Program Evaluation Of A University Volunteer Program

Obrada i analiza dokumenata iz velikih kolekcija zahtijeva određenu organizaciju istih. Tomu služi grupiranje, postupak kojim će računalo, s obzirom na zadane parametre, odrediti grupu za dokumente iz kolekcije. Parametri se zadaju s obzirom na kolekciju i želje korisnika. Algoritam k-means jadan je od najpoznatijih algoritama, dok je poboljšanje dano algoritmom k-means++. Fuzzy k-means je meki algoritam grupiranja koji ovisno o zadanom parametru s određenim postotkom pripadnosti može svrstati dokumente u jednu ili više grupa. Algoritam multiple k-means++ svodi se na izvođenje algoritma k-means++ određeni broj puta. Navedeni algoritmi svrstavaju dokumente u zadani broj grupa, dok algoritam DBSCAN kao parametar ne prima željeni broj grupa, nego najmanji broj točaka u grupi i okolinu ɛ. Ako točka sadrži barem traženi broj točaka u svojoj okolini tada može postati jezgrom grupe, a u suprotnom će biti svrstana u neku grupu ili biti označena kao šum. Algoritam DBSCAN prilagodljiviji je od ostalih algoritama, ali je teško odrediti parametre s kojima bi se dobili dobri rezultati jer jako ovise o kolekciji.Analysis of large collections can be a difficult task that can be simplified by dividing the collection into groups. Each group contains documents that are somehow similar. The process of dividing the collection can be done manually by a human, or automatically by a machine. Clustering is an automated process of dividing the collection into groups (clusters), with respect to parameters set by the user. K-means is a well known clustering algorithm, an improved version also exists, called k-means++. Both algorithms cluster a data point into one cluster. A fuzzy k-means algorithm is different, because it can cluster one data point into several clusters, depending on the user requirements. The DBSCAN algorithm, unlike aforementioned algorithms, does not require a fixed number of groups, but a minimum number of points in the group and ɛ neighborhood size. If a data point contains the minimum number of data points needed in it's neighborhood it can then become a cluster core, otherwise it will be grouped later in the process or labeled as noise. Both parameters are hard to set properly, because they severely depend on the collection

Liquefaction Assessment Using the CPT and Accounting for Soil Ageing

Due to its continuous data recording capability, excellent repeatability and accuracy, relatively low cost and simplicity of operation, the cone penetration test (CPT) offers enhanced liquefaction assessment over its predecessor the standard penetration test (SPT). However, soil ageing, which influences the cyclic resistance ratio (CRR), is difficult, if not impossible, to be detected by the CPT due to disturbance during the test. This situation may lead to excessively conservative estimation of CRR values which result in conservative assessment of liquefaction potential. This paper presents and discusses liquefaction assessment using the CPT and methods for accounting for soil ageing. A field study, conducted at Gillman, South Australia, is presented and the study site is assessed for liquefaction potential. This paper also explores the influence of soil ageing on the subsequent liquefaction assessment

Simple predictors of TcT_c in superconducting cuprates reveal role of interactions between effective Wannier orbitals in the d−pd-p 3-band model

At optimal doping, different cuprate compounds can exhibit vastly different critical temperatures for superconductivity ($T_c$), ranging from about 20 K to about 135 K. The precise properties of the lattice that determine the magnitude of the $T_c$ are currently unknown. In this paper, we investigate the dependence of the optimal doping $T_c$ on the parameters of the Emery ($d-p$) model for the CuO$_2$ planes in the cuprates. We show that the best scaling is obtained not with the parameters of the model written in the real ($d/p$-orbital) space, but rather written in the space of effective Wannier orbitals. In this basis, one obtains a model of three sublattices coupled through all possible 4-point interactions. We identify multiple predictor variables that fit the experimental $T_c$ to about $\pm4$ K and that depend on the coupling constants in the transformed Hamiltonian.Comment: 6 pages, 2 figures + supp. mat. 15 pages, 10 figure

Financial Markets Equilibrium with Heterogeneous Agents

This paper presents an equilibrium model in a pure exchange economy when investors have three possible sources of heterogeneity. Investors may dier in their beliefs, in their level of risk aversion and in their time preference rate. We study the impact of investors heterogeneity on the properties of the equilibrium. In particular, we analyze the consumption shares, the market price of risk, the risk free rate, the bond prices at dierent maturities, the stock price and volatility as well as the stock's cumulative returns, and optimal portfolio strategies. We relate the heterogeneous economy with the family of associated homogeneous economies with only one class of investors. We consider cross sectional as well as asymptotic properties.equilibrium, heterogeneous agents, volatility, optimal portfolios, survival, yield curve, long yield