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Rozprawy doktorskie na temat „Markov Switching”

Autor: Grafiati
Data publikacji: 4 czerwca 2021
Data aktualizacji: 25 lipca 2025

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1

Blagov, Boris [Verfasser], and Michael [Akademischer Betreuer] Funke. "Four Essays on Markov-Switching DSGE and Markov-Switching VAR Models / Boris Blagov. Betreuer: Michael Funke." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2016. http://d-nb.info/1103233408/34.

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Mazali, Rogério. "Improving mutual fund market timing measures: a markov switching approach." reponame:Repositório Institucional do FGV, 2001. http://hdl.handle.net/10438/55.

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Made available in DSpace on 2008-05-13T13:16:08Z (GMT). No. of bitstreams: 1 1429.pdf: 435505 bytes, checksum: 014d927923de455f14c28a151a16c5e1 (MD5) Previous issue date: 2001-07-31<br>Market timing performance of mutual funds is usually evaluated with linear models with dummy variables which allow for the beta coefficient of CAPM to vary across two regimes: bullish and bearish market excess returns. Managers, however, use their predictions of the state of nature to deÞne whether to carry low or high beta portfolios instead of the observed ones. Our approach here is to take this into accou
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Koh, You Beng, and 辜有明. "Bayesian analysis in Markov regime-switching models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B48521644.

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van Norden and Schaller (1996) develop a standard regime-switching model to study stock market crashes. In their seminal paper, they use the maximum likelihood estimation to estimate the model parameters and show that a two-regime speculative bubble model has significant explanatory power for stock market returns in some observed periods. However, it is well known that the maximum likelihood estimation can lead to bias if the model contains multiple local maximum points or the estimation starts with poor initial values. Therefore, a better approach to estimate the parameters in the regime-swi
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Santos, João Ramiro Rodrigues Simões dos. "Credit cycle identification: A Markov-switching application." Master's thesis, NSBE - UNL, 2014. http://hdl.handle.net/10362/11723.

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A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics<br>This project aims to study credit dynamics and to identify phases of credit cycles at the country level. We applied a Markov-switching (MS) autoregressive framework and a MS with regime-invariant macroeconomic variables to a broad concept of credit, domestic credit. We used a sample of 10 developed countries. MS identification power is assessed using smooth probabilities of low growth states, collected as a by-product of models estimation, again
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5

Karadag, Mehmet Ali. "Analysis Of Turkish Stock Market With Markov Regime Switching Volatility Models." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12609787/index.pdf.

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In this study, both uni-regime GARCH and Markov Regime Switching GARCH (SW-GARCH) models are examined to analyze Turkish Stock Market volatility. We investigate various models to find out whether SW-GARCH models are an improvement on the uni-regime GARCH models in terms of modelling and forecasting Turkish Stock Market volatility. As well as using seven statistical loss functions, we apply Superior Predictive Ability (SPA) test of Hansen (2005) and Reality Check test (RC) of White (2000) to compare forecast performance of various models.
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Hrabovska, Yevheniia <1994&gt. "A Markov-Switching Model for Bubble Detection in the Stock Market." Master's Degree Thesis, Università Ca' Foscari Venezia, 2017. http://hdl.handle.net/10579/10797.

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In this study I propose a model for the behaviour of the real stock market prices which allows for the existence of speculative bubbles. The bubble is assumed to follow a Markov-switching process with explosive and collapsing regimes. Inference on the model is performed by using observations on the deviations of the log prices from fundamentals. The fundamental prices are assumed to be a function of the discounted future dividends. Data used for estimation includes major stock market indices: SP 500, NASDAQ, Euro Stoxx 50 and major US companies.
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7

Humala, Acuña Alberto. "Markov switching modelling of interest rate pass-through." Thesis, University of Warwick, 2005. http://wrap.warwick.ac.uk/34676/.

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The first paper, "Interest rate pass-through and financial crises: do switching regimes matter? The case of Argentina", analyses the dynamic relationship between a money market (interbank) rate and different short-term lending rates by measuring their passthrough. Neither linear single-equation modelling nor linear multi-equation systems capture efficiently this relationship. Several financial crises alter the speed and degree of response to interbank rate shocks. Hence, a Markov switching VAR model shows the pass-through increases considerably for all market interest rates in a high-volatilit
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8

Cheng, Jie. "An Extended Class of Markov Switching Autoregressive Models." Thesis, University of Manchester, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.508540.

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9

Dutra, Livia Maria. "Exact Bayesian inference for Markov switching Cox processes." Universidade Federal de Minas Gerais, 2015. http://hdl.handle.net/1843/BUBD-9WGFNQ.

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Statistical modelling of point patterns is an important and common problem in several applications. An important point process, and a generalisation of the Poisson process, is the Cox process, where the intensity function is itself stochastic. We focus on Cox processes in which the intensity function is driven by a nite state space continuous-time Markov chain. We refer to these as Markov switching Cox processes (MSCP). We investigate some probabilistic properties of these processes, three new theorems for these processes are derived and we develop a Bayesian methodology to perform exact infer
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10

Fan, Qianzhu. "Stochastic heat equations with Markovian switching." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/stochastic-heat-equations-with-markovian-switching(8958d026-671e-4c63-a639-b4a7b120a968).html.

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This thesis consists of three parts. In the first part, we recall some background theory that will be used throughout the thesis. In the second part, we studied the existence and uniqueness of solutions of the stochastic heat equations with Markovian switching. In the third part, we investigate the properties of solutions, such as Feller property, strong Feller property and stability.
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11

Stockel, Jakob, and Niklas Skantz. "Regime shifts in the Swedish housing market - A Markov-switching model analysis." Thesis, KTH, Fastigheter och byggande, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-190178.

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Problem statement: Accurate and reliable forecasts of trends in the housing market can be useful information for market participants as well as policy makers. This information may be useful to minimize risk related to market uncertainty. Since the burst of the housing bubble in the early 1990s the price level of single-family houses has risen sharply in Sweden. The Swedish housing market has experienced an unusually long period of high growth rates in transaction prices which has opened up for discussions about the risk of another housing bubble. Business and property cycles have shown to cont
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12

Spagnolo, Fabio. "Nonlinear error-correction models with regime switching." Thesis, Birkbeck (University of London), 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368915.

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13

Chen, Max. "Business cycles and asset allocation : a Markov switching approach /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/7514.

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14

Zheng, Fei. "Learning and smoothing in switching Markov models with copulas." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSEC066/document.

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Les modèles de Markov à sauts (appelés JMS pour Jump Markov System) sont utilisés dans de nombreux domaines tels que la poursuite de cibles, le traitement des signaux sismiques et la finance, étant donné leur bonne capacité à modéliser des systèmes non-linéaires et non-gaussiens. De nombreux travaux ont étudié les modèles de Markov linéaires pour lesquels bien souvent la restauration de données est réalisée grâce à des méthodes d’échantillonnage statistique de type Markov Chain Monte-Carlo. Dans cette thèse, nous avons cherché des solutions alternatives aux méthodes MCMC et proposons deux orig
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15

Elidrissi, Imane <1991&gt. "applying Markov Chain switching model to Systemic Risk measures." Master's Degree Thesis, Università Ca' Foscari Venezia, 2015. http://hdl.handle.net/10579/6943.

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16

Chen, Ping. "Asset-liability management under regime-switching models." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B43223928.

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17

Zhu, Jinxia. "Ruin theory under Markovian regime-switching risk models." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/b40203980.

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18

Sajjad, Rasoul. "Value-at-risk in a Markov regime-switching GARCH framework." Thesis, University of Essex, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.438117.

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19

Moreira, Rafael Henrique Rodrigues. "Modelos multivariados com Markov Switching aplicados à política monetária brasileira." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/12/12140/tde-11072007-140949/.

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RESUMO No início de 1995 foi adotado no Brasil o Plano Real, tendo como um dos seus tripés de sustentação a busca pelo combate ao processo inflacionário crônico brasileiro que já se estendia por um longo período. Assim, a política monetária passou a ter um papel importante na determinação das variáveis macroeconômicas. Este trabalho busca analisar uma regra de política monetária que capte as variações ocorridas em todo o período do Plano Real, se estendendo até meados de 2005, bem como se deram as relações entre as variáveis econômicas neste período. A especificação proposta consiste na estima
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20

Valladares, Frederico Estrella Carneiro. "Real exchange rate misalignments : an application of Markov switching models." reponame:Repositório Institucional do FGV, 2002. http://hdl.handle.net/10438/7951.

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Submitted by Thalita Cristine Landeira Portela Faro (thalita.faro@fgv.br) on 2011-04-28T17:20:53Z No. of bitstreams: 1 1411742.pdf: 2808751 bytes, checksum: 52b19fd70b554fc88a8afcd218b2f07d (MD5)<br>Approved for entry into archive by Thalita Cristine Landeira Portela Faro(thalita.faro@fgv.br) on 2011-04-28T17:21:08Z (GMT) No. of bitstreams: 1 1411742.pdf: 2808751 bytes, checksum: 52b19fd70b554fc88a8afcd218b2f07d (MD5)<br>Made available in DSpace on 2011-04-28T17:21:19Z (GMT). No. of bitstreams: 1 1411742.pdf: 2808751 bytes, checksum: 52b19fd70b554fc88a8afcd218b2f07d (MD5) Previous iss
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21

Fardel, Victor <1990&gt. "Markov-Switching copula models for dependence analysis in time series." Master's Degree Thesis, Università Ca' Foscari Venezia, 2014. http://hdl.handle.net/10579/4815.

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22

Favotto, Alessandro <1989&gt. "Miglioramento del Marginal Expected Shortfall con un modello Markov Switching." Master's Degree Thesis, Università Ca' Foscari Venezia, 2014. http://hdl.handle.net/10579/5168.

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Il seguente lavoro analizza il Marginal Expected Shortfall elaborato da diversi autori per la misurazione del rischio sistemico. Tale misura esprime il contributo al rischio sistemico complessivo che una singola impresa finanziaria trasmette al sistema finanziario, attraverso il valore atteso dei rendimenti equity dell’impresa condizionati all’evento sistemico, ossia il rendimento di mercato al di sotto di una determinata soglia, fissata esogenamente e spesso pari al suo VaR. In particolare la seguente analisi si propone di ricavare in maniera endogena il valore di tale soglia applicando ai d
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23

Chen, Ping, and 陈平. "Asset-liability management under regime-switching models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B43223928.

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24

Emery, Martin Banking &amp Finance Australian School of Business UNSW. "Studies into global asset allocation strategies using the markov-switching model." Publisher:University of New South Wales. Banking & Finance, 2008. http://handle.unsw.edu.au/1959.4/43098.

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This thesis presents the potential opportunities of global asset allocation and the possible enhancement of these opportunities from using a Markov Switching Model. The thesis extends upon previous conditional asset pricing studies in global asset allocation, such as those done by Ilamnen (1995), Harvey, Solnik and Zhou (1992) and Bilson (1993), where expected future returns are forecast based on conditional variables. The finding of these studies, and many others, are combined with the works on Markov Switching models and market segmentation theories to create a uniform structure for analys
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25

Schwendener, Alvin. "Regime-Switching Modell für die Schätzung von Marktdynamiken." St. Gallen, 2006. http://www.biblio.unisg.ch/org/biblio/edoc.nsf/wwwDisplayIdentifier/01654086001/$FILE/01654086001.pdf.

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26

Zhu, Jinxia, and 朱金霞. "Ruin theory under Markovian regime-switching risk models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40203980.

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27

Browne, Perry James. "The filtering of linear dynamic models with switching coefficients." Thesis, University of Sussex, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.295975.

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28

Cheung, Ka-chun. "Optimal asset allocation problems under the discrete-time regime-switching model." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B31311234.

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29

Castoe, Minna, and Teo Raspudic. "Option Pricing Under the Markov-switching Framework Defined by Three States." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-48808.

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An exact solution for the valuation of the options of the European style can be obtained using the Black-Scholes model. However, some of the limitations of the Black-Scholes model are said to be inconsistent such as the constant volatility of the stock price which is not the case in real life. In this thesis, the Black-Scholes model is extended to a model where the volatility is fully stochastic and changing over time, modelled by Markov chain with three states - high, medium and low. Under this model, we price options of both types, European and American, using Monte Carlo simulation.
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30

Cavicchioli, Maddalena <1985&gt. "Essays on Markov Switching models with applications in economics and finance." Doctoral thesis, Università Ca' Foscari Venezia, 2014. http://hdl.handle.net/10579/4602.

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In questa tesi studiamo alcuni problemi legati a modelli Markov Switching (MS) e alle loro applicazioni in Economia e Finanza. Lo scopo del nostro studio è proporre soluzioni per la selezione del modello e per la stima di serie storiche multivariate soggette a cambiamenti di regime. Nel primo Capitolo presentiamo la letteratura che tratta di sistemi dinamici per modellare serie storiche con cambiamenti di regime. Nel secondo Capitolo studiamo il problema della determinazione del numero di regimi nell’ambito di modelli MS-VARMA e proponiamo alcuni metodi per la scelta del modello basati sulla
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31

Frühwirth-Schnatter, Sylvia. "MCMC Estimation of Classical and Dynamic Switching and Mixture Models." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1998. http://epub.wu.ac.at/698/1/document.pdf.

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In the present paper we discuss Bayesian estimation of a very general model class where the distribution of the observations is assumed to depend on a latent mixture or switching variable taking values in a discrete state space. This model class covers e.g. finite mixture modelling, Markov switching autoregressive modelling and dynamic linear models with switching. Joint Bayesian estimation of all latent variables, model parameters and parameters determining the probability law of the switching variable is carried out by a new Markov Chain Monte Carlo method called permutation sampling. Estima
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32

Fitzpatrick, Matthew Anthony. "Multi-regime models involving Markov chains." Thesis, The University of Sydney, 2016. http://hdl.handle.net/2123/14530.

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In this work, we explore the theory and applications of various multi-regime models involving Markov chains. Markov chains are an elegant way to model path-dependent data. We study a series of problems with non-homogeneous data and the various ways that Markov chains come into play. Non-homogeneous data can be modelled using multi-regime models, which apply a distinct set of parameters to distinct population sub-groups, referred to as regimes. Such models essentially allow for a practitioner to understand the nature (and in some cases the existence) of particular regimes within the data withou
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33

Awirothananon, Thatphong. "Information Criterion and Joint Determination of the Numbers of Regimes and Variables in Markov Switching Model: Simulation and Empirical Application." Thesis, Griffith University, 2009. http://hdl.handle.net/10072/367009.

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This study has three purposes. The first one is to examine the performance of four information criteria in the context of joint determination of the numbers of regimes and variables in Markov switching model (hereafter called the MS model). These criteria are Akaike (1974) information criterion (hereafter called AIC), Schwarz (1978) information criterion (hereafter called SIC), HQC (Hannan & Quinn 1979), and Markov switching criterion: MSC (Smith, Naik & Tsai 2006). The second purpose is to investigate further whether the numbers of regimes and variables in aggregate time series are similar to
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34

Schweizer, Andreas. "Analysis and optimisation of stable matching in combined input and output queued switches." Western Australian Telecommunications Research Institute, 2009. http://theses.library.uwa.edu.au/adt-WU2009.0078.

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Output queues in network switches are known to provide a suitable architecture for scheduling disciplines that need to provide quality of service (QoS) guarantees. However, today’s memory technology is incapable of meeting the speed requirements. Combined input and output queued (CIOQ) switches have emerged as one alternative to address the problem of memory speed. When a switch of this architecture uses a stable matching algorithm to transfer packets across the switch fabric, an output queued (OQ) switch can be mimicked exactly with a speedup of only two. The use of a stable matching algorith
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35

Darmanjian, Shalom. "Switching Hidden-Markov Model and hardware implementation for a Brain-Machine Interface." [Gainesville, Fla.] : University of Florida, 2005. http://purl.fcla.edu/fcla/etd/UFE0009426.

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Hayashi, Miwa. "Hidden Markov Models for analysis of pilot instrument scanning and attention switching." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/28912.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.<br>Includes bibliographical references (p. 132-134).<br>(cont.) high workload. The results of another flight simulation experiment demonstrated how the pilots' attention budgeting among these tasks estimated by HMM analysis, combined with the pilots' eye-movement statistical results, could enhance a cockpit display format study. The experiments demonstrated what additional insights can be obtained by incorporating HMM analysis into the analysis of pilots' eye movements.<br>Pilots' eye movements
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Kandemir, Kocaaslan Ozge. "An empirical investigation of the U.S. GDP growth : a Markov switching approach." Thesis, University of Sheffield, 2013. http://etheses.whiterose.ac.uk/3250/.

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This thesis is composed of three separate yet related empirical studies. In Chapter 2, we empirically investigate the effects of inflation uncertainty on output growth for the U.S. economy using both monthly and quarterly data over 1960-2009. Employing a Markov regime switching approach, we show that inflation uncertainty obtained from a Markov regime switching GARCH model exerts a negative and regime dependent impact on growth. We show that the negative impact of inflation uncertainty on growth is almost 2 times higher during the low growth regime than that during the high growth regime. We v
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Dridi, Mohamed Azzeddine <1985&gt. "Markov-switching correlation models for contagion analysis in commodity and stock markets." Master's Degree Thesis, Università Ca' Foscari Venezia, 2014. http://hdl.handle.net/10579/4833.

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Bulfone, Giacomo <1996&gt. "CDS spreads determinants and COVID-19 pandemic: A Bayesian Markov-switching model." Master's Degree Thesis, Università Ca' Foscari Venezia, 2020. http://hdl.handle.net/10579/17624.

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A deep understanding of the CDS spreads determinants is crucial for both policy makers interested in preserving the stability of the financial system and of financial insiders interested in managing credit and financial risks. The literature is mainly focused on the pre-subprime crisis, and either consider linear models with a large number of covariates or nonlinear models, such as regime Markov switching models, with a small number of explanatory variables and two regimes only. The aim of this thesis is to investigate the determinants of the European iTraxx corporate index considering a large
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Cheung, Ka-chun, and 張家俊. "Optimal asset allocation problems under the discrete-time regime-switching model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B31311234.

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41

Hurth, Tobias. "Invariant densities for dynamical systems with random switching." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/52274.

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We studied invariant measures and invariant densities for dynamical systems with random switching (switching systems, in short). These switching systems can be described by a two-component Markov process whose first component is a stochastic process on a finite-dimensional smooth manifold and whose second component is a stochastic process on a finite collection of smooth vector fields that are defined on the manifold. We identified sufficient conditions for uniqueness and absolute continuity of the invariant measure associated to this Markov process. These conditions consist of a Hoermander-
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Bergstrom, Peter D. Jr. "Markov chain models for all-optical shared memory packet switches." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/15361.

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43

Giroud, Xavier. "A Markov-Switching Equilibrium Correction Model for Intraday Futures and Stock Index Returns." St. Gallen, 2004. http://www.biblio.unisg.ch/org/biblio/edoc.nsf/wwwDisplayIdentifier/99630345001/$FILE/99630345001.pdf.

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44

Spagnolo, Nicola. "Nonlinearity testing, model selection and forecasting in the prescence of Markov regime switching." Thesis, Birkbeck (University of London), 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368914.

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45

Ye, Lingyun. "MARKOV REGIME-SWITCHING MODELS." 2012. http://hdl.handle.net/10222/15126.

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A regime-switching model is a time-series model in which parameters change values according to the regime at present time. While regime-switching models have been very popular in applied work, there is a lack of literature for simulation studies. New methods based on regime-switching models are often proposed with neither a proof of convergence nor simulations to demonstrate their basic properties. In this thesis, a detailed simulation study of regime-switching models is conducted. A strategy to generate initial search values in the parameter estimation of regime-switching models is proposed.
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46

Liao, Li-na, and 廖麗娜. "Double Markov Switching GARCH Models." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/37885659092168474199.

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碩士<br>逢甲大學<br>統計與精算所<br>94<br>In this paper we consider a double Markov switching GARCH model with fat-tailed error distribution for analyzing asymmetric effects on mean and volatility in financial markets. The characteristic of our model is that a regime variable from one state to another is an unobserved variable which is assumed to be a first-order Markov process. We use Markov chain Monte Carlo methods to make statistical inference. In simulation study, we set sensitivity analysis for transition probabilities and then compare these results. As to empirical study, we apply for our DMS-GARCH
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Lin, Jia-tien, and 林家田. "Option Pricing with Markov Switching VAR Process." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/37353688316936288372.

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碩士<br>國立高雄第一科技大學<br>風險管理與保險所<br>97<br>The purpose of this study is to investigate options which derivation from multivariate asset prices with Markov switching VAR(p). We employ the VARMA(p,q) model of Wang(2009) to obtain the option prices under risk neutral probability measure Q, Duan(1995), as q=0. However, the system changes in asset prices, there is a nonlinear adjustment, therefore joining the Markov-switching such that the model more in line with reality conditions. Carr and Madan(1998) point to give the characteristic function for concerning distribution, then we are able to get the op
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Huang, Jiun-Yan, and 黃俊諺. "Optimal Sales Promotion Strategy - Markov Switching Approach." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/77043446389566517164.

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碩士<br>國立交通大學<br>經營管理研究所<br>96<br>This paper investigates the optimal sales promotional strategy for the fiercely competitive FMCG (Fast Moving Consuming Goods) industry. We propose a Markov Switching Autoregressive model that incorporates AR(1) retailing demand process to capture nonlinear structure among promotional budget allocation, evaluation of promotion performance, and optimal promotion frequency within a given time span. The past promotion investment is evaluated first by comparing the changes in promotional budget allocation. We then apply Markov switching feedback rules to figure out
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Hung, Ming-Yang, and 洪銘陽. "Option pricing under Markov-switching GARCH Processes." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/77199291988680844155.

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碩士<br>東海大學<br>財務金融學系<br>95<br>This paper supplements the GARCH lattice algorithm for option pricing developed by Ritchken and Trevor (1999) and proposes possible modifications for Markov-switching lattice algorithm of Duan, Popova and Ritchken (2002), respectively. The numerical analyses show that our modifications for these existent lattice algorithms result in either less complicated procedures or faster rates of convergence. On the other hand, the Markov-switching GARCH models (MS-GARCH) which combine GARCH models with Markov-switching processes are highly flexibility and widely used in fi
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楊瑋勻. "Markov-Switching Model for Taiwan financial crises." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/51354153699664215607.

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