Constandina Koki

In this paper, we study unimodality conditions for distributions that describe markets with stochastic demand. Such conditions naturally emerge in the analysis of game-theoretic models of market competition (Cournot games) and supply chain coordination (Stackelberg games). We express the price elasticity of expected demand in terms of the mean residual life (MRL) function of the demand distribution and characterize optimal prices or equivalently, points of unitary elasticity, as fixed points of the MRL function. This leads to economic interpretable conditions on the demand distribution under which such fixed points exist and are unique. We find that markets with increasing price elasticity of expected demand that eventually become elastic correspond to distributions with decreasing generalized mean residual life (DGMRL) and finite second moment. DGMRL distributions strictly generalize the widely used increasing generalized failure rate (IGFR) distributions. We further elaborate on t...

In the big data era, the study of complex multiparameter problems is more than necessary. The development of Machine Learning techniques enhanced the inferential ability of statistical models. In this direction, by leveraging Machine Learning techniques, we propose a new predictive Hidden Markov model with exogenous variables, within a Bayesian framework, for joint inference and variable selection. We propose a computational Markov Chain Monte Carlo algorithm that offers improved forecasting and variable selection performance, compared to existing benchmark models. Our methodology is applied in various simulated and real datasets, such as realized volatility data and cryptocurrency return series. Furthermore, we exploit the Bayesian methodology in implementing the X-ray luminosity function of the Active Galactic Nuclei under the assumption of Poisson errors in the determination of X-ray fluxes and estimation uncertainties.Στην εποχή της πληροφορίας και του μεγάλου όγκου δεδομένων, η...

Στην εποχή της πληροφορίας και του μεγάλου όγκου δεδομένων, η ανάπτυξη τεχνικών εκμάθησης (Machine Learning) με τη βοήθεια των ηλεκτρονικών υπολογιστών, μας έδωσε τη δυνατότητά να μελετήσουμε πολύπλοκα προβλήματα. Η μη εύρεση αναλυτικών λύσεων για εκτίμηση των παραμέτρων διάφορων υποδειγμάτων έχει οδηγήσει στην άνθιση της Μπεϋζιανής συμπερασματολογίας. Σε αυτή την κατεύθυνση στρέφεται και η παρούσα Διδακτορική διατριβή. Με εργαλεία τις τεχνικές εκμάθησης, ασχολούμαστε με τη μοντελοποίηση πολύπλοκων πολυμεταβλητών Μπεϋζιανών μοντέλων. Η διατριβή αυτή χωρίζεται σε δύο βασικά ερευνητικά πεδία. Το πρώτο πεδίο αφορά την ανάπτυξη Κρυμμένων Μαρκοβιανών μοντέλων (Hidden Markov models) με πεπερασμένα στάδια (states/regimes) και εξωγενείς επεξηγηματικές μεταβλητές. Ιδιαίτερα, επεκτείνουμε προηγούμενα Κρυμμένα Μαρκοβιανά μοντέλα, προτείνοντας συγκεκριμένη μεθοδολογία, βασιζόμενη στην Polya-Gamma τεχνική αύξησης δεδομένων (data augmentation) για την εκτίμηση των παραμέτρων, ενώ ταυτόχρονα επιλέ...

Pricing decisions are often made when market information is still poor. In turn, existing theoretical models often reason about the response of optimal prices to changing market characteristics without exploiting all available information about the demand distribution. Our aim is to develop a theory for the optimization and systematic comparison of prices between different instances of the same market under various forms of knowledge about the corresponding demand distributions. We revisit the classic problem of monopoly pricing under demand uncertainty in a vertical market with an upstream supplier and multiple forms of downstream competition between arbitrary symmetric retailers. In all cases, demand uncertainty falls to the supplier who acts first and sets a uniform price before the retailers observe the realized demand and place their orders. Our main methodological contribution is that we express the price elasticity of expected demand in terms of the mean residual demand (MRD) function of the demand distribution. This leads to a closed form characterization of the points of unitary elasticity that maximize the supplier's profits and the derivation of a mild unimodality condition for the supplier's objective function that generalizes the widely used increasing generalized failure rate (IGFR) condition. A direct implication is that optimal prices between different markets can be ordered if the markets can be stochastically ordered according to their MRD functions or equivalently, their elasticities. Using the above, we develop a systematic framework to compare optimal prices between different market instances via the rich theory of stochastic orders. This leads to comparative statics that challenge previously established economic insights about the effects of market size, demand transformations and demand variability on monopolistic prices.

We consider Non-Homogeneous Hidden Markov Models (NHHMMs) for forecasting univariate time series. We introduce two state NHHMMs where the time series are modeled via different predictive regression models for each state. Also, the time-varying transition probabilities depend on exogenous variables through a logistic function. In a hidden Markov setting, inference for logistic regression coefficients becomes complicated and in some cases impossible due to convergence issues. To address this problem, we use a new latent variable scheme, that utilizes the Pólya-Gamma class of distributions, introduced by Po13. Given an available set of predictors, we allow for model uncertainty regarding the predictors that affect the series both linearly -- in the mean -- and non-linearly -- in the transition matrix. Predictor selection and inference on the model parameters are based on a MCMC scheme with reversible jump steps. Single-step and multiple-steps-ahead predictions are obtained based on the...

We revisit the May and June 2012 Greek Parliamentary elections and the December 2014 Presidential election that was held by the June-elected Parliament. The three voting instances provide a political field experiment for the application of power indices and their interpretation in context. We model the Greek Parliament as a weighted majority game and assess voting power with the Shapley-Shubik, Holler and when relevant, Coleman's indices. Also, based on the actual events, we establish connections between parties and evaluate the Myerson index. We focus on the influence of institutional rules on the distribution of power among the elected political parties and add an alternative input to the ongoing political debate about the reform of both the Parliamentary and Presidential electoral system in Greece. Additionally, our findings contribute to the understanding of the coalition formation process in the particular context and provide empirical evidence on the performance of non-sel...

We revisit the May and June 2012 Greek Parliamentary elections and the December 2014 Presidential election that was held by the June-elected Parliament. The three voting instances provide a political field experiment for the application of power indices and their interpretation in context. We model the Greek Parliament as a weighted majority game and assess voting power with the Shapley-Shubik, Holler and when relevant, Coleman's indices. Also, based on the actual events, we establish connections between parties and evaluate the Myerson index. We focus on the influence of institutional rules on the distribution of power among the elected political parties and add an alternative input to the ongoing political debate about the reform of both the Parliamentary and Presidential electoral system in Greece. Additionally, our findings contribute to the understanding of the coalition formation process in the particular context and provide empirical evidence on the performance of non-sel...

The twin elections of 2012 in Greece had a manifest impact on the political scene of Greece and the European Union. In this paper we analyze the negotiations that took place after the May 06, 2012 and June 12, 2012 Parliamentary elections from a game-theoretic perspective. We model the different instances of the Parliament as weighted majority games and apply the Shapley-Shubik, Penrose-Banzhaf, Deegan-Packel and Public Good (Holler) indices. In this retrospective analysis, we aim to enhance our understanding on the reasons that led to certain outcomes in the voting processes and provide a benchmark for future comparisons in the still fluid political system and electoral framework. Our findings explain several attitudes of the political parties by comparing their P-Power and I-Power, highlight discrepancies in the distribution of power due to the disproportionality of the 2012 electoral rule and provide insight on the reasons that led both to the deadlock of the May negotiations and...

In this retrospective study, we revisit the twin Greek Parliamentary elections of May and June 2012 and the Presidential election that led to the dissolution of the Parliament in December 2014. Apart from their political impact at European-wide level, these elections provide a unique political field experiment for the application of power indices and their interpretation in context. We model three different Parliament configurations as weighted majority games and utilize available software to evaluate the Shapley-Shubik, Banzhaf (normalized and absolute), Deegan-Packel, Public Good (Holler) and when applicable the Myerson, Owen and Coleman's indices. By comparing the indices evaluations with the actual events, our findings have twofold implications. On a context specific level, we identify discrepancies between parliamentary seat share and formal power of each party. In this way, we understand parties' motives and strategic considerations that offer an alternative perspectiv...

We study a vertical market with an upsteam supplier and multiple downstream retailers. Demand uncertainty falls to the supplier who acts first and sets a uniform wholesale price before the retailers observe the realized demand and engage in retail competition. Our focus is on the supplier's optimal pricing decision. We express the price elasticity of expected demand in terms of the mean residual demand (MRD) function of the demand distribution. This allows for a closed form characterization of the points of unitary elasticity that maximize the supplier's profits and the derivation of a mild unimodality condition for the supplier's objective function that generalizes the widely used increasing generalized failure rate (IGFR) condition. A direct implication is that optimal prices between different markets can be ordered if the markets can be stochastically ordered according to their MRD functions or equivalently to their elasticities. Based on this, we apply the theory of ...

Conventional financial models fail to explain the economic and monetary properties of cryptocurrencies due to the latter's dual nature: their usage as financial assets on the one side and their tight connection to the underlying blockchain structure on the other. In an effort to examine both components via a unified approach, we apply a recently developed Non-Homogeneous Hidden Markov (NHHM) model with an extended set of financial and blockchain specific covariates on the Bitcoin (BTC) and Ether (ETH) price data. Based on the observable series, the NHHM model offers a novel perspective on the underlying microstructure of the cryptocurrency market and provides insight on unobservable parameters such as the behavior of investors, traders and miners. The algorithm identifies two alternating periods (hidden states) of inherently different activity -- fundamental versus uninformed or noise traders -- in the Bitcoin ecosystem and unveils differences in both the short/long run dynamics...

With Bitcoin, Ether and more than 2000 cryptocurrencies already forming a multi-billion dollar market, a proper understanding of their statistical and financial properties still remains elusive. Traditional economic theories do not explain their characteristics and standard financial models fail to capture their statistic and econometric attributes such as their extreme variability and heteroskedasticity. Motivated by these findings, we study Bitcoin and Ether prices via a Non-Homogeneous Pólya Gamma Hidden Markov (NHPG) model that has been shown to outperform its counterparts in conventional financial data. The NHPG algorithm has good in-sample performance and identifies both linear and non-linear effects of the predictors. Our results indicate that all price series are heteroskedastic with frequent changes between the two states of the underlying Markov process. In a somewhat unexpected result, the Bitcoin and Ether prices, although correlated, are significantly affected by differ...

We study the Bitcoin and Ether price series under a financial perspective. Specifically, we use two econometric models to perform a two-layer analysis to study the correlation and prediction of Bitcoin and Ether price series with traditional assets. In the first part of this study, we model the probability of positive returns via a Bayesian logistic model. Even though the fitting performance of the logistic model is poor, we find that traditional assets can explain some of the variability of the price returns. Along with the fact that standard models fail to capture the statistic and econometric attributes—such as extreme variability and heteroskedasticity—of cryptocurrencies, this motivates us to apply a novel Non-Homogeneous Hidden Markov model to these series. In particular, we model Bitcoin and Ether prices via the non-homogeneous Pólya-Gamma Hidden Markov (NHPG) model, since it has been shown that it outperforms its counterparts in conventional financial data. The transition pr...