Prof. Panagiotis-Christos Vassiliou
Department of Statistical Science, University College London, Gower st, London WC1E 6BT, UK
Emeritus Professor, Mathematics Depaertment, Aristotle Unive...
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Academic Career Length
21Years (2006-Present)
(Calculated once Scilit publication data is synced: current year − year of first publication + 1)
Representative Publications
View All Publications1 March 2006 in Advances in Applied Probability
Journal Article
AVAglaia Vasileiou
Aglaia VasileiouPanagiotis-Christos VassiliouWe model the evolution of the credit migration of a corporate bond as an inhomogeneous semi-Markov chain. The valuation of a defaultable bond is done with the use of the forward probability of no default up to maturity time. It is proved that, under the forward probability measure, the semi-Markov property is maintained. We find the functional relationships between the forward transition probability sequences and the real-world probability sequences. The stochastic monotonicity properties of the inhomogeneous semi-Markov model, which play a prominent role in these issues, are studied in detail. Finally, we study the term structure of credit spread, provide an algorithm for the estimation of the forward probabilities of transitions under the risk premium assumptions, and present an estimation method for the real-world probability sequences.
Journal Article
Panagiotis-Christos Vassiliou
Andreas C. GeorgiouProbability resembles the ancient Roman God Janus since, like Janus, probability also has a face with two different sides, which correspond to the metaphorical gateways and transitions between the past and the future
Journal Article
Panagiotis-Christos VassiliouFor a -inhomogeneous semi-Markov chain and -inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a -inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the -inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.
Journal Article
Panagiotis-Christos VassiliouA more realistic way to describe a model is the use of intervals which contain the required values of the parameters. In practice we estimate the parameters from a set of data and it is natural that they will be in confidence intervals. In the present study, we study Non-Homogeneous Markov Systems (NHMS) processes for which the required basic parameters are in intervals. We call such processes Non-Homogeneous Markov Set Systems (NHMSS). First we study the set of the relative expected population structure of memberships and we prove that under certain conditions of convexity of the intervals of the parameters the set is compact and convex. Next, we establish that if the NHMSS starts with two different initial distributions sets and allocation probability sets under certain conditions, asymptotically the two expected relative population structures coincide geometrically fast. We continue proving a series of theorems on the asymptotic behavior of the expected relative population structure of a NHMSS and the properties of their limit set. Finally, we present an application for geriatric and stroke patients in a hospital and through it we solve problems that surface in an application.
4 January 2018 in Methodology and Computing in Applied Probability
Journal Article
Panagiotis-Christos VassiliouIn the present we establish Laws of Large Numbers for Non-Homogeneous Markov Systems and Cyclic Non-homogeneous Markov systems. We start with a theorem, where we establish, that for a NHMS under certain conditions, the fraction of time that a membership is in a certain state, asymptotically converges in mean square to the limit of the relative population structure of memberships in that state. We continue by proving a theorem which provides the conditions under which the mode of covergence is almost surely. We continue by proving under which conditions a Cyclic NHMS is Cesaro strongly ergodic. We then proceed to prove, that for a Cyclic NHMS under certain conditions the fraction of time that a membership is in a certain state, asymptotically converges in mean square to the limit of the relative population structure in the strongly Cesaro sense of memberships in that state. We then proceed to establish a founding Theorem, which provides the conditions under which, the relative population structure asymptotically converges in the strongly Cesaro sense with geometrical rate. This theorem is the basic instrument missing to prove, under what conditions the Law of Large Numbers for a Cycl-NHMS is with almost surely mode of convergence. Finally, we present two applications firstly for geriatric and stroke patients in a hospital and secondly for the population of students in a University system.
Journal Article
Panagiotis-Christos VassiliouIn this article we study the asymptotic behaviour of the expected population structure of a Markov system that lives in a general state space (MSGS) and its rate of convergence. We continue with the study of the asymptotic periodicity of the expected population structure. We conclude with the study of total variability from the invariant measure in the periodic case for the expected population structure of an MSGS.
About Me
Panagiotis-C.G. Vassiliou is an Emeritous Professor at the Department of Mathematics, Aristotle University of Thessaloniki and was a Visiting Professor and an Honorary Professor at the Department of Statistical Sciences, University College London for more than twelve years. He has spend research and teaching time in cronological order at Ulster University, Ioannina University, Aristotle University of Thessaloniki, University College London. He has also spend research time at Imperial College London. He has also taught at the London Taught Course Center (LTCC), for 3rd and 4th year Ph.D. students of UCL, LSE, King’s, Brunel and Kent. He has published more than 60 papers, indexed in the web of science mainly in the areas of non-homogeneous Markov systems, non-homogeneous semi Markov systems, and stochastic finance. His publications time span is 52 years and the two journals with the highest frequency were Journal of Applied Probability (11 papers, in 140 pages) and Linear Algebra and its Applications (8 papers in 224 pages). He has also written 5 books in English (J. Wiley, Chapman and Hall, UCL, MDPI) and 14 books in Greek. He has been the supervisor of 9 completed Ph.D thesis. Academic Services: Referee in more than 25 scientific journals, Guest Editor in 2 scientific journals and currently a member on the Editorial Board of Mathematics. Metrics: more than 940 citations in Web of Science, H-index =20.