Stability in a non-homogeneous Markov chain model in manpower systems

1981 ◽  
Vol 18 (4) ◽  
pp. 924-930 ◽  
Author(s):  
P.-C. G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Homogeneous Markov Chain ◽  
Initial Structure ◽  
Chain Model ◽  
Limiting Behaviour ◽  
Necessary And Sufficient

Necessary and sufficient conditions for stability, imposed firstly on the initial structure and the sequence of recruitment, and secondly on the initial structure and the sequence of expansion are provided in forms of two theorems. Also the limiting behaviour of the expected relative grade sizes is studied if we drop the conditions for stability imposed on the initial structure and keep the same sequence of expansion. Finally we examine the limiting behaviour of the expected grade sizes if we drop the assumption of a continuously expanding system.

Stability in a non-homogeneous Markov chain model in manpower systems

1981 ◽  
Vol 18 (04) ◽  
pp. 924-930 ◽  
Author(s):  
P.-C. G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Homogeneous Markov Chain ◽  
Initial Structure ◽  
Chain Model ◽  
Limiting Behaviour ◽  
Necessary And Sufficient

Necessary and sufficient conditions for stability, imposed firstly on the initial structure and the sequence of recruitment, and secondly on the initial structure and the sequence of expansion are provided in forms of two theorems. Also the limiting behaviour of the expected relative grade sizes is studied if we drop the conditions for stability imposed on the initial structure and keep the same sequence of expansion. Finally we examine the limiting behaviour of the expected grade sizes if we drop the assumption of a continuously expanding system.

On the limiting behaviour of a non-homogeneous Markovian manpower model with independent Poisson input

1982 ◽  
Vol 19 (2) ◽  
pp. 433-438 ◽  
Author(s):  
P.-C. G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Random Variable ◽  
Homogeneous Markov Chain ◽  
Chain Model ◽  
Poisson Random Variable ◽  
Poisson Input ◽  
Manpower System ◽  
Limiting Behaviour ◽  
Mutually Independent

We study the limiting behaviour of a manpower system where the non-homogeneous Markov chain model proposed by Young and Vassiliou (1974) is applicable. This is done in the cases where the input is a time-homogeneous and time-inhomogeneous Poisson random variable. It is also found that the number in the various grades are asymptotically mutually independent Poisson variates.

On the limiting behaviour of a non-homogeneous Markovian manpower model with independent Poisson input

1982 ◽  
Vol 19 (02) ◽  
pp. 433-438 ◽  
Author(s):  
P.-C. G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Random Variable ◽  
Homogeneous Markov Chain ◽  
Chain Model ◽  
Poisson Random Variable ◽  
Poisson Input ◽  
Manpower System ◽  
Limiting Behaviour ◽  
Mutually Independent

We study the limiting behaviour of a manpower system where the non-homogeneous Markov chain model proposed by Young and Vassiliou (1974) is applicable. This is done in the cases where the input is a time-homogeneous and time-inhomogeneous Poisson random variable. It is also found that the number in the various grades are asymptotically mutually independent Poisson variates.

Risk assessment for financial accounting: modeling probability of default

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Tobias Filusch
Keyword(s):  
Markov Chain ◽  
Business Cycle ◽  
Markov Chain Model ◽  
Accounting Standards ◽  
Financial Accounting ◽  
Homogeneous Markov Chain ◽  
Chain Model ◽  
Probability Of Default ◽  
Content Type ◽  
Term Structures

Purpose This paper aims to introduce and tests models for point-in-time probability of default (PD) term structures as required by international accounting standards. Corresponding accounting standards prescribe that expected credit losses (ECLs) be recognized for the impairment of financial instruments, for which the probability of default strongly embodies the included default risk. This paper fills the research gap resulting from a lack of models that expand upon existing risk management techniques, link PD term structures of different risk classes and are compliant with accounting standards, e.g. offering the flexibility for business cycle-related variations. Design/methodology/approach The author modifies the non-homogeneous continuous-time Markov chain model (NHCTMCM) by Bluhm and Overbeck (2007a, 2007b) and introduces the generalized through-the-cycle model (GTTCM), which generalizes the homogeneous Markov chain approach to a point-in-time model. As part of the overall ECL estimation, an empirical study using Standard and Poor’s (S&P) transition data compares the performance of these models using the mean squared error. Findings The models can reflect observed PD term structures associated with different time periods. The modified NHCTMCM performs best at the expense of higher complexity and only its cumulative PD term structures can be transferred to valid ECL-relevant unconditional PD term structures. For direct calibration to these unconditional PD term structures, the GTTCM is only slightly worse. Moreover, it requires only half of the number of parameters that its competitor does. Both models are useful additions to the implementation of accounting regulations. Research limitations/implications The tests are only carried out for 15-year samples within a 35-year span of available S&P transition data. Furthermore, a point-in-time forecast of the PD term structure requires a link to the business cycle, which seems difficult to find, but is in principle necessary corresponding to the accounting requirements. Practical implications Research findings are useful for practitioners, who apply and develop the ECL models of financial accounting. Originality/value The innovative models expand upon the existing methodologies for assessing financial risks, motivated by the practical requirements of new financial accounting standards.

scholarly journals A Non-Homogeneous Markov Chain Model to Study Ozone Exceedances in Mexico City

10.5772/59728 ◽  
2015 ◽  
Author(s):  
Eliane R. Rodrigues ◽  
Mario H. Tarumoto ◽  
Guadalupe Tzintzun
Keyword(s):  
Markov Chain ◽  
Mexico City ◽  
Markov Chain Model ◽  
Homogeneous Markov Chain ◽  
Chain Model

Convex Necessary and Sufficient Conditions for Density Safety Constraints in Markov Chain Synthesis

2015 ◽  
Vol 60 (10) ◽  
pp. 2813-2818 ◽  
Author(s):  
Behcet Acikmese ◽  
Nazli Demir ◽  
Matthew W. Harris
Keyword(s):  
Markov Chain ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Safety Constraints ◽  
Chain Synthesis ◽  
Necessary And Sufficient

scholarly journals Markov degree of the three-state toric homogeneous Markov chain model

2013 ◽  
Vol 55 (1) ◽  
pp. 161-188 ◽  
Author(s):  
David Haws ◽  
Abraham Martín del Campo ◽  
Akimichi Takemura ◽  
Ruriko Yoshida
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Homogeneous Markov Chain ◽  
Chain Model

Stability of maxima of random variables defined on a Markov chain

1972 ◽  
Vol 4 (2) ◽  
pp. 285-295 ◽  
Author(s):  
Sidney I. Resnick
Keyword(s):  
Markov Chain ◽  
Regularity Condition ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Finite Markov Chain ◽  
Finite Product ◽  
Normalizing Constants ◽  
Necessary And Sufficient

Consider maxima Mn of a sequence of random variables defined on a finite Markov chain. Necessary and sufficient conditions for the existence of normalizing constants Bn such that are given. The problem can be reduced to studying maxima of i.i.d. random variables drawn from a finite product of distributions πi=1mHi(x). The effect of each factor Hi(x) on the behavior of maxima from πi=1mHi is analyzed. Under a mild regularity condition, Bn can be chosen to be the maximum of the m quantiles of order (1 - n-1) of the H's.

scholarly journals Necessary and sufficient conditions for recurrence and transience of Markov chains, in terms of inequalities

1978 ◽  
Vol 15 (4) ◽  
pp. 848-851 ◽  
Author(s):  
Jean-François Mertens ◽  
Ester Samuel-Cahn ◽  
Shmuel Zamir
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Bounded Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Existence Of A Solution ◽  
Necessary And Sufficient ◽  
Irreducible Markov Chain

For an aperiodic, irreducible Markov chain with the non-negative integers as state space it is shown that the existence of a solution to in which yi → ∞is necessary and sufficient for recurrence, and the existence of a bounded solution to the same inequalities, with yk < yo, · · ·, yN–1 for some k ≧ N, is necessary and sufficient for transience.

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