The stochastic dynamics of business evaluations using Markov models

Current assessments of credit and financial risk based on deterministic analyses provide only a limited understanding of current and future solvency rates. This paper offers an alternate model using two-state Markov chains that produces a more comprehensive and accurate system and allows for broader and more complex analyses of present and future situations. Building off findings made in the development of the Altman Z-score, this proposed model applies stochastic processes and probability spaces to multivariate normal populations to account for the uncertainty of market conditions. Where one-step Markov chains demonstrate the relevance of this model for finite and infinite variables, the player’s downfall theorem indicates that the nth value is only dependent on the value before it. Using the Chapman-Kolmogorov equation, multi-step transition probabilities then lead to the final two-state Markov chain.