Applications of Markov Chains in Financial Risk Modeling: A Critical Literature Review

Markov chains represent financial risk as movement between credit or market states. This review examines how that representation supports credit migration analysis, default estimation, market risk forecasting, and portfolio decisions. It compares foundational models with subsequent research on rating heterogeneity, switching volatility, and economic conditions. The literature supports Markov models as interpretable tools for connecting current information to future loss distributions, but their usefulness depends on the state definition and stability of transition probabilities. A three-state numerical illustration shows how persistent adverse conditions can amplify cumulative default risk through repeated migration. The review distinguishes physical probabilities used for forecasting from risk-neutral probabilities used for pricing, and explains why a transition matrix alone cannot determine portfolio tail risk. It concludes that Markov models are most credible when combined with economic conditioning, explicit dependence assumptions, parameter uncertainty, and evaluation on observations unavailable during estimation.