Editing Markov chain (section)

===Economics and finance===
Markov chains are used in finance and economics to model a variety of different phenomena, including the distribution of income, the size distribution of firms, asset prices and market crashes. [[D. G. Champernowne]] built a Markov chain model of the distribution of income in 1953.<ref>{{cite journal| title=A model of income distribution | last=Champernowne | first=D | journal=The Economic Journal | volume=63 | year=1953 | issue=250 | pages=318–51 |doi=10.2307/2227127| jstor=2227127 }}</ref> [[Herbert A. Simon]] and co-author Charles Bonini used a Markov chain model to derive a stationary Yule distribution of firm sizes.<ref>{{cite journal | title=The size distribution of business firms | last=Simon | first=Herbert | author2=C Bonini |  journal=Am. Econ. Rev. | year=1958 | volume=42 | pages=425–40}}</ref> [[Louis Bachelier]] was the first to observe that stock prices followed a random walk.<ref>{{cite journal | title=Théorie de la spéculation | last=Bachelier | first=Louis |  journal=Annales Scientifiques de l'École Normale Supérieure | year=1900 | volume=3 | pages=21–86| doi=10.24033/asens.476 | hdl=2027/coo.31924001082803 | hdl-access=free }}</ref> The random walk was later seen as evidence in favor of the [[efficient-market hypothesis]] and random walk models were popular in the literature of the 1960s.<ref>e.g.{{cite journal | title=The behavior of stock market prices | last=Fama | first=E | journal=Journal of Business | year=1965 | volume=38}}</ref> Regime-switching models of business cycles were popularized by [[James D. Hamilton]] (1989), who used a Markov chain to model switches between periods of high and low GDP growth (or, alternatively, economic expansions and recessions).<ref>{{cite journal|title=A new approach to the economic analysis of nonstationary time series and the business cycle |last=Hamilton |first=James |journal=Econometrica |year=1989 |volume=57 |pages=357–84|doi=10.2307/1912559|jstor=1912559|issue=2 |citeseerx=10.1.1.397.3582}}</ref> A more recent example is the [[Markov switching multifractal]] model of [[Laurent E. Calvet]] and Adlai J. Fisher, which builds upon the convenience of earlier regime-switching models.<ref>{{cite journal |title= Forecasting Multifractal Volatility|first1=Laurent E. |last1=Calvet |first2= Adlai J. |last2=Fisher |year=2001 |journal=[[Journal of Econometrics]] |volume=105 |issue=1 |pages=27–58 |doi=10.1016/S0304-4076(01)00069-0 |url=http://archive.nyu.edu/handle/2451/26894 }}</ref><ref>{{cite journal|title=How to Forecast long-run volatility: regime-switching and the estimation of multifractal processes |last=Calvet |first=Laurent |author2=Adlai Fisher |journal=Journal of Financial Econometrics |year=2004 |volume=2 |pages=49–83|doi=10.1093/jjfinec/nbh003 |citeseerx=10.1.1.536.8334 }}</ref> It uses an arbitrarily large Markov chain to drive the level of volatility of asset returns.

Dynamic macroeconomics makes heavy use of Markov chains. An example is using Markov chains to exogenously model prices of equity (stock) in a [[general equilibrium]] setting.<ref>{{cite web |last1=Brennan |first1=Michael |first2=Yihong |last2=Xiab |title=Stock Price Volatility and the Equity Premium |website=Department of Finance, the Anderson School of Management, UCLA |url=http://bbs.cenet.org.cn/uploadImages/200352118122167693.pdf |archive-url=https://web.archive.org/web/20081228200849/http://bbs.cenet.org.cn/uploadImages/200352118122167693.pdf |url-status=dead |archive-date=2008-12-28}}</ref>

[[Credit rating agency|Credit rating agencies]] produce annual tables of the transition probabilities for bonds of different credit ratings.<ref>{{Cite web|website=Columbia University|url=http://www.columbia.edu/~ww2040/4106S11/MC_BondRating.pdf|archive-url=https://web.archive.org/web/20160324112501/http://www.columbia.edu/~ww2040/4106S11/MC_BondRating.pdf|url-status=dead |title=A Markov Chain Example in Credit Risk Modelling |archive-date=March 24, 2016}}</ref>