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Bayesian Estimation for Markov Modulated Asset Prices

A Stochastic Differential Equation (SDE) appearing in mathematical finance is considered in random environment by assuming that its two parameters are switched by an unobserved continuous-time Markov chain whose states represent the states of the market environment. A Dirichlet process is placed as a prior on the space of the sample paths of this chain, leading to a hierarchical Dirichlet model whose estimation is done both on simulated data and on a real data set from the Indian market.