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Non-linearities are often important considerations in many applications in finance and economics such as pricing securities, computing equilibria, and conducting structural estimations. This paper generalizes the class of transform analysis for affine jump diffusions in Duffie, Pan, and Singleton (2000), which facilitates analytical treatment of a wide range of such problems. The authors apply their method to several examples, including option pricing, modeling nonlinear Taylor rules, modeling correlated defaults, and GMM estimation. They also provide detailed analysis of the power of their method in three concrete examples: pricing defaultable bonds with state-dependent recovery; computing the equilibrium of a Lucas economy with non-i.i.d. trees; and computing equilibrium in an economy with investors having heterogeneous beliefs about a variety of fundamentals.
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