Markov Chain and Its Use in Economic Modeling .


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Markov Chain and Its Utilization in Financial Demonstrating . Markov process Move network Meeting Probability capacity Expected qualities and Approach Choice . A stochastic procedure . has the Markov process if for all . and all t. A Markov procedure is portrayed by three components:.
Transcripts
Slide 1

Markov Chain and Its Use in Economic Modeling Markov prepare Transition framework Convergence Likelihood work Expected qualities and Policy Decision Ecocomic Modeling: PG

Slide 2

A stochastic procedure has the Markov procedure if for all and all t A Markov procedure is described by three components: Ecocomic Modeling: PG

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A normal Transition lattice Ecocomic Modeling: PG

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Chapman-Kolmogorov Equations Ecocomic Modeling: PG

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Likelihood Function for a Markov Chain Two employments of probability capacity to study elective histories of a Markov Chain to assess the parameter Ecocomic Modeling: PG

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Convergence of Markov Process with Finite States A Markov Process Converges when every component of the of the move network ways to deal with a breaking point this way. Process is stationary in this illustration. Reference: Stokey and Lucas (page 321) Ecocomic Modeling: PG

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Recurrent or engrossing State or Transient State in a Markov Chain S1 is the intermittent state at whatever point the procedure leaves, re-enters in it and remains there until the end of time. It is transient when it doesn\'t come back to S1 when it abandons it. Here S1 is the intermittent state at whatever point the procedure leaves, re-enters in it. S2 and S3 are transient. Ecocomic Modeling: PG

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Converging and Non-meeting Sequences Even Odd Ecocomic Modeling: PG

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One Example of Markov Chain Stochastic life cycle streamlining model (preparatory variant of Bhattarai and Perroni) Prob of Transient state Probability of intermittent state If transient High wage Low pay Ecocomic Modeling: PG Probability of being in Ambiguous state

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Impact of Risk Aversion and Ambiguity in Expected Wealth with Markov Process Ecocomic Modeling: PG

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Markov Decision issue (allude Ross (187)). Ecocomic Modeling: PG

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Use of Markov Chain in examination of Duopoly Sargent and Ljungqvist (133) Markov culminate harmony is the combine of significant worth capacities and a couple of arrangement capacities for i=1,2 that fulfills the above Bellman condition. Harmony is registered by in reverse acceptance and he advancing practices of firms by repeating forward for all possible future states. Ecocomic Modeling: PG

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Other Application of Markov Process Regime - Switch examination in financial time arrangement (Hamilton pp. 677-699; Harvey (285)) Industry venture under instability (SL chap 10) Stochastic element programming (SL part 8,9) Weak and solid meeting examination (SLChap 11-13) Arrow Securities ( Ljungqvist and Sargent Chapter 7). Life cycle utilization and sparing: An illustration Precautionary sparing Ecocomic Modeling: PG

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References: Ecocomic Modeling: PG

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Markov Chain Example in GAMS Ecocomic Modeling: PG

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Markov Chain Example in GAMS Ecocomic Modeling: PG

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Markov Chain Example in GAMS: Model Equations Ecocomic Modeling: PG

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Calculation of Weight Among Various States Ecocomic Modeling: PG

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