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Stochastic Processes in Finance

  • Dilip B. Madan

    ()

    (Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742)

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    Stochastic processes arising in the description of the risk-neutral evolution of equity prices are reviewed. Starting with Brownian motion, I review extensions to L�vy and Sato processes. These processes have independent increments; the former are homogeneous in time, whereas the latter are inhomogeneous. One-dimensional Markov processes such as local volatility and local L�vy are discussed next. Finally, I take up two forms of stochastic volatility that are due to either space scaling or time changing. An encompassing discrete-time model closes the presentation.

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    File URL: http://www.annualreviews.org/doi/abs/10.1146/annurev.financial.050808.114506
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    Article provided by Annual Reviews in its journal Annual Review of Financial Economics.

    Volume (Year): 2 (2010)
    Issue (Month): 1 (December)
    Pages: 277-314

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    Handle: RePEc:anr:refeco:v:2:y:2010:p:277-314
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