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An infinite dimensional stochastic analysis approach to local volatility dynamic models. (English) Zbl 1331.91201
Summary: The difficult problem of the characterization of arbitrage free dynamic stochastic models for the equity markets was recently given a new life by the introduction of market models based on the dynamics of the local volatility. Typically, market models are based on ItĂ´ stochastic differential equations modeling the dynamics of a set of basic instruments including, but not limited to, the option underliers. These market models are usually recast in the framework of the HJM philosophy originally articulated for Treasury bond markets. In this paper we streamline some of the recent results on the local volatility dynamics by employing an infinite dimensional stochastic analysis approach as advocated by the pioneering work of L. Gross and his students.

91G70 Statistical methods; risk measures
91B24 Microeconomic theory (price theory and economic markets)
91B70 Stochastic models in economics