| Purdue Computational Finance Program | |
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Branching and Interacting Particle Systems for Stochastic PDEs, and a Connection to Stochastic Portfolio Optimization?
March 6, 2002
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Abstract:
Stochastic PDEs (SPDEs) are not generally associated with the stochastic theory of finance [except in the context of the theory of random interest rates]. The problem of maximizing the expected future wealth of a portfolio of stochastic stocks and a risk-free asset is closely related to a new type of optimal stochastic filtering of diffusion processes. A new particle method of del Moral, Jacod, and Protter for addressing this filering issue is itself closely related to branching and interacting particle systems. We will describe a wide class of SPDEs that can be approximated by a new type of branching and interacting particle system, generalizing a known efficient particle method for classical non-linear stochastic filtering. We will TRY to (i) explain in what sense there may be a real connection between these SPDEs and the portfolio optimization problem, and (ii) describe interesting mathematical and practical questions that emerge as a consequence. |
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