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Viscosity Solutions of an Infinite-Dimensional Black-Scholes-Barenblatt Equation

Journal Article · · Applied Mathematics and Optimization

We study an infinite-dimensional Black-Scholes-Barenblatt equation which is a Hamilton-Jacobi-Bellman equation that is related to option pricing in the Musiela model of interest rate dynamics. We prove the existence and uniqueness of viscosity solutions of the Black-Scholes-Barenblatt equation and discuss their stochastic optimal control interpretation. We also show that in some cases the solution can be locally uniformly approximated by solutions of suitable finite-dimensional Hamilton-Jacobi-Bellman equations.

OSTI ID:
21067472
Journal Information:
Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 47; ISSN 0095-4616
Country of Publication:
United States
Language:
English

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