doi: 10.1685/journal.caim.484

A fractional Hamilton Jacobi Bellman equation for scaled limits of controlled Continuous Time Random Walks

Vassili N Kolokoltsov, Maria A Veretennikova

Abstract


In the article we study a controlled Continuous Time Random Walk and their position-dependent extensions. We heuristically derive the optimal payoff function equa- tions for their scaling limits. The general equation for the corresponding optimal payoff of the limiting process may be called a fractional Hamilton Jacobi Bellman equation. This paper is an improved version of the preprint: M. Veretennikova and V. Kolokoltsov. Controlled continuous time ran- dom walks and fractional Hamilton Jacobi Bellman equations. Arxiv, http://arxiv.org/abs/1203.6333, 2012.

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Communications in Applied and Industrial Mathematics
ISSN: 2038-0909