Path-Dependent Optimal Stochastic Control and Viscosity Solution of Associated Bellman Equations
By Shanjian Tang, Fu Zhang. 2012
50 citations recorded by the source corpus.
In this paper we study the optimal stochastic control problem for a path-dependent stochastic system under a recursive path-dependent cost functional, whose associated Bellman equation from dynamic programming principle is a path-dependent fully nonlinear partial differential equation of second order. A novel notion of viscosity solutions is introduced. Using Dupire's functional It\^o calculus, we characterize the value functional of the optimal stochastic control problem as the unique viscosity solution to the associated path-dependent Bellman equation.
Subfields: Economics and Econometrics, Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/e4c8ab4cb8877ca46f7adc08e6e771d2b180f649
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In Economics and Econometrics
In Finance
- Giovanni Zanco
- Franco Flandoli
- Xicheng Zhang
- Massimiliano Gubinelli
- Lucio Galeati
- E. Fedrizzi
- Enrico Priola
- Feng-Yu Wang
In Management Science and Operations Research
Citations in the corpus
- An infinite-dimensional approach to path-dependent Kolmogorov equations (2013, background): “y, 2016, Vol. 44, No. 4, 2643–2693. This reprint differs from the original in pagination and typographic detail. 1 2 F. FLANDOLI AND G. ZANCO systems and viscosity solutions [see Peng and Wang (2011), Tang and Zhang (2013), Ekren et al. (2014), Ekren, Touzi and Zhang (2016a, 2016b), Cosso (2012)]. Al”