On a class of path-dependent singular stochastic control problems
Elie, Romuald; Moreau, Ludovic; Possamaï, Dylan (2018), On a class of path-dependent singular stochastic control problems, SIAM Journal on Control and Optimization, 56, 5, p. 3260-3295. 10.1137/17M1114235
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01481393
Journal nameSIAM Journal on Control and Optimization
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Abstract (EN)This paper studies a class of non-Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a Z-constrained BSDE, with dynamics associated to a non singular underlying forward process. Due to the non-Markovian environment, our main argumentation relies on the use of comparison arguments for path dependent PDEs. Our representation allows in particular to quantify the regularity of the solution to the singular stochastic control problem in terms of the space and time initial data. Our framework also extends to the consideration of degenerate diffusions, leading to the representation of the solution as the infimum of solutions to Z-constrained BSDEs. As an application, we study the utility maximization problem with transaction costs for non-Markovian dynamics.
Subjects / Keywordssingular control; constrained BSDEs; path-dependent PDEs; viscosity solutions; transaction costs; regularity
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