Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE

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Subfields: Finance

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Counterparty Risk Valuation: A Marked Branching Diffusion Approach (2012, unknown): “4 in [17]).”
TRADING WITH SMALL PRICE IMPACT (2014, background): “(∂xxv0σSσ⊤ S θ 0)(ζ) := µS∂xv0 +σS¯σ⊤ 0 D(s,y)(∂xv 0)(ζ), (3.5) with σ¯0 := σS σY . Indeed, given suﬃcient regularity of the coeﬃcients of the SDEs, standard veriﬁcation arguments (compare, e.g., [57]) show that the Markovian feedback policy θ0 u := θ 0 u,St,s,y u ,Xˆt,s,y,x,θ 0 u ,Y t,y u , u∈ ”
Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems (2013, methodology): “In particular, by choosing the stopping time ¯ τ in a local way, one can obtain local characterization of the value function, such as the viscosity solution property (see e.g Touzi [43]).”
Mean field and n‐agent games for optimal investment under relative performance criteria (2017, methodology): “t and thus admissible. Using the explicit form (14) and the 8 admissibility of this candidate control, we can establish a veriﬁcation theorem following well known arguments in stochastic optimization [24, 50, 55]. Alternatively, we note that the stochastic optimization problem (11) can be alternativ”
Option Hedging with Smooth Market Impact (2016, unknown): “With (4), the system (9,10) has a strong solution (𝑃𝑡, 𝑌𝑡) for 𝜃𝑡 ∈ Θ [Touzi, 2013, sect.”