Deterministic and Stochastic Optimal Control

By Pierre Devolder, Jacques Janssen, Raimondo Manca. 2013

1,188 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/39c94e7ecd86a9348ab20617c4e7f93f138d390c

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Citations in the corpus

A stochastic differential game for optimal investment of an insurer with regime switching (2011, methodology): “Since both the state process and the control are Markov, the dynamic programming principle can be applied (see, for example, Fleming and Rishel 1975 ).”
Optimal arbitrage under model uncertainty. (2011, methodology): “…Jacobi–Bellman (HJB) equation (∂/∂τ)U(τ,z) = L̂U(τ,z) on (0,∞)× (0,∞)n.(1.7) Relation to extant work : Stochastic control problems of the “maximal probability of containment” type were apparently pioneered by Van Mellaert and Dorato (1972) (see also Fleming and Rishel (1975), pages 157–158).”
Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit (2019, background): “On the other hand, the process X in (9) is Gaussian (in fact, all Gaussian diffusion processes are of this form), and the probability law of X 1 can be computed in closed form [Fleming and Rishel, 1975, Chap.”
A stochastic volatility model and optimal portfolio selection (2013, neutral): “;X ðtÞ ¼ x : ð7Þ For any function V ðx; y; tÞ 2 C2;2;1, define a differential operator ApV ðx; y; tÞ ¼ Vt þ xrVx þ ðl rÞpxVx þ p 2 2 g2x2Vxx þAðy; tÞVy þ 12B 2ðy; tÞVyy þ qpgxBðy; tÞVxy: Then the value function V ðx; y; tÞ satisfies the following Hamilton–Jacobi–Bellman equation (see Fleming and Ris”
Optimal mean-variance portfolio selection (2016, methodology): “[5]) that can be solved using a classic HJB approach.”
Optimization Problems (2019, background): “For a survey on the OCTand, in general, on the dynamic OP, see Fleming and Rishel (1975), Bardi and Capuzzo Dolcetta (1997), Yong and Zhou (1999), Fleming and Soner (2006), Kamien and Schwartz (1991).”
On the Relation Between Optimal Transport and Schrödinger Bridges: A Stochastic Control Viewpoint (2014, neutral): “If φ(x, t) solves (29) with terminal condition φ1(x), then, the same argument as before shows that u∗(x, t) = ∇ ln φ(x, t) is optimal and that S(x, t) = − ln φ(x, t) = infu J (u) is the value function [55] of the control problem.”
$N$-player games and mean-field games with absorption (2016, methodology): “However, a careful inspection of the proof by Fleming and Rishel shows that we can apply their approximation argument excluding the last sentence.”
Latin Hypercube Sampling and Partial Rank Correlation Coefficient Analysis Applied to an Optimal Control Problem (2012, methodology): “According to Fleming and Rishel [20], we must begin our analysis by first showing that the optimal control exists.”
Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems (2013, background): “…of the control problem, or to consider its semi-continuous envelope, and then to utilize the separability property of the time-state space (see e.g. Fleming and Rishel (1975, [22]), Krylov (1980, [30]), Fleming and Soner (1993, [23]), Touzi (2012, [43]), Bouchard and Touzi (2011, [6]), etc.).”