Numerical Methods for Stochastic Control Problems in Continuous Time

By Harold J. Kushner. 2000

1,790 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Finance

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Citations in the corpus

Increasing the Action Gap: New Operators for Reinforcement Learning (2015, background): “…underpins Baird’s advantage learning (Baird 1999), designed for continuous time control, and occurs naturally when considering the discretized solution of continuous time and space MDPs (e.g. Munos and Moore 1998; 2002), whose limit is the Hamilton-Jacobi-Bellman equation (Kushner and Dupuis 2001).”
European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs (2003, neutral): “The method of solution of such problems was suggested by Kushner (see, for example, Kushner and Martins (1991) and Kushner and Dupuis (1992)).”
Investment Shocks and Asset Prices (2011, methodology): “I solve the social planner’s value function f(ω) through value function and policy iteration following Kushner and Dupuis (1992).”
Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions) (2012, result): “This point of view would relate our results with Kushner (2002), Kushner and Dupuis (2001).”
Ordered Upwind Methods for Static Hamilton-Jacobi Equations: Theory and Algorithms (2003, methodology): “PDE; a number of related methods, treatment of more general control problems (including the case f1 = 0), and the proof of convergence can be found in [25, 26], and [18].”
Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule (2003, background): “…by Boyle (1979) into the option pricing literature, have become increasingly popular for pricing complex derivative securities (see Geweke (1996) for an overview of 1See Kushner and Dupuis (1992) for a complete treatment of the use of lattice methods to solve general optimal control problems.”
A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS (2005, background): “However, let us mention the pioneering work by Kushner in 1977 (see [28] and also [29]) in which Markov chain approximation was first introduced, including its links with the finite difference method.”
Variational representations for continuous time processes (2011, background): “1, and a chattering lemma as in [15], Theorem 3.”
Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance (2007, methodology): “6) as the solution of an infinite horizon controlled Markov chain [27].”
Patchy Solutions of Hamilton-Jacobi-Bellman Partial Differential Equations (2007, background): “There are several other approaches to solving HJB PDEs, and a large literature, for example see [3], [6], [13], [9], [10], [16], [18], [19], [21] and their references.”
Reflected Diffusions Defined via the Extended Skorokhod Map (2006, methodology): “ons for the existence of a pathwise unique, strong solution to the SDER. Since the proof employs standard arguments that are used to construct reﬂected diﬀusions deﬁned via the SP (see, for instance, [20, 45]) or, more generally, to construct solutions REFLECTED DIFFUSIONS DEFINED VIA THE EXTENDED S”