Controlled Markov processes and viscosity solutions

By Wendell H. Fleming, H. Mete Soner, H. M. Soner, Div Applied Mathematics, F. Fleming, Serpil Soner. 1992

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Citations in the corpus

Optimal control as a graphical model inference problem (2009, positive): “ quadratic Gaussian case [10]. It relies on the exponential relation between the value function in the Bellman equation and posterior marginal probabilities in the DBN and was previously exploited in [2, 11] for the non-linear continuous space and time Gaussian case and in [1] for the discrete case.”
A solution approach to valuation with unhedgeable risks (2001, background): “We refer the reader to the book of Friedlin (1985) or Fleming and Soner (1993) for more general assumptions.”
A Study of Reinforcement Learning in the Continuous Case by the Means of Viscosity Solutions (2000, methodology): “Moreover, from a result of uniqueness, we obtain the following theorem (whose proof is in Crandall et al. (1992) or Fleming and Soner (1993) ):”
Dynamic programming for stochastic target problems and geometric flows (2002, background): “Necessarily, this equation is a geometric flow equation as defined in Barles, Soner and Souganidis [4].”
Stochastic control for a class of nonlinear kernels and applications (2015, unknown): “ was to bypass the measurable selection argument by proving, under additional assumptions, a priori regularity of the value function. This was the strategy adopted, among others, by Fleming and Soner [39], and in the so-called weak DPP of Bouchard and Touzi [13], which has then been extended by Bouc”
Optimal dynamic excess-of-loss reinsurance and multidimensional portfolio selection (2010, methodology): “To solve the problem of maximizing expected exponential utility, we use the dynamic programming approach described in [ 5 ].”
An equilibrium model of irreversible investment (2001, background): “The problem faced by the central planner is of singular control type (for background on singular control of diffusion processes, see Fleming and Soner (1993, Ch. 8)). Similar problems arise in analysis of portfolio decisions under transactions costs. A good example of a (highly technical) rigorous a”
Time-Dependent Mean-Field Games in the Subquadratic Case (2013, background): “Then, see for instance [20], u is the value function for the following stochastic optimal control problem”
GUARANTEED MINIMUM WITHDRAWAL BENEFIT IN VARIABLE ANNUITIES (2008, unknown): “Using the standard procedure of deriving the HJB equation in stochastic control problems (Yong and Zhou 1999; Fleming and Soner 2006), the governing equation for V̄ is found to be ∂ V̄ ∂t + LV̄ + max γ h(γ ) = 0,(2.6) where LV̄ = σ 2 2 W2 ∂2V̄ ∂W2 + (r − α)W ∂ V̄ ∂W − r V̄ and h(γ ) = f (γ ) − γ ∂…”
Model Predictive Path Integral Control using Covariance Variable Importance Sampling (2015, unknown): “(3) The Stochastic Hamilton-Jacobi-Bellman equation [1], [11] for the type of system in (1) and for the cost function in (3) is given as:”
A Martingale Characterization of Consumption Choices and Hedging Costs with Margin Requirements (2000, methodology): “This is an immediate consequence of Theorem 4 and of Theorem IV.3.1 in Fleming and Soner (1993).”