نتایج جستجو برای: hamilton jacobi belman equation

تعداد نتایج: 246225  

2012
Khai T. Nguyen

The course deals with the analysis of optimal control problems and of the related first order PDEs of dynamic programming. In particular, we shall focus our attention on time optimal control problems for linear and nonlinear systems. We shall present some recent results concerning the regularity and the compactness of viscosity solutions to Hamilton-Jacobi and Hamilton-Jacobi-Bellmann Equations...

2018

We give a short introduction to the stochastic calculus for Itô-Lévy processes, and review brie‡y the two main methods of optimal control of stochastic systems described by such processes, namely: (i) Dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equation (ii) The stochastic maximum principle and its associated adjoint backward stochastic di¤erential equation (BSDE). The two methods...

Journal: :Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 2012
V P Belavkin

A brief account of the quantum information dynamics and dynamical programming methods for optimal control of quantum unstable systems is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme, we exploit the separation theorem of filtering and cont...

2011
Eric A. Hansen

We consider how to use the Bellman residual of the dynamic programming operator to compute suboptimality bounds for solutions to stochastic shortest path problems. Such bounds have been previously established only in the special case that “all policies are proper,” in which case the dynamic programming operator is known to be a contraction, and have been shown to be easily computable only in th...

Journal: :Risk and Decision Analysis 2012
Andrew Ledvina Ronnie Sircar

We study continuous time oligopolies in which a small number of firms producing similar goods compete with one another by setting prices or quantities. We study a deterministic version of the problem using an asymptotic expansion of the relevant HJB partial differential equations. We find in this setting that for firms with highly differentiated goods, the type of competition matters little. Fo...

2004
XIAOWEI XU WALLACE J. HOPP

This paper studies the effects of customer heterogeneity and strategic behavior on dynamic pricing strategies. We assume that heterogenous customers arrive during a fixed season according to a Poisson process with intensity as a function of price. We obtain an implicit optimal pricing policy by solving a HJB equation. Our results show that optimal prices follow a submartingale (supermartingale)...

Journal: :Math. Meth. of OR 2014
Marcus Eriksson Jukka Lempa Trygve K. Nilssen

We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional Lévy process. We set up a valuation model in terms of a dynamic programming problem where the option can be exercised continuously in time. Here, the number of swing rights is given by a total volume constr...

2015
Erik J. Bekkers Remco Duits Alexey Mashtakov Gonzalo Sanguinetti

We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group SE(2) = R o S with a metric tensor depending on a smooth external cost C : SE(2) → [δ, 1], δ > 0, computed from image data. The method consists of a first step where geodesically equidistant surfaces are computed as a viscosity solution of a Ha...

Journal: :SIAM J. Financial Math. 2016
Mykhaylo Shkolnikov Ronnie Sircar Thaleia Zariphopoulou

We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochastic volatility). We analyze the associated forward performance SPDE and provide explicit formulae...

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