1,720,977 research outputs found
Second order Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control: L2 approach.
No full textHJB Equations for the Optimal Control of DDE’s with State Constraints, I: Regularity of Viscosity Solutions
No full textHJB Equations for the Optimal Control of Differential Equations with Delays and State Constraints, II: Optimal Feedbacks and Approximations
No full textHJB equations for the optimal control of differential equations with delays and state constraints, I: Regularity of viscosity solutions
No full textWe study a class of optimal control problems with state constraints, where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular, the so-called models with time to build; see [P. K. Asea and P. J. Zak, J. Econom. Dynam. Control, 23 (1999), pp. 1155-1175; M. Bambi, J. Econom. Dynam.. Control, 32 (2008), pp. 1015-1040; F. E. Kydland and E. C. Prescott, Econometrica, 50 (1982), pp. 1345-1370]. We embed the problem in a suitable Hilbert space H and consider the associated Hamilton-Jacobi-Bellman (HJB) equation. This kind of infinite dimensional HJB equation has not been previously studied and is difficult due to the presence of state constraints and the lack of smoothing properties of the state equation. Our main result on the regularity of solutions to such an HJB equation seems to be entirely new. More precisely, we prove that the value function is continuous in a sufficiently big open set of H, that it solves in the viscosity sense the associated HJB equation, and that it has continuous classical derivative in the direction of the "present." This regularity result is the starting point to define a feedback map in the classical sense, which gives rise to a candidate optimal feedback strategy. © 2010 Society for Industrial and Applied Mathematics
A pricing formula for delayed claims: appreciating the past to value the future
Full text linkWe consider the valuation of contingent claims with delayed dynamics in a Samuelson complete
market model. We find a pricing formula that can be decomposed into terms reflecting the
current market values of the past and the future, showing how the valuation of prospective
cashflows cannot abstract away from the contribution of the past. As a practical application,
we provide an explicit expression for the market value of human capital in a setting with
wage rigidity. The formula we derive has successfully been used to explicitly solve the infinite
dimensional stochastic control problems addressed in [7], [6] and [16]
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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