1,523 research outputs found
A Bellman approach for two-domains optimal control problems in
This article is the starting point of a series of works whose aim is the
study of deterministic control problems where the dynamic and the running cost
can be completely different in two (or more) complementary domains of the space
. As a consequence, the dynamic and running cost present discontinuities
at the boundary of these domains and this is the main difficulty of this type
of problems. We address these questions by using a Bellman approach: our aim is
to investigate how to define properly the value function(s), to deduce what is
(are) the right Bellman Equation(s) associated to this problem (in particular
what are the conditions on the set where the dynamic and running cost are
discontinuous) and to study the uniqueness properties for this Bellman
equation. In this work, we provide rather complete answers to these questions
in the case of a simple geometry, namely when we only consider two different
domains which are half spaces: we properly define the control problem, identify
the different conditions on the hyperplane where the dynamic and the running
cost are discontinuous and discuss the uniqueness properties of the Bellman
problem by either providing explicitly the minimal and maximal solution or by
giving explicit conditions to have uniqueness
Value function for regional control problems via dynamic programming and Pontryagin maximum principle
In this paper we focus on regional deterministic optimal control problems,
i.e., problems where the dynamics and the cost functional may be different in
several regions of the state space and present discontinuities at their
interface. Under the assumption that optimal trajectories have a locally finite
number of switchings (no Zeno phenomenon), we use the duplication technique to
show that the value function of the regional optimal control problem is the
minimum over all possible structures of trajectories of value functions
associated with classical optimal control problems settled over fixed
structures, each of them being the restriction to some submanifold of the value
function of a classical optimal control problem in higher dimension.The lifting
duplication technique is thus seen as a kind of desingularization of the value
function of the regional optimal control problem. In turn, we extend to
regional optimal control problems the classical sensitivity relations and we
prove that the regularity of this value function is the same (i.e., is not more
degenerate) than the one of the higher-dimensional classical optimal control
problem that lifts the problem
A hybrid approach for the implementation of the Heston model
We propose a hybrid tree-finite difference method in order to approximate the
Heston model. We prove the convergence by embedding the procedure in a
bivariate Markov chain and we study the convergence of European and American
option prices. We finally provide numerical experiments that give accurate
option prices in the Heston model, showing the reliability and the efficiency
of the algorithm
A hybrid tree/finite-difference approach for Heston-Hull-White type models
We study a hybrid tree-finite difference method which permits to obtain
efficient and accurate European and American option prices in the Heston
Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we
provide a new simulation scheme to be used for Monte Carlo evaluations.
Numerical results show the reliability and the efficiency of the proposed
method
On the dynamics of capital accumulation across space
We solve an optimal growth model in continuous space, continuous and bounded time. The optimizer chooses the optimal trajectories of capital and consumption across space and time by maximizing an objective function with both space and time discounting. We extract the corresponding Pontryagin conditions and prove their sufficiency. We end up with a system of two parabolic differential equations with the corresponding boundary conditions. Then, we study the roles of initial capital and technology distributions over space in various scenarios.economics, economic geography, parabolic differential equations, optimal control
Effects of Anti-Nutritional Compounds in Pongamia Seedcake on Intake, Digestion, and Ruminal Fermentation in Beef Cattle
Effects of increasing levels of the anti-nutritional compounds karanjin and
pongamol on intake, nutrient utilization and ruminal fermentation were evaluated with a
growing diet (trial I) and a forage diet (trial II).
Steers had ad libitum access to growing diet and Bermuda grass hay during trial
1 and trial 2, respectively. At the same time diets were fed, steers received their allocated
doses of karanjin and pongamol via ruminal cannula to determine acceptable inclusion
level of pongamia seedcakes containing varying levels of karanjin and pongamol, which
are contained in the residual oil of commercially available pongamia seedcakes. Twelve
steers in both studies were assigned to completely randomized block design consisting of
a control (no karanjin and no pongamol) and one of 3 levels of karanjin and pongamol.
Dosing increasing levels karanjin and pongamol linearly (P < 0.01) decreased
intake in Trial 1. No significant effects (P ≥ 0.12) were observed for total DMD, OMD,
NDFD, ADFD and CPD. Ruminal total VFA concentration and pH were not affected by
inclusion levels (P = 0.19 and P = 0.51, respectfully). The lowest dose of karanjin and
pongamol resulted in a greater (P < 0.01) molar proportion of propionate than other
treatments, resulting in a reduction in acetate:propionate ratio (P = 0.02) for that
treatment. Among all VFA molar concentration measurements, only isobutyrate
exhibited a treatment × hour effect (P = 0.02).
When a forage diet was fed (Trial 2) increasing levels of karanjin and pongamol
dosing resulted in a quadratic decrease (P < 0.05) in intake of total DM, OM, NDF and
ADF with the. Crude protein intake did not differ (P = 0.14) among treatments. There
was no effect (P ≥ 0.22) among treatments on DMD, OMD, NDFD and ADFD. Total
VFA concentration and ruminal pH were not affected by inclusion level (P = 0.59 and
0.72, respectively. Therefore, acetate:propionate ratio also had no treatment effect (P =
0.84).
Increasing levels of karanjin and pongamol decrease intake, although
digestibility is not impacted. Ruminal fermentation of steers fed with complete ration is
slightly altered with karanjin and pongamol intake, however, none alteration was
observed when steers were fed only Bermuda grass hay
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