Optimal feedback control rules sensitive to controlled endogenous risk-aversion

The objective of this paper is to correct and improve the results obtained by Van der Ploeg (1984a, 1984b) and utilized in the theoretical literature related to feedback stochastic optimal control sensitive to constant exogenous risk-aversion (see, Jacobson, 1973, Karp, 1987 and Whittle, 1981, 1989, 1990, among others) or to the classic context of risk-neutral decision-makers (see, Chow, 1973, 1976a, 1976b, 1977, 1978, 1981, 1993). More realistic and attractive, this new approach is placed in the context of a time-varying endogenous risk-aversion which is under the control of the decision-maker. It has strong qualitative implications on the agent's optimal policy during the entire planning horizon.

A unified framework for linear function approximation of value functions in stochastic control

This paper contributes with a unified formulation that merges previ- ous analysis on the prediction of the performance ( value function ) of certain sequence of actions ( policy ) when an agent operates a Markov decision process with large state-space. When the states are represented by features and the value function is linearly approxi- mated, our analysis reveals a new relationship between two common cost functions used to obtain the optimal approximation. In addition, this analysis allows us to propose an efficient adaptive algorithm that provides an unbiased linear estimate. The performance of the pro- posed algorithm is illustrated by simulation, showing competitive results when compared with the state-of-the-art solutions.

A Stochastic Control Approach to a Parabolic Equation, Reciprocal Processes

2000 Mathematics Subject Classi cation: 49L60, 60J60, 93E20.

Optimal investment under stochastic volatility and power type utility function

2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20.

Lack of correlation between the optimal glycaemic control and coronary micro vascular dysfunction in patients with diabetes mellitus: a cross sectional study.

Background Coronary microvascular dysfunction (CMD) is associated with cardiovascular events in type 2 diabetes mellitus (T2DM). Optimal glycaemic control does not always preclude future events. We sought to assess the effect of the current target of HBA1c level on the coronary microcirculatory function and identify predictive factors for CMD in T2DM patients. Methods We studied 100 patients with T2DM and 214 patients without T2DM. All of them with a history of chest pain, non-obstructive angiograms and a direct assessment of coronary blood flow increase in response to adenosine and acetylcholine coronary infusion, for evaluation of endothelial independent and dependent CMD. Patients with T2DM were categorized as having optimal (HbA1c < 7 %) vs. suboptimal (HbA1c ≥ 7 %) glycaemic control at the time of catheterization. Results Baseline characteristics and coronary endothelial function parameters differed significantly between T2DM patients and control group. The prevalence of endothelial independent CMD (29.8 vs. 39.6 %, p = 0.40) and dependent CMD (61.7 vs. 62.2 %, p = 1.00) were similar in patients with optimal vs. suboptimal glycaemic control. Age (OR 1.10; CI 95 % 1.04–1.18; p < 0.001) and female gender (OR 3.87; CI 95 % 1.45–11.4; p < 0.01) were significantly associated with endothelial independent CMD whereas glomerular filtrate (OR 0.97; CI 95 % 0.95–0.99; p < 0.05) was significantly associated with endothelial dependent CMD. The optimal glycaemic control was not associated with endothelial independent (OR 0.60, CI 95 % 0.23–1.46; p 0.26) or dependent CMD (OR 0.99, CI 95 % 0.43–2.24; p = 0.98). Conclusions The current target of HBA1c level does not predict a better coronary microcirculatory function in T2DM patients. The appropriate strategy for prevention of CMD in T2DM patients remains to be addressed. Keywords: Endothelial dysfunction; Diabetes mellitus; Coronary microcirculation

Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.