Weak Dynamic Programming for Generalized State Constraints

We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the viscosity sense. We treat open state constraints as a special case of expectation constraints and prove a comparison theorem to obtain the equation for closed state constraints.Comment: 36 pages;forthcoming in 'SIAM Journal on Control and Optimization

The value function of an asymptotic exit-time optimal control problem

We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this paper we obtain such properties and a uniqueness result under some explicit sufficient conditions. We briefly investigate also the infinite horizon problem

Optimal portfolio choice with path dependent labor income: the infinite horizon case

We consider an infinite horizon portfolio problem with borrowing constraints, in which an agentreceives labor income which adjusts to financial market shocks in a path dependent way. Thispath-dependency is the novelty of the model, and leads to an infinite dimensional stochasticoptimal control problem. We solve the problem completely, and find explicitly the optimalcontrols in feedback form. This is possible because we are able to find an explicit solutionto the associated infinite dimensional Hamilton-Jacobi-Bellman (HJB) equation, even if stateconstraints are present. To the best of our knowledge, this is the first infinite dimensionalgeneralization of Merton’s optimal portfolio problem for which explicit solutions can be found.The explicit solution allows us to study the properties of optimal strategies and discuss theirfinancial implications

Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems

The minimal time function of a class of semilinear control systems is considered in Banach spaces, with the target set being a closed ball. It is shown that the minimal time functions of the Yosida approximation equations converge to the minimal time function of the semilinear control system. Complete characterization is established for the subdifferential of the minimal time function satisfying the Hamilton–Jacobi–Bellman equation. These results extend the theory of finite dimensional linear control systems to infinite dimensional semilinear control systems

The prognostic value of the suPARnostic® ELISA in HIV-1 infected individuals is not affected by uPAR promoter polymorphisms

<p>Abstract</p> <p>Background</p> <p>High blood levels of soluble urokinase Plasminogen Activator Receptor (suPAR) are associated with poor outcomes in human immunodeficiency-1 (HIV-1) infected individuals. Research on the clinical value of suPAR in HIV-1 infection led to the development of the suPARnostic^®assay for commercial use in 2006. The aim of this study was to: 1) Evaluate the prognostic value of the new suPARnostic^®assay and 2) Determine whether polymorphisms in the active promoter of uPAR influences survival and/or suPAR values in HIV-1 patients who are antiretroviral therapy (ART) naive.</p> <p>Methods</p> <p>DNA samples were collected retrospectively from 145 Danes infected with HIV-1 with known seroconversion times. In addition, plasma was collected retrospectively from 81 of these participants for use in the suPAR analysis. Survival was analysed using Kaplan Meier analysis.</p> <p>Results</p> <p>Survival was strongly correlated to suPAR levels (p < 0.001). Levels at or above 6 ng/ml were associated with death in 13 of 27 patients within a two-years period; whereas only one of 54 patients with suPAR levels below 6 ng/ml died during this period. We identified two common uPAR promoter polymorphisms: a G to A transition at -118 and an A to G transition at -465 comparative to the transcription start site. These promoter transitions influenced neither suPAR levels nor patient survival.</p> <p>Conclusion</p> <p>Plasma suPAR levels, as measured by the suPARnostic^®assay, were strongly predictive of survival in ART-naïve HIV-1 infected patients. Furthermore, plasma suPAR levels were not influenced by uPAR promoter polymorphisms.</p

A micro costing of NHS cancer genetic services

This paper presents the first full micro costing of a commonly used cancer genetic counselling and testing protocol used in the UK. Costs were estimated for the Cardiff clinic of the Cancer Genetics Service in Wales by issuing a questionnaire to all staff, conducting an audit of clinic rooms and equipment and obtaining gross unit costs from the finance department. A total of 22 distinct event pathways were identified for patients at risk of developing breast, ovarian, breast and ovarian or colorectal cancer. The mean cost per patient were £97–£151 for patients at moderate risk, £975–£3072 for patients at high risk of developing colorectal cancer and £675–£2909 for patients at high risk of developing breast or ovarian cancer. The most expensive element of cancer genetic services was labour. Labour costs were dependent upon the amount of labour, staff grade, number of counsellors used and the proportion of staff time devoted to indirect patient contact. With the growing demand for cancer genetic services and the growing number of national and regional cancer genetic centers, there is a need for the different protocols being used to be thoroughly evaluated in terms of costs and outcomes

Unusual presentation of Lynch Syndrome

Lynch Syndrome/HNPCC is a syndrome of cancer predisposition linked to inherited mutations of genes participating in post-replicative DNA mismatch repair (MMR). The spectrum of cancer associated with Lynch Syndrome includes tumours of the colorectum, endometrium, ovary, upper gastrointestinal tract and the urothelium although other cancers are rarely described. We describe a family of Lynch Syndrome with an hMLH1 mutation, that harbours an unusual tumour spectrum and its diagnostic and management challenges