Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

Stopping smoking made easier

This booklet takes smokers through the stages of stopping smoking as well as answers common questions smokers ask about smoking

Stopping smoking made easier (English and translations)

This booklet takes smokers through the stages of stopping smoking:preparing to stopstoppingstaying stoppedIt also provides advice on the various forms of nicotine replacement therapy (NRT) and non-nicotine medications available, as well as a list of contacts for advice and support.Note: translations are of the 2009 leaflet, which will have lower costs for packets of cigarettes.

From Full stopping to transparency in a holographic model of heavy ion collisions

We numerically simulate planar shock wave collisions in anti-de Sitter space as a model for heavy ion collisions of large nuclei. We uncover a crossover between two different dynamical regimes as a function of the collision energy. At low energies the shocks first stop and then explode in a manner approximately described by hydrodynamics, in close similarity with the Landau model. At high energies the receding fragments move outwards at the speed of light, with a region of negative energy density and negative longitudinal pressure trailing behind them. The rapidity distribution of the energy density at late times around midrapidity is not approximately boost invariant but Gaussian, albeit with a width that increases with the collision energy.

Geometric stopping of a random walk and its applications to valuing equity-linked death benefits

We study discrete-time models in which death benefits can depend on a stock price index, the logarithm of which is modeled as a random walk. Examples of such benefit payments include put and call options, barrier options, and lookback options. Because the distribution of the curtate-future-lifetime can be approximated by a linear combination of geometric distributions, it suffices to consider curtate-future-lifetimes with a geometric distribution. In binomial and trinomial tree models, closed-form expressions for the expectations of the discounted benefit payment are obtained for a series of options. They are based on results concerning geometric stopping of a random walk, in particular also on a version of the Wiener-Hopf factorization.

An analysis of protocols and publications suggested that most discontinuations of clinical trials were not based on preplanned interim analyses or stopping rules.

OBJECTIVES: To investigate the frequency of interim analyses, stopping rules, and data safety and monitoring boards (DSMBs) in protocols of randomized controlled trials (RCTs); to examine these features across different reasons for trial discontinuation; and to identify discrepancies in reporting between protocols and publications. STUDY DESIGN AND SETTING: We used data from a cohort of RCT protocols approved between 2000 and 2003 by six research ethics committees in Switzerland, Germany, and Canada. RESULTS: Of 894 RCT protocols, 289 prespecified interim analyses (32.3%), 153 stopping rules (17.1%), and 257 DSMBs (28.7%). Overall, 249 of 894 RCTs (27.9%) were prematurely discontinued; mostly due to reasons such as poor recruitment, administrative reasons, or unexpected harm. Forty-six of 249 RCTs (18.4%) were discontinued due to early benefit or futility; of those, 37 (80.4%) were stopped outside a formal interim analysis or stopping rule. Of 515 published RCTs, there were discrepancies between protocols and publications for interim analyses (21.1%), stopping rules (14.4%), and DSMBs (19.6%). CONCLUSION: Two-thirds of RCT protocols did not consider interim analyses, stopping rules, or DSMBs. Most RCTs discontinued for early benefit or futility were stopped without a prespecified mechanism. When assessing trial manuscripts, journals should require access to the protocol.

Excessive functions, Appell polynomials and optimal stopping

The main topic of the thesis is optimal stopping. This is treated in two research articles. In the first article we introduce a new approach to optimal stopping of general strong Markov processes. The approach is based on the representation of excessive functions as expected suprema. We present a variety of examples, in particular, the Novikov-Shiryaev problem for Lévy processes. In the second article on optimal stopping we focus on differentiability of excessive functions of diffusions and apply these results to study the validity of the principle of smooth fit. As an example we discuss optimal stopping of sticky Brownian motion. The third research article offers a survey like discussion on Appell polynomials. The crucial role of Appell polynomials in optimal stopping of Lévy processes was noticed by Novikov and Shiryaev. They described the optimal rule in a large class of problems via these polynomials. We exploit the probabilistic approach to Appell polynomials and show that many classical results are obtained with ease in this framework. In the fourth article we derive a new relationship between the generalized Bernoulli polynomials and the generalized Euler polynomials.

Secondary prevention of type 1 diabetes mellitus: stopping immune destruction and promoting ß-cell regeneration

Type 1 diabetes mellitus results from a cell-mediated autoimmune attack against pancreatic ß-cells. Traditional treatments involve numerous daily insulin dosages/injections and rigorous glucose control. Many efforts toward the identification of ß-cell precursors have been made not only with the aim of understanding the physiology of islet regeneration, but also as an alternative way to produce ß-cells to be used in protocols of islet transplantation. In this review, we summarize the most recent studies related to precursor cells implicated in the regeneration process. These include embryonic stem cells, pancreas-derived multipotent precursors, pancreatic ductal cells, hematopoietic stem cells, mesenchymal stem cells, hepatic oval cells, and mature ß-cells. There is controversial evidence of the potential of these cell sources to regenerate ß-cell mass in diabetic patients. However, clinical trials using embryonic stem cells, umbilical cord blood or adult bone marrow stem cells are under way. The results of various immunosuppressive regimens aiming at blocking autoimmunity against pancreatic ß-cells and promoting ß-cell preservation are also analyzed. Most of these regimens provide transient and partial effect on insulin requirements, but new regimens are beginning to be tested. Our own clinical trial combines a high dose immunosuppression with mobilized peripheral blood hematopoietic stem cell transplantation in early-onset type 1 diabetes mellitus.

Lower Bounds for Achieving Synchronous Early Stopping Consensus with Orderly Crash Failures

In this paper, we discuss the consensus problem for synchronous distributed systems with orderly crash failures. For a synchronous distributed system of n processes with up to t crash failures and f failures actually occur, first, we present a bivalency argument proof to solve the open problem of proving the lower bound, min (t + 1, f + 2) rounds, for early-stopping synchronous consensus with orderly crash failures, where t < n - 1. Then, we extend the system model with orderly crash failures to a new model in which a process is allowed to send multiple messages to the same destination process in a round and the failing processes still respect the order specified by the protocol in sending messages. For this new model, we present a uniform consensus protocol, in which all non-faulty processes always decide and stop immediately by the end of f + 1 rounds. We prove that the lower bound of early stopping protocols for both consensus and uniform consensus are f + 1 rounds under the new model, and our proposed protocol is optimal.