5,649 research outputs found
Some numerical methods for solving stochastic impulse control in natural gas storage facilities
The valuation of gas storage facilities is characterized as a stochastic impulse control problem with finite horizon resulting in Hamilton-Jacobi-Bellman (HJB) equations for the value function. In this context the two catagories of solving schemes for optimal switching are discussed in a stochastic control framework. We reviewed some numerical methods which include approaches related to partial differential equations (PDEs), Markov chain approximation, nonparametric regression, quantization method and some practitioners’ methods. This paper considers optimal switching problem arising in valuation of gas storage contracts for leasing the storage facilities, and investigates the recent developments as well as their advantages and disadvantages of each scheme based on dynamic programming principle (DPP
On the Wiener disorder problem
In the Wiener disorder problem, the drift of a Wiener process changes
suddenly at some unknown and unobservable disorder time. The objective is to
detect this change as quickly as possible after it happens. Earlier work on the
Bayesian formulation of this problem brings optimal (or asymptotically optimal)
detection rules assuming that the prior distribution of the change time is
given at time zero, and additional information is received by observing the
Wiener process only. Here, we consider a different information structure where
possible causes of this disorder are observed. More precisely, we assume that
we also observe an arrival/counting process representing external shocks. The
disorder happens because of these shocks, and the change time coincides with
one of the arrival times. Such a formulation arises, for example, from
detecting a change in financial data caused by major financial events, or
detecting damages in structures caused by earthquakes. In this paper, we
formulate the problem in a Bayesian framework assuming that those observable
shocks form a Poisson process. We present an optimal detection rule that
minimizes a linear Bayes risk, which includes the expected detection delay and
the probability of early false alarms. We also give the solution of the
``variational formulation'' where the objective is to minimize the detection
delay over all stopping rules for which the false alarm probability does not
exceed a given constant.Comment: Published in at http://dx.doi.org/10.1214/09-AAP655 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Interpretable statistics for complex modelling: quantile and topological learning
As the complexity of our data increased exponentially in the last decades, so has our
need for interpretable features. This thesis revolves around two paradigms to approach
this quest for insights.
In the first part we focus on parametric models, where the problem of interpretability
can be seen as a “parametrization selection”. We introduce a quantile-centric
parametrization and we show the advantages of our proposal in the context of regression,
where it allows to bridge the gap between classical generalized linear (mixed)
models and increasingly popular quantile methods.
The second part of the thesis, concerned with topological learning, tackles the
problem from a non-parametric perspective. As topology can be thought of as a way
of characterizing data in terms of their connectivity structure, it allows to represent
complex and possibly high dimensional through few features, such as the number of
connected components, loops and voids. We illustrate how the emerging branch of
statistics devoted to recovering topological structures in the data, Topological Data
Analysis, can be exploited both for exploratory and inferential purposes with a special
emphasis on kernels that preserve the topological information in the data.
Finally, we show with an application how these two approaches can borrow strength
from one another in the identification and description of brain activity through fMRI
data from the ABIDE project
DTR Bandit: Learning to Make Response-Adaptive Decisions With Low Regret
Dynamic treatment regimes (DTRs) are personalized, adaptive, multi-stage
treatment plans that adapt treatment decisions both to an individual's initial
features and to intermediate outcomes and features at each subsequent stage,
which are affected by decisions in prior stages. Examples include personalized
first- and second-line treatments of chronic conditions like diabetes, cancer,
and depression, which adapt to patient response to first-line treatment,
disease progression, and individual characteristics. While existing literature
mostly focuses on estimating the optimal DTR from offline data such as from
sequentially randomized trials, we study the problem of developing the optimal
DTR in an online manner, where the interaction with each individual affect both
our cumulative reward and our data collection for future learning. We term this
the DTR bandit problem. We propose a novel algorithm that, by carefully
balancing exploration and exploitation, is guaranteed to achieve rate-optimal
regret when the transition and reward models are linear. We demonstrate our
algorithm and its benefits both in synthetic experiments and in a case study of
adaptive treatment of major depressive disorder using real-world data
Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure
We further develop the numerical algorithm for computing the gauge connection
of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In
particular, recent work on the generalized Donaldson algorithm is extended to
bundles with Kahler cone substructure on manifolds with h^{1,1}>1. Since the
computation depends only on a one-dimensional ray in the Kahler moduli space,
it can probe slope-stability regardless of the size of h^{1,1}. Suitably
normalized error measures are introduced to quantitatively compare results for
different directions in Kahler moduli space. A significantly improved numerical
integration procedure based on adaptive refinements is described and
implemented. Finally, an efficient numerical check is proposed for determining
whether or not a vector bundle is slope-stable without computing its full
connection.Comment: 38 pages, 10 figure
Computational fluid dynamics of coupled free/porous regimes: a specialised case of pleated cartridge filter
The multidisciplinary project AEROFIL has been defined and coordinated
with the idea of developing novel filter designs to be employed in aeronautic
hydraulic systems. The cartridge filters would be constructed using eco-friendly
filtration media supported by unconventional disposable or reusable solid
components. My main contribution to this project is the development of a robust
and cost-effective design and analysis tool for simulating the hydrodynamics in
these pleated cartridge filters. The coupled free and porous flow regimes are
generally observed in filtration processes. These processes have been the subject of
intense investigation for researchers over the decades who are striving hard to
resolve some of the critical issues related to the free/porous interfacial constraints
and their mathematical representations concerning its industrial applications. [Continues.
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