Archivio della ricerca di Triestehttps://arts.units.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Thu, 15 Apr 2021 05:47:32 GMT2021-04-15T05:47:32Z10201Generalising the pari-mutuel modelhttp://hdl.handle.net/11368/2940145Titolo: Generalising the pari-mutuel model
Abstract: We introduce two models for imprecise probabilities which generalise the Pari-Mutuel Model while retaining its simple structure. Their consistency properties are investigated, as well as their capability of formalising an assessor’s different attitudes. It turns out that one model is always coherent, while the other is (occasionally coherent but) generally only 2-coherent, and may elicit a conflicting attitude towards risk.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11368/29401452019-01-01T00:00:00ZEssential mathematics for economicshttp://hdl.handle.net/11368/2929245Titolo: Essential mathematics for economics
Abstract: This short book is aimed at undergraduate students with a very standard knowledge of algebra learnt at the high school, and it appears as "self contained". According to the long teaching experience of the authors, it was written in order to furnish nearly all the material both for a 90-hour course of "Mathematics for Economics", and for a 45-hour course of "Financial Mathematics", the first part being covered by the chapters from 1 to 10, and the second by the chapters from 11 to 14.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11368/29292452018-01-01T00:00:00ZPOSITIVE RADIAL SOLUTIONS OF THE DIRICHLET PROBLEM FOR THE MINKOWSKI-CURVATURE EQUATION IN A BALLhttp://hdl.handle.net/11368/2921638.7Titolo: POSITIVE RADIAL SOLUTIONS OF THE DIRICHLET PROBLEM FOR THE MINKOWSKI-CURVATURE EQUATION IN A BALL
Abstract: We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation
$$
\begin{cases}
\displaystyle
-\text{div}\bigg(\frac{\nabla v}{\sqrt{1-|\nabla v|^2}}\bigg)=f(|x|,v) & \text{in } B_R,\\v=0 & \text{on } \partial B_R,
\end{cases}
$$
where $B_R$ is a ball in $\mathbb{R}^N$ ($N\ge 2$). According to the behaviour of $f=f(r,s)$ near $s=0$, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11368/2921638.72014-01-01T00:00:00ZExtending Nearly-Linear Modelshttp://hdl.handle.net/11368/2945506Titolo: Extending Nearly-Linear Models
Abstract: Nearly-Linear Models are a family of neighbourhood models, obtaining lower/upper probabilities from a given probability by a linear affine transformation with barriers. They include a number of known models as special cases, among them the Pari-Mutuel Model, the ε-contamination model, the Total Variation Model and the vacuous lower/upper probabilities. We classified Nearly-Linear models, investigating their consistency properties, in previous work. Here we focus on how to extend those Nearly-Linear Models that are coherent or at least avoid sure loss. We derive formulae for their natural extensions, interpret a specific model as a natural extension itself of a certain class of lower probabilities, and supply a risk measurement interpretation for one of the natural extensions we compute.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11368/29455062019-01-01T00:00:00ZSubharmonic solutions of the prescribed curvature equationhttp://hdl.handle.net/11368/2830905Titolo: Subharmonic solutions of the prescribed curvature equation
Abstract: We study the existence of subharmonic solutions of the prescribed curvature equation
\begin{equation*}
-\Big( u'/{ \sqrt{1+{u'}^2}}\Big)'
= f(t,u).
\end{equation*}
According to the behaviour at zero, or at infinity, of the prescribed curvature $f$, we prove the existence of arbitrarily small classical subharmonic solutions, or bounded variation subharmonic solutions with arbitrarily large oscillations.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11368/28309052016-01-01T00:00:00ZPositive solutions of the Dirichlet problem for the one-dimensional Minkowski-curvature equationhttp://hdl.handle.net/11368/2507945Titolo: Positive solutions of the Dirichlet problem for the one-dimensional Minkowski-curvature equation
Abstract: We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation
\begin{equation*}
-\Big( u'/{ \sqrt{1-{u'}^2}}\Big)'
= f(t,u).
\end{equation*}
Depending on the behaviour of $f=f(t,s)$ near $s=0$, we prove the existence of either
one, or two, or three, or infinitely many positive solutions. In general,
the positivity of $f$ is not required.
All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11368/25079452012-01-01T00:00:00ZWeak Dutch Books versus strict consistency with lower previsionshttp://hdl.handle.net/11368/2903912Titolo: Weak Dutch Books versus strict consistency with lower previsions
Abstract: Several consistency notions for lower previsions (coherence, convexity, others) require that the suprema of certain gambles, having the meaning of gains, are non-negative. The limit situation that a gain supremum is zero is termed Weak Dutch Book (WDB). In the literature, the special case of WDBs with precise probabilities has mostly been analysed, and strict coherence has been proposed as a radical alternative. In this paper the focus is on WDBs and generalised strict coherence, termed strict consistency, with imprecise previsions. We discuss properties of lower previsions incurring WDBs and conditions for strict consistency, showing in both cases how they are differentiated by the degree of consistency of the given uncertainty assessment.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11368/29039122017-01-01T00:00:00ZA one-dimensional prescribed curvature equation modeling the corneal shapehttp://hdl.handle.net/11368/2776925Titolo: A one-dimensional prescribed curvature equation modeling the corneal shape
Abstract: We prove existence, uniqueness and stability of solutions of the prescribed curvature problem
\begin{equation*}
\begin{cases}
\bigl({u'}/{\sqrt{1 + u'^2}}\bigr)' = au -{b}/{\sqrt{1 + u'^2}} \quad \text{in }[0,1]\\
u'(0)=u(1)=0,
\end{cases}
\end{equation*}
for any given $a>0$ and $b>0$.
We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper \cite{OkPl}, where a simplified version obtained by partial linearization has been investigated.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11368/27769252014-01-01T00:00:00ZRadially symmetric solutions of an anisotropic mean curvature equation modeling the corneal shapehttp://hdl.handle.net/11368/2922393Titolo: Radially symmetric solutions of an anisotropic mean curvature equation modeling the corneal shape
Abstract: We prove existence and uniqueness of classical solutions of the anisotropic prescribed mean curvature problem
egin{equation*}
{
m -div}left({
abla u}/{sqrt{1 + |
abla u|^2}}
ight) = -au + {b}/{sqrt{1 + |
abla u|^2}}, ext{ in } B, quad u=0, ext{ on } partial B,
end{equation*}
where $a,b>0$ are given parameters and $B$ is a ball in ${mathbb R}^N$. The solution we find is positive, radially symmetric, radially decreasing and concave. This equation has been proposed as a model of the corneal shape in the recent papers [13,14,15,18,17], where however a linearized version of the equation has been investigated.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11368/29223932015-01-01T00:00:00ZPositive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski spacehttp://hdl.handle.net/11368/2589620Titolo: Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space
Abstract: We prove the existence of multiple positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space
\begin{equation*}
\begin{cases}
-{\rm div}\Big( \nabla u /\sqrt{1 - |\nabla u|^2}\Big)= f(x,u, \nabla u)
& \hbox{ in } \Omega,
\\
u=0& \hbox{ on } \partial \Omega.
\end{cases}
\end{equation*}
Here $\Omega$ is a bounded regular domain in $\RR^N$
and the function $f=f(x,s,\xi)$ is
either sublinear, or superlinear, or sub-superlinear near $s=0$.
The proof combines topological and variational methods.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11368/25896202013-01-01T00:00:00Z