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real analysis - Proof of "every convex function is ...

The best alternative proof (in my humble opinion) is a function is convex if and only if its epigraph is a convex set. If a function is NOT continuous then the epigraph can't be convex (obviously... draw a picture); but then by the above, the function can't be convex. This proof used the contrapositive.
real analysis - Proof of "every convex function is ...

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share …
plotting - Function Convex Hull - Mathematica Stack Exchange

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share …
Why is it that a function needs to be coercive to have a ...

10/26/2016 · It’s not necessarily true that a function needs to be coercive to have a minimizer; but you’re guaranteed that if it’s continuous and coercive, then there is always a minimizer (much like the guarantee that you have for convex functions[1]). There...
INSURANCE PREMIUM CALCULATIONS WITH ANTICIPATED …

INSURANCE PREMIUM CALCULATIONS WITH ANTICIPATED UTILITY THEORY BY CUNCUN LUAN Department of Mathematics Nanjing University, Nanjing, China ABSTRACT This paper examines an insurance or risk premium calculation method called the mean-value-distortion pricing principle in the general framework of anticipated utility theory.
The origins of quasi-concavity: a development between ...

The origins of quasi-concavity: a development between mathematics and economics. Author links open overlay panel Angelo Guerraggio a b Elena ... some continuity assumption is left out or some proof that is deemed evident and immediate in a geometric three-dimensional intuition is omitted. ... the smallest convex set containing the epigraph of a ...
Are the Hamiltonian and Lagrangian always convex functions?

The Lagrangian is convex, but not strictly so. Consider the linear path: $$\sigma(t) = t\,\dotX_0\tag2$$ in the tangent space i.e. where one moves by scaling the tangent vector $\dotX_0$. In response, the Lagrangian in (1) also scales linearly, so the linear path lies exactly within in the graph / on the edge of the epigraph of the ...
(PDF) Category-measure duality: convexity, mid-point ...

Category-measure duality: convexity, mid-point convexity and Berz sublinearity. ... Our proof is simpler than that of the. ... so again convex with epigraph a conv ex cone pointed at the origin. ...
(PDF) Optimal risk allocation for convex risk functionals ...

PDF | In this paper, we formulate the classical optimal risk allocation problem for convex risk functionals defined on products of real Banach spaces as risk domains. This generality includes in ...
UNIVERSITA DEGLI STUDI DI PADOVA Convex measures of risk ...

DEGLI STUDI DI PADOVA UNIVERSITA ` DI SCIENZE STATISTICHE FACOLTA CORSO DI LAUREA IN STATISTICA, ECONOMIA, FINANZA E AZIENDA RELAZIONE FINALE Convex measures of risk: comparison of different approaches and applications to utility maximization and pricing rules.