Monthly Archives: December, 2017

Mean Square Stable MJLS, but higher moments diverge

By psopasakis on December 31, 2017 | Leave a comment

It is well known that MJLS can be mean-stable (the expected value of the state’s norm converges to 0), but not mean-square stable. It makes sense to assume that an MJLS can be mean-square stable, but some higher-order norms do not converge to 0. Despite the fact that mean-square stability conditions for MJLS are well studied and are easy to check, this is not always the case for moments of other order. In this post we present a counterexample and state conditions for p-order mean stability.
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Posted in: Stochastics | Tagged: counterexample, Markov, Mean stability, MJLS, Moment, Moment stability, Stability

Interchangeability of infimum in risk measures

By psopasakis on December 19, 2017 | Leave a comment

In this post we discuss the interchangeability of the infimum with (monotone) risk measures in finite probability spaces. In particular, we show that under the common monotonicity assumption (which is satisfied by all well-behaving risk measures), for a risk measure $\rho:\mathbb{R}^n\to\mathbb{R}$ and a mapping $f:\mathbb{R}^m\to\mathbb{R}^n$ , we have

$\begin{aligned} \rho\left(\inf_x f(x)\right) = \inf_x \rho(f(x)) \end{aligned}$

and $\mathbf{argmin}_x f(x) \subseteq \mathbf{argmin}_x \rho(f(x))$ , while, under additional conditions (which are typically met in finite-dimensional spaces), we have $\mathbf{argmin}_x f(x) = \mathbf{argmin}_x \rho(f(x))$ Continue reading →

Posted in: Optimisation, Probability theory, Risk Measures, Variational analysis | Tagged: Analysis, duality, Optimisation, optimization, risk, risk-measures

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Monthly Archives: December, 2017

Mean Square Stable MJLS, but higher moments diverge

Interchangeability of infimum in risk measures

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