This paper illustrates how the use of random set theory can benefit partial identification analysis. We revisit the origins of Manski’s work in partial identification (e.g., Manski (1989, 1990)) focusing our discussion on identification of probability distributions and conditional expectations...

A particle system is a family of i.i.d. stochastic processes with values translated by Poisson points. We obtain conditions that ensure the stationarity in time of the particle system in Rd and in some cases provide a full characterisation of the stationarity property. In particular, a full...

We describe several simulation algorithms that yield random probability distributions with given values of risk measures. In case of vanilla risk measures, the algorithms involve combining and transforming random cumulative distribution functions or random Lorenz curves obtained by simulating...

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to...

Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are set-valued. Furthermore, it is reasonable to include the...

It is known that each symmetric stable distribution in is related to a norm on that makes embeddable in Lp([0,1]). In the case of a multivariate Cauchy distribution the unit ball in this norm is the polar set to a convex set in called a zonoid. This work interprets symmetric stable laws using...

Transaction costs involved while trading several assets may be described using bid-ask spread of the asset prices. We assume that the prices of several assets may be linked, so that transactions involving several assets have prices that are not necessarily equal to the sums of (bid or ask)...