Predictable projections of conformal stochastic integrals: an application to Hermite series and to Widder's representation

In this article, we study predictable projections of stochastic integrals with respect to the conformal Brownian motion, extending the connection between powers of the conformal Brownian motion and the corresponding Hermite polynomials. As a consequence of this result, we then investigate the relation between analytic functions and $L^p$-convergent series of Hermite polynomials. Finally, our results are applied to Widder's representation for a class of Brownian martingales, retrieving a characterization for the moments of Widder's measure.Comment: 16 pages. Added keywords, MSC classification, contact informatio

Surplus sharing with coherent utility functions

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e. the shareholders

Monetary Utility Functions on Cb(X)C_b(X) Spaces

We will characterise robust monetary utility functions defined on the space of real valued (bounded) continuous functions on a Polish space

Commonotonicity and time-consistency for Lebesgue-continuous monetary utility functions

It is proved that monetary utility functions that are commonotonic and time-consistent are conditional expectations. We also give additional results on atomless and conditionally atomless probability spaces. These notions describe that in a filtration, there are many new events at each time step

Convex Increasing Functionals on Cb(X)C_b(X) Spaces

We prove that convex functions on a $C_b(X)$ space satisfying a mild continuity condition can be represented using sigma additive measures. This generalises a result of Cheridito, Kupper and Tangpi