140 research outputs found
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 -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 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 Spaces
We prove that convex functions on a space satisfying a mild
continuity condition can be represented using sigma additive measures. This
generalises a result of Cheridito, Kupper and Tangpi
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