Symbolic manipulation of Levy polynomial processes

What is it about?

Non-centred Levy processes are not martingales. This circumstance limits its employment within mathematical finance. Time-space harmonic polynomials are such that when the indeterminate is replaced by a non-centred Levy process, the resulting stochastic family is a martingale. The paper deals with this family of polynomials investigating properties and applications by using a symbolic moment method known in the literature as umbral calculus.

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Why is it important?

The main feature of the paper consists in dealing with Levy processes by using purely algebraic methods differently from those usually proposed in the literature.