Article2015

Nonlinear Lévy processes and their characteristics

77 citations0/0 files storedTransactions of the American Mathematical Society

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Stochastic processes and financial applications Probability and Risk Models Fuzzy Systems and Optimization

Abstract

We develop a general construction for nonlinear Lévy processes with given characteristics. More precisely, given a set Θ \Theta of Lévy triplets, we construct a sublinear expectation on Skorohod space under which the canonical process has stationary independent increments and a nonlinear generator corresponding to the supremum of all generators of classical Lévy processes with triplets in Θ \Theta . The nonlinear Lévy process yields a tractable model for Knightian uncertainty about the distribution of jumps for which expectations of Markovian functionals can be calculated by means of a partial integro-differential equation.

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References

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