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Seminario di Equazioni Differenziali e Applicazioni: “Nonlinear Kolmogorov equation, Nonlinear Levy Processes and Utility Maximization under Knightian Uncertainty”

Martedì 5 Dicembre 2017, ore 14:30 - Aula 2BC30 - Ariel Neufeld

ARGOMENTI: Seminari

Martedì 5 Dicembre 2017 alle ore 14:30 in Aula 2BC30, Ariel Neufeld (ETH, Zurigo) terrà un seminario dal titolo “Nonlinear Kolmogorov equation, Nonlinear Levy Processes and Utility Maximization under Knightian Uncertainty”.

Abstract
We present a tractable framework for Knightian uncertainty, the so-called Nonlinear Levy processes. These are, roughly speaking, Levy processes with uncertain drift, volatility and jumps, which are characterized by the solution of their Nonlinear Kolmogorov equation. We use it to formulate and solve problems of utility maximization under simultaneously drift, volatility and jump uncertainty for an investor with logarithmic or power utility. We show that an optimal investment strategy exists and compute it in semi-closed form. Moreover, we provide a saddle point analysis describing a worst-case model. No compactness on the set of probability measures is necessary. We discuss the general difficulty of providing compactness (i.e. closedness) of semimartingale laws and present a compactness criterion.
The first part is joint work with Marcel Nutz, the second part is joint work with Chong Liu.

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