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Variational sensitivity analysis of parametric Markovian market models

Norbert Hilber, Christoph Schwab, Christoph Winter (2008)

Banach Center Publications

Parameter sensitivities of prices for derivative contracts play an important role in model calibration as well as in quantification of model risk. In this paper a unified approach to the efficient numerical computation of all sensitivities for Markovian market models is presented. Variational approximations of the integro-differential equations corresponding to the infinitesimal generators of the market model differentiated with respect to the model parameters are employed. Superconvergent approximations...

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general...

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