arXiv subjects

Georg Ch. Pflug

Publications and source records attributed to Georg Ch. Pflug.

2 recordsLinked to original sources

arXiv2020

New Algorithms And Fast Implementations To Approximate Stochastic Processes

We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the goal is always to find a finite model, which represents a given knowledge about the real data process as accurate as possible, the ways of estimating the discrete approximating model may be quite different: (i) if the stochastic model is known as a solution of a stochastic differential equation, e.g., one may generate the scenario tree directly from the specified model; (ii) if a simulation algorithm is available, which allows simulating trajectories from all conditional distributions, a scenario tree can be generated by stochastic approximation; (iii) if only some observed trajectories of the scenario process are available, the construction of the approximating process can be based on non-parametric conditional density estimates.

math.OC↗

arXiv2019

Incorporating statistical model error into the calculation of acceptability prices of contingent claims

The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However, the model for the underlying asset price process is typically based on data and found by a statistical estimation procedure. We define a confidence set of possible estimated models by a nonparametric neighborhood of a baseline model. This neighborhood serves as ambiguity set for a multi-stage stochastic optimization problem under model uncertainty. We obtain distributionally robust solutions of the acceptability pricing problem and derive the dual problem formulation. Moreover, we prove a general large deviations result for the nested distance, which allows to relate the bid and ask prices under model ambiguity to the quality of the observed data.

q-fin.PR↗