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In this work we consider one-dimensional generalized affine processes underthe paradigm of Knightian uncertainty (so-called non-linear generalized affinemodels). This extends and generalizes previous results in Fadina et al. (2019)and L\"utkebohmert et al. (2022). In particular, we study the case when thepayoff is allowed to depend on the path, like it is the case for barrieroptions or Asian options. To this end, we develop the path-dependent settingfor the value function which we do by relying on functional It\^o calculus. Weestablish a dynamic programming principle which then leads to a functionalnon-linear Kolmogorov equation describing the evolution of the value function.While for Asian options, the valuation can be traced back to PDE methods, thisis no longer possible for more complicated payoffs like barrier options. Tohandle such payoffs in an efficient manner, we approximate the functionalderivatives with deep neural networks and show that the numerical valuationunder parameter uncertainty is highly tractable. Finally, we consider theapplication to structural modelling of credit and counterparty risk, where bothparameter uncertainty and path-dependence are crucial and the approach proposedhere opens the door to efficient numerical methods in this field.

Affine models with path-dependence under parameter uncertainty and their application in finance