<p style='text-indent:20px;'>In this paper we extend the reduced-form setting under model uncertainty introduced in [<xref ref-type="bibr" rid="b5">5</xref>] to include intensities following an affine process under parameter uncertainty, as defined in [<xref ref-type="bibr" rid="b15">15</xref>]. This framework allows us to introduce a longevity bond under model uncertainty in a way consistent with the classical case under one prior and to compute its valuation numerically. Moreover, we price a contingent claim with the sublinear conditional operator such that the extended market is still arbitrage-free in the sense of “no arbitrage of the first kind” as in [<xref ref-type="bibr" rid="b6">6</xref>]. </p>

In this paper we provide a generalization of the Feynmac-Kac formula under volatility uncertainty in presence of discounting. We state our result under different hypothesis with respect to the derivation in [9], where the Lipschitz continuity of some functionals is assumed which is not necessarily satisfied in our setting. In particular, we obtain the G-conditional expectation of a discounted payoff as the limit of C 1,2 solutions of some regularized PDEs, for different kinds of convergence. In applications, this permits to approximate such a sublinear expectation in a computationally efficient way.

We present a probabilistic construction of -valued non-linear affine processes with jumps. Given a set of affine parameters, we define a family of sublinear expectations on the Skorokhod space under which the canonical process X is a (sublinear) Markov process with a non-linear generator. This yields a tractable model for Knightian uncertainty for which the sublinear expectation of a Markovian functional can be calculated via a partial integro-differential equation.

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