We present a probabilistic construction of R^(d)-valued non-linear affine processes with jumps.Given a setΘof affine parameters,we define a family of sublinear expectations on the Skorokhod space under which the cano...We present a probabilistic construction of R^(d)-valued non-linear affine processes with jumps.Given a setΘof 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.展开更多
In this paper,we study strongly robust optimal control problems under volatility uncertainty.In the G-framework,we adapt the stochastic maximum principle to find necessary and sufficient conditions for the existence o...In this paper,we study strongly robust optimal control problems under volatility uncertainty.In the G-framework,we adapt the stochastic maximum principle to find necessary and sufficient conditions for the existence of a strongly robust optimal control.展开更多
In this paper we extend the reduced-form setting under model uncertainty introduced in[5]to include intensities following an affine process under parameter uncertainty,as defined in[15].This framework allows us to int...In this paper we extend the reduced-form setting under model uncertainty introduced in[5]to include intensities following an affine process under parameter uncertainty,as defined in[15].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[6].展开更多
We study the concept of financial bubbles in a market model endowed with a set P of probability measures,typically mutually singular to each other.In this setting,we investigate a dynamic version of robust superreplic...We study the concept of financial bubbles in a market model endowed with a set P of probability measures,typically mutually singular to each other.In this setting,we investigate a dynamic version of robust superreplication,which we use to introduce the notions of bubble and robust fundamental value in a way consistent with the existing literature in the classical case P={P}.Finally,we provide concrete examples illustrating our results.展开更多
文摘We present a probabilistic construction of R^(d)-valued non-linear affine processes with jumps.Given a setΘof 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.
基金The research leading to these results received funding from the European Research Council under the European Community’s Seventh Framework Program(FP7/2007-2013)/ERC grant agreement 228087.
文摘In this paper,we study strongly robust optimal control problems under volatility uncertainty.In the G-framework,we adapt the stochastic maximum principle to find necessary and sufficient conditions for the existence of a strongly robust optimal control.
文摘In this paper we extend the reduced-form setting under model uncertainty introduced in[5]to include intensities following an affine process under parameter uncertainty,as defined in[15].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[6].
文摘We study the concept of financial bubbles in a market model endowed with a set P of probability measures,typically mutually singular to each other.In this setting,we investigate a dynamic version of robust superreplication,which we use to introduce the notions of bubble and robust fundamental value in a way consistent with the existing literature in the classical case P={P}.Finally,we provide concrete examples illustrating our results.
