Before and after default: information and optimal portfolio via anticipating calculus

José Antonio Salmerón Garrido, Giulia Di Nunno and Bernardo D'Auria

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: Default risk calculus emerges naturally in a portfolio optimization problem whenthe risky asset is threatened with a bankruptcy. The usual stochastic control techniques do not hold in this case and some additional assumptions are generally added to achieve the optimization in a before-and-after default context. We show how it is possible to avoid one of theses restrictive assumptions, the so-called Jacod density hypothesis, by using the framework of the forward integration. In particular, in the logarithmic utility case, in order to get the optimal portfolio the right condition it is proved to be the intensity hypothesis. We use the anticipating calculus to analyze the existence of the optimal portfolio for the logarithmic utility, and than under the assumption of existence of the optimal portfolio we prove the semimartingale decomposition of the risky asset in the filtration enlarged with the default process.

Keywords: Optimal; Portfolio; Default; Risk; Progressive; Enlargement; Forward; Integrals; Malliavin; Calculus (search for similar items in EconPapers)
Date: 2022-07-06
New Economics Papers: this item is included in nep-rmg and nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:35411

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