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

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  • Jos'e A. Salmer'on
  • Giulia Di Nunno
  • Bernardo D'Auria

Abstract

Default risk calculus plays a crucial role in portfolio optimization when the risky asset is under threat of bankruptcy. However, traditional stochastic control techniques are not applicable in this scenario, and additional assumptions are required to obtain the optimal solution in a before-and-after default context. We propose an alternative approach using forward integration, which allows to avoid one of the restrictive assumptions, the Jacod density hypothesis. We demonstrate that, in the case of logarithmic utility, the weaker intensity hypothesis is the appropriate condition for optimality. Furthermore, we establish the semimartingale decomposition of the risky asset in the filtration that is progressively enlarged to accommodate the default process, under the assumption of the existence of the optimal portfolio. This work aims to provide valueable insights for developing effective risk management strategies when facing default risk.

Suggested Citation

  • Jos'e A. Salmer'on & Giulia Di Nunno & Bernardo D'Auria, 2022. "Before and after default: information and optimal portfolio via anticipating calculus," Papers 2208.07163, arXiv.org, revised May 2023.
    • Handle: RePEc:arx:papers:2208.07163
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    References listed on IDEAS

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