## Crash Hedging Strategies and Optimal Portfolios

- In traditional portfolio optimization under the threat of a crash the investment horizon or time to maturity is neglected. Developing the so-called crash hedging strategies (which are portfolio strategies which make an investor indifferent to the occurrence of an uncertain (down) jumps of the price of the risky asset) the time to maturity turns out to be essential. The crash hedging strategies are derived as solutions of non-linear differential equations which itself are consequences of an equilibrium strategy. Hereby the situation of changing market coefficients after a possible crash is considered for the case of logarithmic utility as well as for the case of general utility functions. A benefit-cost analysis of the crash hedging strategy is done as well as a comparison of the crash hedging strategy with the optimal portfolio strategies given in traditional crash models. Moreover, it will be shown that the crash hedging strategies optimize the worst-case bound for the expected utility from final wealth subject to some restrictions. Another application is to model crash hedging strategies in situations where both the number and the height of the crash are uncertain but bounded. Taking the additional information of the probability of a possible crash happening into account leads to the development of the q-quantile crash hedging strategy.
- Crash Hedging Strategien und Optimale Portfolios

Author: | Olaf Arnd Menkens |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-18010 |

Advisor: | Ralf Korn |

Document Type: | Doctoral Thesis |

Language of publication: | English |

Year of Completion: | 2004 |

Year of Publication: | 2004 |

Publishing Institute: | Technische Universität Kaiserslautern |

Granting Institute: | Technische Universität Kaiserslautern |

Acceptance Date of the Thesis: | 2004/11/30 |

Tag: | Betrachtung des Schlimmstmöglichen Falles; Crash Hedging; Gleichgewichtsstrategien; Portfolio Optimierungchanging market coefficients; crash hedging; equilibrium strategies; portfolio optimization; worst-case scenario |

GND-Keyword: | Hamilton-Jacobi-Differentialgleichung ; Portfolio Selection; Stochastische dynamische Optimierung |

Faculties / Organisational entities: | Fachbereich Mathematik |

DDC-Cassification: | 510 Mathematik |

MSC-Classification (mathematics): | 49J15 Optimal control problems involving ordinary differential equations |

49J20 Optimal control problems involving partial differential equations | |

60H15 Stochastic partial differential equations [See also 35R60] | |

91B70 Stochastic models |