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## Stochastic modelling and optimization with applications to actuarial models

This thesis is devoted to Ruin Theory which sometimes referred to the collective ruin theory. In Actuarial Science, one of the most important problems is to determine the finite time or infinite time ruin probability of the risk process in an insurance company. To treat a realistic economic situation, the random interest factor should be taken into account. We first define the model with the interest rate and approximate the ruin probability for the model by the Brownian motion and develop several numerical methods to evaluate the ruin probability. Then we construct several models which incorporate possible investment strategies. We estimate the parameters from the simulated data. Then we find the optimal investment strategy with a given upper bound on the ruin probability. Finally we study the ruin probability for our class of models with the Heavy- Tailed claim size distribution.

Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:559692 |

Date | January 2012 |

Creators | Li, Mengdi |

Publisher | University of Nottingham |

Source Sets | Ethos UK |

Detected Language | English |

Type | Electronic Thesis or Dissertation |

Source | http://eprints.nottingham.ac.uk/12702/ |

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