In recent years, the Markov Regime-Switching model and the class of Archimedean
copulas have been widely applied to a variety of finance-related fields. The
Markov Regime-Switching model can reflect the reality that the underlying economy
is changing over time. Archimedean copulas are one of the most popular
classes of copulas because they have closed form expressions and have great flexibility in modeling different kinds of dependencies.
In the thesis, we first consider a discrete-time risk process based on the compound
binomial model with regime-switching. Some general recursive formulas
of the expected penalty function have been obtained. The orderings of ruin probabilities are investigated. In particular, we show that if there exists a stochastic
dominance relationship between random claims at different regimes, then we can
order ruin probabilities under different initial regimes.
Regarding capital allocation problems, which are important areas in finance
and risk management, this thesis studies the problems of optimal allocation of
policy limits and deductibles when the dependence structure among risks is modeled
by an Archimedean copula. By employing the concept of arrangement
increasing and stochastic dominance, useful qualitative results of the optimal
allocations are obtained.
Then we turn our attention to a new family of risk measures satisfying a set
of proposed axioms, which includes the class of distortion risk measures with
concave distortion functions. By minimizing the new risk measures, we consider
the optimal allocation of policy limits and deductibles problems based on the
assumption that for each risk there exists an indicator random variable which
determines whether the risk occurs or not. Several sufficient conditions to order
the optimal allocations are obtained using tools in stochastic dominance theory. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy
| Identifer | oai:union.ndltd.org:HKU/oai:hub.hku.hk:10722/167205 |
| Date | January 2012 |
| Creators | Liu, Binbin, 刘彬彬 |
| Contributors | Cheung, KC |
| Publisher | The University of Hong Kong (Pokfulam, Hong Kong) |
| Source Sets | Hong Kong University Theses |
| Language | English |
| Detected Language | English |
| Type | PG_Thesis |
| Source | http://hub.hku.hk/bib/B48199291 |
| Rights | The author retains all proprietary rights, (such as patent rights) and the right to use in future works., Creative Commons: Attribution 3.0 Hong Kong License |
| Relation | HKU Theses Online (HKUTO) |
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