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Insurance modeling in continuous time
Insurance modeling in continuous time
In this dissertation we consider the problem of pricing and hedging insurance liabilities, by extending concepts and methodologies recently introduced in the mathematical literature for financial markets to the modeling of life and non-life insurance markets. We propose for the first time a unified framework for both life and non-life insurance, which are traditionally studied separately, by generalizing the classic reduced-form framework, in order to introduce a nontrivial dependence structure between the financial market and the insurance market. The pricing and hedging problem of insurance products is solved by using risk-minimization method combined with the benchmark approach. The case of life insurance is then studied in detail in a polynomial diffusion model, which offers at the same time flexibility and the possibility of obtaining explicit pricing and hedging formulas. Beside model-dependent setting, we develop also a model-free framework for insurance markets, where we consider a family of probability measures, possibly mutually singular to each other. On one hand, we introduce and analyze for the first time the problem of superhedging payment streams under model uncertainty in continuous time. On the other hand, we construct explicitly a consistent sublinear conditional expectation on a progressively enlarged filtration, which generalizes existing results valid only on the canonical space endowed with the natural filtration. This sublinear conditional expectation is then used as pricing operator for insurance claims in view of the superhedging results.
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Zhang, Yinglin
2018
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Zhang, Yinglin (2018): Insurance modeling in continuous time. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics
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Abstract

In this dissertation we consider the problem of pricing and hedging insurance liabilities, by extending concepts and methodologies recently introduced in the mathematical literature for financial markets to the modeling of life and non-life insurance markets. We propose for the first time a unified framework for both life and non-life insurance, which are traditionally studied separately, by generalizing the classic reduced-form framework, in order to introduce a nontrivial dependence structure between the financial market and the insurance market. The pricing and hedging problem of insurance products is solved by using risk-minimization method combined with the benchmark approach. The case of life insurance is then studied in detail in a polynomial diffusion model, which offers at the same time flexibility and the possibility of obtaining explicit pricing and hedging formulas. Beside model-dependent setting, we develop also a model-free framework for insurance markets, where we consider a family of probability measures, possibly mutually singular to each other. On one hand, we introduce and analyze for the first time the problem of superhedging payment streams under model uncertainty in continuous time. On the other hand, we construct explicitly a consistent sublinear conditional expectation on a progressively enlarged filtration, which generalizes existing results valid only on the canonical space endowed with the natural filtration. This sublinear conditional expectation is then used as pricing operator for insurance claims in view of the superhedging results.