Time-Consistent and Market-Consistent Evaluations
AbstractWe consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call `two step market evaluation.' This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two step market evaluations. We show further that in a dynamic setting with a continuous stock prices process every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also give characterization results and examples in terms of g-expectations in a Brownian-Poisson setting.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1109.1749.
Date of creation: Sep 2011
Date of revision: Dec 2013
Publication status: Published in Mathematical Finance, Vol. 24, No. 1 (January 2014), 25-65
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-09-16 (All new papers)
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