Time-Consistent and Market-Consistent Evaluations
We 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.
|Date of creation:||Sep 2011|
|Date of revision:||Dec 2013|
|Publication status:||Published in Mathematical Finance, Vol. 24, No. 1 (January 2014), 25-65|
|Contact details of provider:|| Web page: http://arxiv.org/|
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