Dynamically Consistent Nonlinear Evaluations and Expectations

Details Dynamically Consistent Nonlinear Evaluations and Expectations Dynamically Consistent Nonlinear Evaluations and Expectations

2005-01-24

arxiv.org/abs/math/0501415v1

Mathematics

Probability

46 pages

Scientific paper

How an economic agent (a firm, an investor or a financial market) evaluates a contingent claim, say a European type of derivatives X, with maturity t? In this paper we study a mechanism of dynamic expectations and evaluations. We give the axiomatic conditions of the time consistency. We prove that, under a domination condition, a time consistent nonlinear evaluation is in fact a g-expectation, i.e., it is completely determined a BSDE in which the generator is a given function g.

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