Dynamically Consistent Nonlinear Evaluations and Expectations

2005/01/24 by Shi-Ge Peng, Peng, Shi-Ge · 1 citation
Mathematics · #60H10 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.FA #math.PR #msc:60H10

paper · pdf · doi:10.48550/arxiv.math/0501415

46 pages

arxiv created 2005/01/24 · arxiv updated 2009/12/01

Abstract

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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