Dynamically Consistent Nonlinear Evaluations and Expectations

TL;DR

This paper investigates the evaluation of contingent claims by economic agents, establishing axiomatic conditions for dynamic, time-consistent nonlinear evaluations and demonstrating their equivalence to g-expectations via BSDEs under certain conditions.

Contribution

It provides a rigorous axiomatic framework for dynamic evaluations and proves their equivalence to g-expectations, advancing the theoretical understanding of nonlinear evaluation mechanisms.

Findings

Time consistency characterized by axiomatic conditions

Nonlinear evaluations under domination are g-expectations

Evaluation mechanism linked to BSDEs with generator g

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.