Dynamically Consistent Nonlinear Evaluations and Expectations

By Shige Peng. 2005

75 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/0fd55fa22d45dfc0db9a4df3698a8c856d6d5bbf

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In Control and Systems Engineering

In Finance

In Management Science and Operations Research

Citations in the corpus

VALUATIONS AND DYNAMIC CONVEX RISK MEASURES (2007, background): “…as the cash balance I [τ,T ] K, which pays nothing up until time τ , then a lump sum of Kτ . dynamic consistency appears much simpler: see, for example, Peng (2005) and Detlefsen and Scandolo (2005), where it is possible to express dynamic consistency as πτ = πτπσ for any stopping times τ ≤ σ .”
Existence and Comparisons for BSDEs in general spaces (2010, background): “These operators, discussed in [19], are closely related to the theory of dynamic risk measures, as in [1, 3, 21] and others, as each concave nonlinear expectation E (·|Ft ) corresponds to a dynamic convex risk measure through the relationship ρt(Q) = −E (Q|Ft ).”
Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011, methodology): “We prefer to call (3.2) a BSDE under nonlinear expectation, (see Peng (2005b)), or a fully nonlinear BSDE, instead of 2BSDE.”
G -Expectation, G -Brownian Motion and Related Stochastic Calculus of Itô Type (2006, unknown): “Since then many results have been obtained in this subject (see, among others, [3], [4], [5], [6], [10], [11], [7], [8], [22], [23], [34], [38], [39], [41], [43], [24]).”
Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation (2006, unknown): “Since then many results have been obtained in this subject (see, among others, [3], [4], [5], [6], [10], [11], [7], [8], [24], [25], [35], [38], [39], [41], [45]).”
Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions (2008, methodology): “As noted in (15), the theory of nonlinear expectations provides an ideal setting for the discussion of risk measures in the sense of (1) and others.”
A general theory of finite state Backward Stochastic Difference Equations (2008, unknown): “We shall not discuss in detail the more general theory of nonlinear evaluations, as in [8] or [4].”
The smallest g-supermartingale and reflected BSDE with single and double L2 obstacles (2005, result): “We also refer to [23,22,20,14,5] for some related studies on this su The paper is organized as follows: In the next section, we state our main problems of the reflected B Definition 2.”