A CONVERSE COMPARISON THEOREM FOR BSDES AND RELATED PROPERTIES OF g–EXPECTATION
نویسندگان
چکیده
In [1], Z. Chen proved that, if for each terminal condition ξ, the solution of the BSDE associated to the standard parameter (ξ, g1) is equal at time t = 0 to the solution of the BSDE associated to (ξ, g2) then we must have g1 ≡ g2. This result yields a natural question: what happens in the case of an inequality in place of an equality? In this paper, we try to investigate this question and we prove some properties of “g–expectation”, notion introduced by S. Peng in [8].
منابع مشابه
On Quadratic g-Evaluations/Expectations and Related Analysis
In this paper we extend the notion of g-evaluation, in particular g-expectation, of Peng [10, 11] to the case where the generator g is allowed to have a quadratic growth. We show that some important properties of the g-expectations, including a representation theorem between the generator and the corresponding g-expectation, and consequently the reverse comparison theorem of quadratic BSDEs as ...
متن کاملComparisons for Backward Stochastic Differential Equations on Markov Chains and related No-Arbitrage Conditions
Abstract: Most previous contributions on BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov Chains, we develop a theory of nonlinear expectations in the spirit of (15). We prove basic properties of these ...
متن کاملN ov 2 00 7 Mean - Field Backward Stochastic Differential Equations and Related Partial Differential Equations ∗
In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward SDEs, corresponding to a large number of “particles” (or “agents”). The objective of the present paper is to deepen the investigation of such Mean-Field BSD...
متن کاملA simple constructive approach to quadratic BSDEs with or without delay
This paper provides a simple approach for the consideration of quadratic BSDEs with bounded terminal conditions. Using solely probabilistic arguments, we retrieve the existence and uniqueness result derived via PDE-based methods by Kobylanski [11]. This approach is related to the study of quadratic BSDEs presented by Tevzadze [14]. Our argumentation, as in [14], highly relies on the theory of B...
متن کاملAbout the Pricing Equations in Finance
In this article we study a Markovian BSDE and the associated system of partial integro-differential obstacle problems, in a flexible set-up made of a jump-diffusion with regimes. These equations are motivated by numerous applications in financial modeling, whence the title of the paper. This financial motivation is developed in the first part of the paper, which provides a synthetic view of the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999