Showing papers by "Shige Peng published in 2005"
TL;DR: In this paper, a nonlinear generalization of the well-known Kolmogorov's consistent theorem is used to construct filtrationconsistent nonlinear expectations via nonlinear Markov chains.
Abstract: This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared to the author's previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probability measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations. The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
181 citations
TL;DR: In this paper, a solution of BSDE can be reflected by a very irregular L 2 -obstacle, and it is shown that this problem is equivalent to finding the smallest g-supermartingale that dominates this obstacle.
Abstract: In this paper we show how a solution of BSDE can be reflected by a very irregular L 2 -obstacle. We prove that this problem is equivalent to find the smallest g-supermartingale of BSDE that dominates this obstacle. We then obtain the existence and uniqueness and continuous dependence theorem for this reflected BSDE. We also consider the problem of existence and uniqueness of reflected BSDE with double L 2 obstacles, by using a penalization method. A new monotonic limit theorem is developed to prove the convergence of the penalization sequence, and to prove the existence theorem. We also prove that this reflected BSDE with double obstacles is equivalent to a problem of the smallest g-supermartingale and the largest g-submartingale.
143 citations
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TL;DR: In this article, the authors study a mechanism of dynamic expectations and evaluations of contingent claims and prove that 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.
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.
72 citations