Showing papers by "Shige Peng published in 2006"
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TL;DR: In this article, the authors developed a notion of nonlinear expectation generated by a nonlinear heat equation with infinitesimal generator G. They also derived the existence and uniqueness of stochastic differential equation under their G-expectation.
Abstract: We develop a notion of nonlinear expectation --G-expectation-- generated by a nonlinear heat equation with infinitesimal generator G. We first study multi-dimensional G-normal distributions. With this nonlinear distribution we can introduce our G-expectation under which the canonical process is a multi dimensional G-Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of Ito's type with respect to our G-Brownian motion and derive the related Ito's formula. We have also obtained the existence and uniqueness of stochastic differential equation under our G-expectation.
346 citations
TL;DR: In this article, the authors presented a new approach to obtain the comparison theorem of two 1-dimensional SDEs with diffusion and jumps, where the comparison requirement was regarded as to keep the solution ( X t 1, X t 2 ) within the constraint K = { ( x 1, x 2 ) ; x 1 ⩽ x 2 }.
146 citations
TL;DR: Hu et al. as discussed by the authors gave a necessary and sufficient condition under which the comparison theorem holds for multidimensional backward stochastic differential equations (BSDEs) and for matrix-valued BSDEs.
81 citations
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TL;DR: In this article, the domination condition (A5) in (25) was used to test if a dynamic pricing mechanism under investigation is a g-pricing mechanism, which was statistically tested using CME data documents.
Abstract: In this paper we study dynamic pricing mechanisms of financial derivatives A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a backward stochastic differential equation with g as its generating function Black-Scholes pricing model is a special linear case of this pricing mechanism We are mainly concerned with two types of pricing mechanisms in an option market: the market pricing mechanism through which the market prices of options are produced, and the ask-bid pricing mechanism operated through the system of market makers The later one is a typical nonlinear pricing mechanism Data of prices produced by these two pricing mechanisms are usually quoted in an option market
We introduce a criteria, ie, the domination condition (A5) in (25) to test if a dynamic pricing mechanism under investigation is a g--pricing mechanism This domination condition was statistically tested using CME data documents The result of test is significantly positive We also provide some useful characterizations of a pricing mechanism by its generating function
30 citations
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TL;DR: In this article, the domination condition (A5 in (2.5) was introduced to test if a dynamic pricing mechanism under investigation is a g-pricing mechanism, and the result of test was significantly positive.
Abstract: In this paper we study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a backward stochastic differential equation with g as its generating function. Black-Scholes pricing model is a special linear case of this pricing mechanism. We are mainly concerned with two types of pricing mechanisms in an option market: the market pricing mechanism through which the market prices of options are produced, and the ask-bid pricing mechanism operated through the system of market makers. The later one is a typical nonlinear pricing mechanism. Data of prices produced by these two pricing mechanisms are usually quoted in an option market. We introduce a criteria, i.e., the domination condition (A5) in (2.5) to test if a dynamic pricing mechanism under investigation is a g--pricing mechanism. This domination condition was statistically tested using CME data documents. The result of test is significantly positive. We also provide some useful characterizations of a pricing mechanism by its generating function.
18 citations
Posted Content•
TL;DR: In this paper, different algorithms for backward stochastic differential equations (BSDEs) based on random walk framework for 1-dimensional Brownian motion are studied and convergence results for different types of BSDEs are presented.
Abstract: In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.
4 citations
Posted Content•
28 Nov 2006
TL;DR: In this paper, different algorithms for backward stochastic differential equations (BSDEs) based on random walk framework for 1-dimensional Brownian motion are studied and convergence results for different types of BSDEs are presented.
Abstract: In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.
4 citations
Posted Content•
TL;DR: In this paper, a new nonlinear expectation via reflected BSDE with a constraint was introduced and the Doob-Meyer decomposition with respect to the super(sub)martingale was proved.
Abstract: In this paper, we study a type of reflected BSDE with a constraint and introduce a new kind of nonlinear expectation via BSDE with a constraint and prove the Doob-Meyer decomposition with respect to the super(sub)martingale introduced by this nonlinear expectation. We then apply the results to the pricing of American options in incomplete market.
2 citations