it In this paper, the properties of set-valued Eventual Supermartingle are discussed. The main result is that suppose {Fn, n ≥ 1） Lfc^1（X） be set-valued Eventual Supermartingle, ifsupE（d（0,Fτ）） 〈 ∞, then ...it In this paper, the properties of set-valued Eventual Supermartingle are discussed. The main result is that suppose {Fn, n ≥ 1） Lfc^1（X） be set-valued Eventual Supermartingle, ifsupE（d（0,Fτ）） 〈 ∞, then Fn →KF and SF^1≠φ, here T is the sets of all T bounded stopping times.展开更多
In this paper the regularity of set-valued martingales in the sense of JL is given first. Then we show some kinds of Doob's stopping theorems for set-valued (super, sub) martingales with continuous time.
Based on Refs. [1—8], we discuss the following problem in this note.Let (Ω, A, P)be a complete probability space and X be a separable Banach space with the dual X~*.
Let {S t H, t ≥ 0） be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 〈 H 〈 1. Its main properties are studied. They suggest that SH lies between the ...Let {S t H, t ≥ 0） be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 〈 H 〈 1. Its main properties are studied. They suggest that SH lies between the sub-fractional Brownian motion and the mixed fractional Brownian motion. We also determine the values of H for which SH is not a semi-martingale.展开更多
This article studies European contingent claims in a randomly constrained market and derives their lower-hedging costs by means of a family of auxiliary risk premiums.
In this paper, we prove that under the F<sub>4</sub> condition, any L log<sup>+</sup> L bounded two-parameter Banach space valued martingale converges almost surely to an integrable Banach spac...In this paper, we prove that under the F<sub>4</sub> condition, any L log<sup>+</sup> L bounded two-parameter Banach space valued martingale converges almost surely to an integrable Banach space valued random variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains true if the F<sub>4</sub> condition is replaced by the weaker local F<sub>4</sub> condition.展开更多
文摘it In this paper, the properties of set-valued Eventual Supermartingle are discussed. The main result is that suppose {Fn, n ≥ 1） Lfc^1（X） be set-valued Eventual Supermartingle, ifsupE（d（0,Fτ）） 〈 ∞, then Fn →KF and SF^1≠φ, here T is the sets of all T bounded stopping times.
基金Supported by the National Natural Science Foundation of China !(19971072)
文摘In this paper the regularity of set-valued martingales in the sense of JL is given first. Then we show some kinds of Doob's stopping theorems for set-valued (super, sub) martingales with continuous time.
文摘Based on Refs. [1—8], we discuss the following problem in this note.Let (Ω, A, P)be a complete probability space and X be a separable Banach space with the dual X~*.
文摘Let {S t H, t ≥ 0） be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 〈 H 〈 1. Its main properties are studied. They suggest that SH lies between the sub-fractional Brownian motion and the mixed fractional Brownian motion. We also determine the values of H for which SH is not a semi-martingale.
文摘This article studies European contingent claims in a randomly constrained market and derives their lower-hedging costs by means of a family of auxiliary risk premiums.
基金Project supported by the National Natural Science Foundation of Chinathe State Education Commission Ph. D. Station Foundation
文摘In this paper, we prove that under the F<sub>4</sub> condition, any L log<sup>+</sup> L bounded two-parameter Banach space valued martingale converges almost surely to an integrable Banach space valued random variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains true if the F<sub>4</sub> condition is replaced by the weaker local F<sub>4</sub> condition.
