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On existence,uniqueness and convergence of multi-valued stochastic diferential equations driven by continuous semimartingales

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Science China Mathematics 2014年第3期57卷 589-607页

作者： REN JiaGang WU Jing ZHANG Hua School of Mathematics and Computational Science Sun Yat-sen University

In this paper we study the existence and uniqueness of solutions of multi-valued stochastic differen- tial equations driven by continuous semimartingales when the coefficients are stochastically Lipschitz continuous. ... 详细信息

关键词： multi-valued stochastic differential equation semimartingale existence uniqueness convergence

THE CHANGE OF VARIABLES FORMULA FOR THE LOCAL TIMES OF semimartingaleS

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Chinese Science Bulletin 1988年第21期33卷 1755-1757页

作者：严加安 Institute of Applied Mathematics Academia Sinica Beijing

Let (X_t) be a semimartingale. We denote by (L_t~α(X)) the local time at a of (X_t). If f is the difference of two convex functions on R, it is well known that f(X) is a semimartingale. The purpose of this note is to give the change of variables formula for the local times of semimartingales, that is, a formula expressing the local times of f(X) in terms of {L_t~α(X),α∈R}.

关键词： semimartingale local time the change of variables formula

Testing long memory based on a discretely observed process

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Applied Mathematics(A Journal of Chinese Universities) 2016年第3期31卷 253-268页

作者： LIU Guang-ying ZHANG Xin-sheng ZHANG Shi-bin Department of Statistics Nanjing Audit University School of Mathematical Sciences Zhejiang University Department of Statistics Fudan University Department of Mathematics Shanghai Maritime University

In this paper we consider the problem of testing long memory for a continuous time process based on high frequency data. We provide two test statistics to distinguish between a semimartingale and a fractional integral process with jumps, where the integral is driven by a fractional Brownian motion with long memory. The small-sample performances of the statistics are evidenced by means of simulation studies. The real data analysis shows that the fractional integral process with jumps can capture the long memory of some financial data.

关键词： long memory jump fractional Brownian motion semimartingale high frequency data power variation

Stochastic regression and its application to hedging in finance

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Science China Mathematics 2009年第6期52卷 1365-1372页

作者： JING BingYi KONG XinBing LIU Zhi ZHANG Bo Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina School of Statistics Renmin University of ChinaBeijing 100072China

In this paper we investigate how to employ stochastic regression to hedge risks in finance,where the risk of a security is measured by its quadratic variation *** and Zhang used this technique to demonstrate how to reduce the risk of a given security by introducing another *** this paper,we investigate how to further reduce the remaining unhedgable risk by adding more hedging *** practical guidelines on how to choose those hedging securities in practice is also given.

关键词： risks hedging semimartingale Ito process

Affine processes under parameter uncertainty

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Probability, Uncertainty and Quantitative Risk 2019年第1期4卷 80-114页

作者： Tolulope Fadina Ariel Neufeld Thorsten Schmidt Department of Mathematical Stochastics University of FreiburgErnst-Zermelo Str.179104 FreiburgGermany Nanyang Technological University Division of Mathematical SciencesSingaporeSingapore Freiburg Institute of Advanced Studies(FRIAS) Freiburg im BreisgauGermany University of Strasbourg Institute for Advanced Study(USIAS) StrasbourgFrance

We develop a one-dimensional notion of affine processes under parameter uncertainty,which we call nonlinear affine *** is done as follows:given a setof parameters for the process,we construct a corresponding nonlinear expectation on the path space of continuous *** a general dynamic programming principle,we link this nonlinear expectation to a variational form of the Kolmogorov equation,where the generator of a single affine process is replaced by the supremum over all corresponding generators of affine processes with parameters *** nonlinear affine process yields a tractable model for Knightian uncertainty,especially for modelling interest rates under *** then develop an appropriate Ito formula,the respective term-structure equations,and study the nonlinear versions of the Vasiˇcek and the Cox–Ingersoll–Ross(CIR)***,we introduce the nonlinear Vasicek–CIR *** model is particularly suitable for modelling interest rates when one does not want to restrict the state space a priori and hence this approach solves the modelling issue arising with negative interest rates.

关键词： Affine processes Knightian uncertainty Riccati equation Vasicek model Cox-Ingersoll-Ross model Nonlinear Vasicek/CIR model Heston model Ito formula Kolmogorov equation Fully nonlinear PDE semimartingale

Information-based approach:Pricing of a credit risky asset in the presence of default time

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Probability, Uncertainty and Quantitative Risk 2024年第3期9卷 405-430页

作者： Mohammed Louriki Mathematics Department Faculty of Sciences SemalaliaCadi Ayyad UniversityBoulevard Prince Moulay AbdellahP.O.Bor 2390Marrakesh 40000Morocco

We extend the information-based asset-pricing framework by Brody,Hughston&Macrina to incorporate a stochastic bankruptcy time for the writer of the *** model introduces a non-defaultable cash flow Zr to be made at time T,alongside the time T of a possible bankruptcy of the writer of the asset are in line with the filtration generated by a Brownian random bridge with length v=T^T and pinning point ZT,where is a *** Z and T are not necessarily *** model does not depend crucially on the interpretation of as a bankruptcy *** derived the price process of the asset and compute the prices of associated *** dynamics of the price process satisfy a diffusion *** the approach of P.-***,we provide the explicit computation of the compensator of *** special properties of the bridge process,we also provide the explicit expression of the compensator of Zr I(v,+o).The resulting conclusion highlights the totally inaccessible property of the stopping time *** characteristic is particularly suitable for financial markets where the time of default of a writer cannot be predictable from any other signal in the system until default happens.

关键词： Brownian random bridge semimartingale Local time Compensator process Information-based asset pricing Credit risk Default time Totally inaccessible stopping time