2017/09/01 by Panpan Ren, Ren, Panpan, Jiang-Lun Wu +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Market Dynamics and Volatility #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1709.00471
28 pages, 1 figure
arxiv created 2017/09/01 · openalex publication_date 2017/09/01 · arxiv updated 2017/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, motivated by modelling currency exchange markets with matrix-valued stochastic processes, matrix-valued stochastic differential equations (SDEs) are formulated. This is done based on the matrix trace, as for the purpose of modelling currency exchange markets. To be more precise, we set up a Hilbert space structure for n× n square matrices via the trace of the Hadamard product of two matrices. With the help of this framework, one can then define stochastic integral of Itô type and Itô SDEs. Two types of sufficient conditions are discussed for the existence and uniqueness of solutions to the matrix-valued SDEs.