An infinite-dimensional model of liquidity in financial markets

作     者：Sergey V Lototsky Henry Schellhorn Ran Zhao 

作者机构：Department of MathematicsUniversity of Southern CaliforniaLos AngelesCA 90089USA Institute of Mathematical SciencesClaremont Graduate UniversityClaremontCA 91711USA Drucker School of ManagementClaremont Graduate UniversityClaremontCA 91711USA 

出 版 物：《Probability, Uncertainty and Quantitative Risk》 (概率、不确定性与定量风险（英文）)

年 卷 期：2021年第6卷第2期

页      面：117-138页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Liquidity modeling Brownian sheet Itô-Wentzell formula No-arbitrage condition Stochastic partial differential equations 

摘      要：We consider a dynamic market model of liquidity where unmatched buy and sell limit orders are stored in order *** resulting net demand surface constitutes the sole input to the *** model demand using a two-parameter Brownian motion because(i)different points on the demand curve correspond to orders motivated by different information,and(ii)in general,the market price of risk equation of no-arbitrage theory has no solutions when the demand curve is driven by a finite number of factors,thus allowing for *** prove that if the driving noise is infinite-dimensional,then there is no arbitrage in the *** the equivalent martingale measure,the clearing price is a martingale,and options can be priced under the no-arbitrage *** consider several parameterizations of the model and show advantages of specifying the demand curve as a quantity that is a function of price,as opposed to price as a function of *** online appendix presents a basic empirical analysis of the model:calibration using information from actual order books,computation of option prices using Monte Carlo simulations,and comparison with observed data.