Research ArticleOpen accessIn the keywordsDrawdown and Drawup of Bi-Directional Grid Constrained Stochastic ProcessesAldo Taranto, Shahjahan KhanThe Grid Trading Problem (GTP) of mathematical finance, used in portfolio loss minimization, generalized dynamic hedging and algorithmic trading, is researched by examining the impact of the drawdown and drawup of discrete random walks and of Itô diffusions on the Bi-Directional Grid Constrained (BGC) stochastic process for profit Pt and equity Et over time. A comprehensive Discrete Difference Equation (DDE) … …Journal of Mathematics and Statistics, Vol. 16, Issue 1 · 14 Sep 2020 · 9,153 accessesView PDFCite
Research ArticleOpen accessIn the abstractStatistical Inference on a Black-Scholes Model with Jumps. Application in HydrologyJ. Cesars, S.P. Nuiro, J. VaillantWe consider a Stochastic Differential Equation (SDE) driven by a Wiener process and a Poisson measure. This latter measure is associated with a sequence of identically distributed jump amplitudes. Properties of the SDE solution are presented with respect to the associated Wiener and Poisson processes. An algorithm is provided allowing exact numerical simulations of such SDE and implementable within R … …Journal of Mathematics and Statistics, Vol. 15, Issue 1 · 24 Jul 2019 · 7,502 accessesView PDFCite