Research ArticleOpen accessEvery word in the titleASYMPTOTIC BEHAVIOR OF FINITE-TIME RUIN PROBABILITY IN A BY-CLAIM RISK MODEL WITH CONSTANT INTEREST RATELei WangThis study investigates the ruin probability of a renewal risk model with constant interest rate and by-claim parts. We assume that the claim size and the inter-arrival time satisfy a certain dependent structure with some additional assumptions on their distribution functions. In particular, we study the asymptotic behavior of P(R*δ´ (t, x) >x), which holds uniformly in a finite interval. … …Journal of Mathematics and Statistics, Vol. 10, Issue 3 · 5 Aug 2014 · 6,985 accessesView PDFCite
Research ArticleOpen accessIn the keywordsNumerical Ultimate Ruin Probabilities under Interest ForceJuma Kasozi, Jostein PaulsenThis work addresses the issue of ruin of an insurer whose portfolio is exposed to insurance risk arising from the classical surplus process. Availability of a positive interest rate in the financial world forces the insurer to invest into a risk free asset. We derive a linear Volterra integral equation of the second kind and apply an order four Block-by-block … …Journal of Mathematics and Statistics, Vol. 1, Issue 3 · 30 Sep 2005 · 6,491 accessesView PDFCite
Research ArticleOpen accessIn the keywordsApplication of Bi-Directional Grid Constrained Stochastic Processes to Algorithmic TradingAldo Taranto, Shahjahan KhanBi-directional Grid Constrained (BGC) Stochastic Processes (BGCSP) become more constrained the further they drift away from the origin or time axis are examined here. As they drift further away from the time axis, then the greater the likelihood of stopping, as if by two hidden reflective barriers. The theory of BGCSP is applied to a trading environment in which long … …Journal of Mathematics and Statistics, Vol. 17, Issue 1 · 6 Mar 2021 · 8,524 accessesView PDFCite
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 abstractMathematical Approach to the Ruin Problem with Compounding AssetsMercy Amaebi OrukariThis study considered the Ruin problem with an income process with stationary independent increments. The characterization is obtained which is general for the probability of $r(y)$, that the asset of a firm will never be zero whenever the initial asset level of the firm is $y$. The aim of this study is also to determine $r(y) = P \{ T … …Journal of Mathematics and Statistics, Vol. 18, Issue 1 · 8 Oct 2022 · 5,627 accessesView PDFCite