Stochastic calculus in a risk model with stochastic return on investments. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Elghribi, Moncef
• Is Part Of: Stochastics. Volume 93:Issue 1(2021)
• Page Start: 110
• Page End: 129
• Publication Date: 2021-01-02
• Subjects: Ruin theory -- risk process -- laplace transform -- stochastic return -- integro-differential equation; 60K10 -- 60G51 -- 60J35 -- 60J55 and 60J60; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2019.1708912
• Languages: English
• ISSNs: 1744-2508

Abstract

ABSTRACT: In this paper, we consider a perturbed risk model with stochastic return on investments. After discretizing of the renewal risk process, using the elementary properties of the classical conditional expectation, the Markov property and considerating the ordinary differential equation of a common density function of the inter-arrival times, we introduce a general integro-differential equation for the Laplace transform of the time of ruin with a positive initial surplus. The special cases, for different inter-arrival times distributions, are given in some details in the discrete renewal risk process.