Numerical Method for the Perturbed Risk Model with Randomized Observation and Two-sided Jumps

Abstract

In this paper, we considered the perturbed risk model with two-sided jumps, where ruin can only occur at some Poisson times. A generalized Gerber-Shiu-type function is discussed involving the number of observations, the ruin time and the deficit at ruin. Integro-differential equations with certain boundary conditions are derived. As it is difficult to get closed-form solutions, a numerical sinc method is proposed.

Modeling the Effect of Random Environmental Perturbation on Data Precision in Niger Delta Crude Oil Production

“…Similarly, the evaluation of the historical influence of petroleum activities on various episodes of economic crises in Nigeria, using a descriptive technique to analyse data obtained from secondary sources and affirming that transmogrification of the economy from agricultural-based to petroleum-based laid the foundation for the current economic crises in Nigeria according to Paul [4]. Also, while exploring the extent of the environmental degradation in the Niger Delta region and examining the efforts of oil companies in remediating the degraded farmlands in the Niger Delta, finds that oil pollution causes damage to human health, agricultural land and fish ponds as well as long-standing ecological malfunctioning [5][6][7][8].…”