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In this paper, we consider a risk process with deterministic growth andmultiplicative jumps to model the capital of a low-income household. Reflectingthe high-risk nature of the low-income environment, capital losses are assumedto be proportional to the level of accumulated capital at the jump time. Ouraim is to derive the probability that a household falls below the poverty line,i.e. the trapping probability, where ``trapping" occurs when the level ofcapital of a household holds falls below the poverty line, to an area fromwhich it is difficult to escape without external help. Considering theremaining proportion of capital to be distributed as a special case of the betadistribution, closed-form expressions for the trapping probability are obtainedvia analysis of the Laplace transform of the infinitesimal generator of theprocess. To study the impact of insurance on this probability, introduction ofan insurance product offering proportional coverage is presented. Theinfinitesimal generator of the insured process gives rise to non-localdifferential equations. To overcome this, we propose a recursive method forderiving a closed-form solution of the integro-differential equation associatedwith the infinitesimal generator of the insured process and provide a numericalestimation method for obtaining the trapping probability. Constraints on therate parameters of the process that prevent certain trapping are derived inboth the uninsured and insured cases using classical results from risk theory.

On the impact of insurance on households susceptible to random proportional losses: An analysis of poverty trapping