Abstract
In this work, the non-homogeneous risk model is considered. In such a model, claims and inter-arrival times are independent but possibly non-identically distributed. The easily verifiable conditions are found such that the ultimate ruin probability of the model satisfies the exponential estimate exp { − ϱ u } for all values of the initial surplus u ⩾ 0 . Algorithms to estimate the positive constant ϱ are also presented. In fact, these algorithms are the main contribution of this work. Sharpness of the derived inequalities is illustrated by several numerical examples.
Highlights
Insurance is a means of protection from random and untoward events, which can lead to significant financial losses
We further give the statement on the upper bound of the ultimate ruin probability ψ(u) in the homogeneous renewal risk model
Three assertions are presented on the Lundberg-type inequalities for the ultimate ruin probability in the case of the non-homogeneous renewal risk model
Summary
Insurance is a means of protection from random and untoward events, which can lead to significant financial losses. It is a method of risk management, that is used in order to hedge against a contingent loss risk. Risk theory came into being and was developed in order to provide a basis for the existence and significance of the insurance system. One of the most fundamental problems in risk theory is the ruin problem. It analyzes the behavior of a stochastic process, that represents the evolution of the capital of an insurance company. From an insurer’s point of view, the surplus can be defined as “initial surplus + premium income − claim payment”
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