In a diffusion model of risk, we focus on the initial capital needed to make the probability of ruin within finite time equal to a prescribed value. It is defined as a solution of a nonlinear equation. The endeavor to write down and to investigate analytically this solution as a function of the...

Underwriters’ desire to show a good annual review is known to be a rationale of the aggressive pricing conduct. On the competitive insurance market, it impacts the global insurance processes and can lead to the competition-originated underwriting cycles. Applying Lundberg’s model of the...

In this paper we analyze a measure of the insurance company’s value in an extended Lundberg model which includes the effect of competition on pricing. The extended model is designed to be an integral part of a multi-year controlled risk model of a company operating on both competitive...

In insurance two major types of cycles are known: (a) regular many years long up- and down-swings referred to as underwriting cycles and (b) irregular short-range fluctuations. The key rationale of the underwriting cycles is migration of insureds triggered by the insurers’ price competition...

This paper deals with ruin capital uα,t(c∣λ,μ) in the classical Lundberg model of risk. It is defined as the initial capital needed to keep the probability of ruin within finite time t equal to a predefined value α. Considered as a decreasing function of premium rate c, the ruin capital is...

In Malinovskii (2012), level premium rate and level initial capital were used to construct solvent and equitable strategies in a multi-period game model of risk. Focused there was the level initial capital regarded as a function of the annual premium rate. With the prospective goal to study...

Ruin capital is a function of premium rate set to render the probability of ruin within finite time equal to a given value. The analytical studies of this function in the classical Lundberg model of risk with exponential claim sizes done in Malinovskii (2014) have shown that the ruin capital’s...

type="main" xml:lang="en" <title type="main">Abstract</title> <p>This article addresses the fundamental observation that aggressive newcom- ers seeking greater market share trigger the industry response of reducing rates that may gradually fall below marginal cost. In this study, the concept of reflexivity as connection...</p>

The main purpose of this paper is a risk theory insight into the problem of asset-liability and solvency adaptive management. In the multiperiodic insurance risk model composed of chained classical risk models, a zone-adaptive control strategy, essentially similar to that applied in Directives...

The paper is devoted to risk theory insight into the problem of asset-liability and solvency adaptive management. Two adaptive control strategies in the multiperiodic insurance risk model composed of chained classical risk models are introduced and their performance in terms of probability of...