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...

Risk measures in finance and insurance -- Fixed-probability level in a diffusion model -- Fixed-probability level in an exceptional renewal model -- Implicit function defined by M-equation -- Fixed-probability level in general renewal model -- Case study : numerical evaluation of...

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...

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...