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Risks 2014, 2(3), 249-259; doi:10.3390/risks2030249

Elementary Bounds on the Ruin Capital in a Diffusion Model of Risk

Central Economics and Mathematics Institute (CEMI) of Russian Academy of Science, Nakhimovskiy prosp., 47, Moscow 117418, Russia
Received: 29 March 2014 / Revised: 19 June 2014 / Accepted: 30 June 2014 / Published: 8 July 2014
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Abstract

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 premium rate seems not technically feasible. Instead, we obtain informative bounds for this capital in terms of elementary functions.
Keywords: level premium rate; level initial capital; diffusion model of risk level premium rate; level initial capital; diffusion model of risk
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Malinovskii, V.K. Elementary Bounds on the Ruin Capital in a Diffusion Model of Risk. Risks 2014, 2, 249-259.

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