Opuscula Math. 35, no. 3 (2015), 333-352
http://dx.doi.org/10.7494/OpMath.2015.35.3.333

Opuscula Mathematica

# Ruin probability in a risk model with variable premium intensity and risky investments

Yuliya Mishura
Mykola Perestyuk
Olena Ragulina

Abstract. We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion. We get an exponential bound for the infinite-horizon ruin probability. To this end, we allow the surplus process to explode and investigate the question concerning the probability of explosion of the surplus process between claim arrivals.

Keywords: risk process, infinite-horizon ruin probability, variable premium intensity, risky investments, exponential bound, stochastic differential equation, explosion time, existence and uniqueness theorem, supermartingale property.

Mathematics Subject Classification: 91B30, 60H10, 60G46.

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• Yuliya Mishura
• Taras Shevchenko National University of Kyiv, Department of Probability Theory, Statistics and Actuarial Mathematics, 64 Volodymyrska, 01601 Kyiv, Ukraine
• Mykola Perestyuk
• Taras Shevchenko National University of Kyiv, Department of Probability Theory, Statistics and Actuarial Mathematics, 64 Volodymyrska, 01601 Kyiv, Ukraine
• Olena Ragulina
• Taras Shevchenko National University of Kyiv, Department of Probability Theory, Statistics and Actuarial Mathematics, 64 Volodymyrska, 01601 Kyiv, Ukraine
• Communicated by Ekkehard Kopp.
• Revised: 2014-08-18.
• Accepted: 2014-09-05.
• Published online: 2014-12-15.