Dividend payments in a perturbed compound Poisson model with stochastic investment and debit interest

Abstract

UDC 519.21
We consider a compound Poisson insurance risk model perturbed by diffusion with stochastic return on investment and debit interest. If the initial surplus is nonnegative, then the insurance company can invest its surplus in a risky asset and risk-free asset based on a fixed proportion. Otherwise, the insurance company can get the business loan when the surplus is negative. The integrodifferential equations for the moment generating function of the cumulative dividends value are obtained under the barrier and threshold dividend strategies, respectively. The closed-form of the expected dividend value is obtained when the claim amount is exponentially distributed.