Dividend payments in a perturbed compound Poisson model with stochastic investment and debit interest. (English) Zbl 1435.91159

Ukr. Math. J. 71, No. 5, 718-734 (2019) and Ukr. Mat. Zh. 71, No. 5, 631-644 (2019).
Summary: 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 this surplus in a risky asset and risk-free asset based on a fixed proportion. Otherwise, if the surplus is negative, then the insurance company can get the business loan. The integrodifferential equations for the function generating moments of the values of cumulative dividends are obtained for the barrier and threshold dividend strategies, respectively. The expected dividend value is obtained in the closed form in the case where the claim amount is exponentially distributed.


91G05 Actuarial mathematics
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