Abstract: We consider three closely related problems in optimal control: (1) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market; (2) minimizing the probability of lifetime ruin when the rate of consumption is constant but the individual can invest in two risky correlated assets; and (3) a ...

In this work, we investigate a multi-risk model describing insurance business with two or more independent series of claim amounts. Each series of claim amounts consists of independent nonnegative random variables. Claims of each series occur periodically with some fixed inter-arrival time. Claim amounts occur until they can be compensated by a common premium rate and the initial insurer’s surp...

We modify the compound Poisson surplus model for an insurer by including liquid reserves and interest on the surplus. When the surplus of an insurer is below a fixed level, the surplus is kept as liquid reserves, which do not earn interest. When the surplus attains the level, the excess of the surplus over the level will receive interest at a constant rate. If the level goes to infinity, the mo...

Abstract: We consider three closely related problems in optimal control: (1) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market; (2) minimizing the probability of lifetime ruin when the rate of consumption is constant but the individual can invest in two risky correlated assets; and (3) a ...

Abstract The classical Cramér–Lundberg model was the first attempt to describe financial condition of insurance company. incomes were approximated by a steady stream money, and payments not limited could take any value from zero infinity. society did invest part its money does have employees, shareholders, or enterprise maintenance costs. There exist many modifications that cover at least some ...

In this note we give, for a spectrally negative Lévy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero which length exceeds a certain fixed period r. The formula involves only the scale function of the spectrally negative Lévy process and the distribution of the process at time r.