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We consider ruin probabilities for an insurance company, which can also invest in the stock market. The risk process is modeled by a compound Poisson process and the stock price by geometric Brownian motion. We show that if the tails of the claims are light tailed, then the optimal strategy is...
An optimal portfolio/control problem is considered for a two-dimen\-sional model in finance. A pair consisting of the wealth process and cumulutative consumption process driven by a geometric Lévy process is controlled by adapted processes. The value function appears and turns out to be a...
This note addresses the global strong solvability of a phase-field system arising in connection with the phase transition theory recently proposed by Frémond. The novelty of this modelization consists in considering the macroscopic effect of the microscopic movements of particles of the system...
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