We consider an equity-linked contract whose payoff depends on the lifetime of the policy holder and the stock price. We provide the best strategy for an insurance company assuming limited capital for the hedging. The main idea of the proof consists in reducing the construction of such strategies...

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process in the absence of dividend payments. The classical dividend problem for an insurance company consists in finding a dividend payment policy that...

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance...

W niniejszej pracy rozważamy problem maksymalizacji oczekiwanej zdyskontowanej użyteczności wypłat dywidend przez firmę ubezpieczeniową, której rezerwy modelowane są przez klasyczny proces Cramera-Lundberga. Na wstępie analizujemy sytuację, gdy wielkość szkód opisana jest rozkładem...

We derive the exact asymptotics of P(supu<=tX(u)>x) if x and t tend to infinity with x/t constant, for a general Lévy process X that admits exponential moments. The proof is based on a renewal argument and a two-dimensional renewal theorem of Höglund [Höglund, T., 1990. An asymptotic expression for...</=tx(u)>

We discuss how to prove exponential upper bounds for simple fluid models driven by a finite state CTMC. In particular, we consider the fluid model of Anick, Mitra and Sondhi, in which the fluid is generated by N independent 0-1 Markovian sources. We also give a result on a generalized...

We consider a queuing model with the workload evolving between consecutive i.i.d. exponential timers according to a spectrally positive Lévy process Y(t) which is reflected at 0. When the exponential clock ends, the additional state-dependent service requirement modifies the workload so that...