We consider a two-dimensional optimal dividend problem in the context of two insurance companies with compound Poisson surplus processes, who collaborate by paying each other’s deficit when possible. We solve the stochastic control problem of maximizing the weighted sum of expected discounted dividend payments (among all admissible dividend strategies) until ruin of both companies, by extending...

We construct efficient and accurate numerical algorithms for pricing discretely monitored barrier and Bermudan style options under time-changed Lévy processes by applying the fast Hilbert transform method to the log-asset return dimension and quadrature rule to the dimension of log-activity rate of stochastic time change. Some popular stochastic volatility models, like the Heston model, can be ...

This paper analyzes the theoretical problem of the real option with barrier. It models an investment decision with a double irreversibility concern: investing is irreversible, but waiting runs the risk of loosing the opportunity to invest. The optimal strategy leads to earlier investment when the barrier increases, or when uncertainty decreases. Uncertainty has ambiguous effects on the expected...

The current paper presents a short survey of stochastic models of risk control and dividend optimization techniques for a nancial corporation. While being close to consump-tion/investment models of Mathematical Finance, dividend optimization models possess special features which do not allow them to be treated as a particular case of consumption/investment models. In a typical model of this sor...

An upper bound for the ruin probability of a joint-stock insurance company is obtained, provided that intervals between claim times have gamma distribution and uses linear barrier dividend strategy.

We consider the classical optimal dividend control problem which was proposed by de Finetti [Trans. XVth Internat. Congress Actuaries 2 (1957) 433–443]. Recently Avram, Palmowski and Pistorius [Ann. Appl. Probab. 17 (2007) 156–180] studied the case when the risk process is modeled by a general spectrally negative Lévy process. We draw upon their results and give sufficient conditions under whic...