Motivated by the EU Solvency II Directive, we study the one-year ruin probability of an insurer who makes investments and hence faces both insurance and financial risks. Over a time horizon of one year, the insurance risk is quantified as a nonnegative random variable X equal to the aggregate amount of claims, and the financial risk as a d-dimensional random vector Y consisting of stochastic di...

New two-sided bounds are proposed for the ruin probability in classical risk process.

Let Z(t)=(Z1(t),…,Zd(t))⊤,t∈R where Zi(t),t∈R, i=1,…,d are mutually independent centered Gaussian processes with continuous sample paths a.s. and stationary increments. For X(t)=AZ(t),t∈R, A is a nonsingular d×d real-valued matrix, u,c∈Rd T>0 we derive tight bounds for P∃t∈[0,T]:∩i=1d{Xi(t)−cit>ui}and find exact asymptotics as (u1,…,ud)⊤=(ua1,…,uad)⊤ any (a1,…,ad)⊤∈Rd∖(−∞,0]d u→∞.

Periodicity and Ruin Probabilities for Compound Non-Homogenous Poisson Processes Compound non-homogenous Poisson processes with periodic claim intensity rates are stiidied in this work. A risk process related to a short term periodic environment and the periodicity for its compound claim counting process are discussed. The ruin probabilities of compo~md non-homogenous Poisson processes with per...

In this work-in-progress, we consider perturbed risk processes that have an underlying Markov structure, including Markovian risk processes, and Sparre–Andersen risk processes when both inter claim times and claim sizes are phase–type. We apply the Erlangization method to this risk process in order to obtain an accurate approximation of the finite time ruin probability. In addition, we recogniz...