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...

Let ξ1,ξ2,… be an iid sequence with negative mean. The (m,n)-segment is the subsequence ξm+1,…,ξn and its score is given by max{∑m+1nξi,0}. Let Rn be the largest score of any segment ending at time n, Rn∗ the largest score of any segment in the sequence ξ1,…,ξn, and Ox the...

Static and discrete time pricing operators for two price economies are reviewed and then generalized to the continuous time setting of an underlying Hunt process. The continuous time operators define nonlinear partial integro–differential equations that are solved numerically for the three...

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 present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a number of widely used models. In particular, we use the...

No abstract received.

In this paper we propose a transform method to compute the prices and Greeks of barrier options driven by a class of Levy processes. We derive analytical expressions for the Laplace transforms in time of the prices and sensitivities of single barrier options in an exponential Levy model with...