Landy Rabehasaina

Series Expansions for the First Passage Distribution of Wong–Pearson Jump-Diffusions

Abstract We explore the Erlang series approach for the first-time passage problem for a particular class of jump-diffusions with polynomial state-dependent coefficients. This approach may be viewed as a discrete analog of the Laplace transform, which replaces the differential equations with polynomial coefficients satisfied by this function by algebraic recurrences. We identify cases in which the expansion is finite and in which the recurrence is of second order, and thus more easily solved.

Risk Processes with Interest Force in Markovian Environment

We consider risk processes modulated by an external Markov chain, with claim amounts following phase-type distributions, featuring an interest rate factor. We are interested in the distribution of exit times, which we study through proper transformations of the original processes, through duality and Markovian embeddings. In dimension 1, this corresponds to the classic ruin time of which we compute the distribution. We also consider K dimensional processes, of which exits out of quadrants are studied.

Ruin time and aggregate claim amount up to ruin time for the perturbed risk process

We consider the classical Sparre-Andersen risk process perturbed by a Wiener process, and study the joint distribution of the ruin time and the aggregate claim amounts until ruin by determining its Laplace transform. This is first done when the claim amounts follow respectively an exponential/Phase-type distribution, in which case we also compute the distribution of recovery time and study the case of a barrier dividend. Then the general distribution is considered when ruin occurs by oscillation, in which case a renewal equation is derived.

On a multivariate renewal-reward process involving time delays and discounting: applications to IBNR processes and infinite server queues

This paper considers a particular renewal-reward process with multivariate discounted rewards (inputs) where the arrival epochs are adjusted by adding some random delays. Then, this accumulated reward can be regarded as multivariate discounted Incurred But Not Reported claims in actuarial science and some important quantities studied in queueing theory such as the number of customers in

A two-dimensional risk model with proportional reinsurance

G/G/\infty

Moments of a Markov-modulated, irreducible network of fluid queues

G/G/∞ queues with correlated batch arrivals. We study the long-term behaviour of this process as well as its moments. Asymptotic expressions and bounds for quantities of interest, and also convergence for the distribution of this process after renormalization, are studied, when interarrival times and time delays are light tailed. Next, assuming exponentially distributed delays, we derive some explicit and numerically feasible expressions for the limiting joint moments. In such a case, for an infinite server queue with a renewal arrival process, we obtain limiting results on the expectation of the workload, and the covariance of queue size and workload. Finally, some queueing theoretic applications are provided.

On a class of dependent Sparre Andersen risk models and a bailout application

Abstract We consider a Markovian queue and its associated exponentially averaged length. The set of partial differential equations satisfied by the joint distribution of the queue and the averaged queue length is given. We obtain a recursive expression for the moments of the averaged queue length, and develop a stable algorithm to compute them. These results are illustrated through numerical examples.