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In this paper we consider the classical and Erlang(2) risk processes when the inter-claim times and claim amounts are dependent. We assume that the dependence structure is defined through a Farlie-Gumbel-Morgenstern (FGM) copula and show that the methods used to derive results in the classical risk model can be modified to derive results in a dependent risk process. We find expressions for the survival probability and the probability of maximum surplus before ruin.
We show that the problem of existence of equilibrium in Kyles continuous time insider trading model ([31]) can be tackled by considering a system of quasilinear parabolic equation and a Fokker-Planck equation coupled via a transport type constraint.
Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase
A meticulous assessment of the risk of impacts associated with extreme wind events is of great necessity for populations, civil authorities as well as the insurance industry. Using the concept of spatial risk measure and related set of axioms introdu
Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative errors. M
Mean-field games with absorption is a class of games, that have been introduced in Campi and Fischer [7] and that can be viewed as natural limits of symmetric stochastic differential games with a large number of players who, interacting through a mea