Proportional reinsurance for fractional Brownian risk model

Abstract

This paper investigates the ruin probabilities for a two-dimensional fractional Brownian risk model with a proportional reinsurance scheme. The author focused on the joint and simultaneous ruin probabilities in a finite-time horizon. The risk processes of both insurance and reinsurance companies are composed of a large number of i.i.d. sub-risk processes, representing independent businesses. The asymptotics were derived as the initial capital tends to infinity.

Parisian ruin with power-asymmetric variance near the optimal point with application to many-inputs proportional reinsurance

“…where B (i) H , i ≥ 1 are independent fractional Brownian motions and α, µ, σ ∈ R d . In a recent contribution [2], the authors derived the exact asymptotics of the simultaneous ruin probability P {∃t ∈ [0, T ] : R N (t) < 0} , N → ∞ in the case of d = 2. In the present work we shall concentrate on the simultaneous Parisian ruin probability Parisian stopping times have been first introduced in relation to barrier options in mathematical finance, see [3],…”

“…This problem has been studied in [14], also for the bivariate Brownian motion with ρ ∈ (−1, 1). A third possible extension would be the notion of "at least one" ruin, suggested in the classical ruin context in [2]: the ruin is declared if either of the processes has a Parisian ruin over time.…”