Largest Claims Reinsurance Premiums under Possible Claims Dependence

Abstract

Largest claims reinsurance covers are reconsidered. Allowing the original claims sizes to be not necessarily independent, a new, upper premium bound is derived and explored.

Reinsurance under the LCR and ECOMOR treaties with emphasis on light-tailed claims

“…Through a series of papers since 1980's, Kremer made numerous efforts on general formulas or upper bounds for the expectations of reinsured amounts, interpreted as net reinsurance premiums, under some general reinsurance treaties including the present two; see Kremer (1985Kremer ( , 1998 and references therein. Assuming that the number l of the order statistics in (1.1) and (1.2) is fixed or increases in t at a certain rate and that the claim-size distribution F belongs to the maximum domain of attraction of certain extremal value distributions, Beirlant and Teugels (1992) as well as Ladoucette and Teugels (2006) obtained limiting distributions for the quantities L l (t) and E l (t) as t → ∞.…”

Actuarial comparisons for aggregate claims with randomly right-truncated claims

“…For another reinsurance treaty, called the largest claims reinsurance, for short LCR, that was introduced by Ammeter (1964), the reinsurer covers completely the r largest claims (for details, see Rolski et al (1999)). In the actuarial literature, recursive calculations and algebraic bounds of the net premiums (i.e., the expected value) for the reinsurer risk have constituted a topic of interest for the excess-loss and LCR treaties (see e.g., Kremer (1998), Hürliman (2000) and references * Corresponding author. Fax: +34 966749619. therein).…”

The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation

“…This is given by (4) in the case of an EOL treaty, and by (5) for the LCR treaty. The reinsured claim surplus process has ruin time τ * u = inf{t : Y * t > u}, and the dividend income Equation (20) and the valuation Equation (21) are then modified by replacing d and τ u with d * and τ * u respectively. Thus…”

“…A series of approximate premium calculations for LCR treaties has been made in the literature; see, for example, [15,16], and [17][18][19][20], and their references.…”