The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a...

Abstract Asymptotic expansions for the tails of sums of random variables with regularly varying tails are mainly derived in the case of identically distributed random variables or in the case of random variables with the same tail index. Moreover, the higher-order terms are often given under...

We present two new classes of stationary max-stable random fields. For the first class, we use the spectral representation due to Schlather (2002) and assume that the stationary process used in the representation is proportional to a power of a max-stable random field. We derive the finite...

We consider two continuous-time Gaussian processes, one being partially correlated to a time-lagged version of the other. We first give the limiting spectral distribution for the covariance matrices of the increments of the processes when the span between two observations tends to zero. Then, we...

Using a market-making inventory model, we analyze the impact of order preferencing on dealers' quoting behavior by changing the degree of quote disclosure. We find that preferenced orders raise the inventory-holding costs of preferenced dealers, making them less able to post attractive quotes....

In this paper, we provide a model which accommodates the assumption of a continuous efficient price with the inherent properties of ultra-high-frequency transaction data (price discreteness, irregular temporal spacing, diurnal patterns...). Our approach consists in designing a stochastic...

In the Solvency II framework, insurance companies need to calculate the Best Estimate valuation of Liabilities (BEL) and the Market Value Margin (MVM) for non-hedgeable insurance-technical risks. The Cost-of-Capital approach defines the MVM as the present value of the current and future Solvency...