We study optimal buying and selling strategies in target zone models. In these models the price is modeled by a diffusion process which is reflected at one or more barriers. Such models arise for example when a currency exchange rate is kept above a certain threshold due to central bank...

We consider the regularity of sample paths of Volterra–Lévy processes. These processes are defined as stochastic integrals M(t)=∫0tF(t,r)dX(r),t∈R+, where X is a Lévy process and F is a deterministic real-valued function. We derive the spectrum of singularities and a result on the...

Let X denote the loss initially assumed by an insurer. In a reinsurance design, the insurer cedes part of its loss, say f(X), to a reinsurer, and thus the insurer retains a loss If(X)=X-f(X). In return, the insurer is obligated to compensate the reinsurer for undertaking the risk by paying the...

This paper investigates optimal reinsurance strategies for an insurer with multiple lines of business under the criterion of minimizing its total capital requirement calculated based on the multivariate lower-orthant Value-at-Risk. The reinsurance is purchased by the insurer for each line of...

Consider the problem of approximating the tail probability of randomly weighted sums and their maxima, where {Xi,i=1} is a sequence of identically distributed but not necessarily independent random variables from the extended regular variation class, and {[Theta]i,i=1} is a sequence of...

Recently a new multiple dimensional stochastic order named correlation order was proposed to examine how the dependence among the individual risks effects riskness of the portfolios. This paper aims to discuss the relationship between correlation order and the supermodular order in general....

The quest for optimal reinsurance design has remained an interesting problem among insurers, reinsurers, and academicians. An appropriate use of reinsurance could reduce the underwriting risk of an insurer and thereby enhance its value. This paper complements the existing research on optimal...

The multivariate regular variation (MRV) is one of the most important tools in modeling multivariate heavy-tailed phenomena. This paper characterizes the MRV distributions through the tail dependence function of the copula associated with them. Along with some existing results, our studies...

By formulating a constrained optimization model, we address the problem of optimal reinsurance design using the criterion of minimizing the conditional tail expectation (CTE) risk measure of the insurer's total risk. For completeness, we analyze the optimal reinsurance model under both binding...