We examine a class of utility maximization problems with a non-necessarily law-invariant utility, and with a non-necessarily law-invariant risk measure constraint. Under a consistency requirement on the risk measure that we call Vigilance, we show the existence of optimal contingent claims, and...

The inverse of the (additive) generator of an Archimedean copula is a strictly decreasing and convex function, while utility functions (applying to risk averse decision makers) are nondecreasing and concave. This provides a basis for deriving an inverse generator of an Archimedean copula from a...

In this paper we investigate the local risk-minimization approach for a combined financial-insurance model where there are restrictions on the information available to the insurance company. In particular we assume that, at any time, the insurance company may observe the number of deaths from a...

Motivated by the Guaranteed Minimum Death Benefits in various deferred annuities, we investigate the calculation of the expected discounted value of a payment at the time of death. The payment depends on the price of a stock at that time and possibly also on the history of the stock price. If...

The family of extremality stochastic orders was introduced in Laniado et al. (2012) (Portfolio selection through an extremality stochastic order. Insurance: Mathematics and Economics 51, 1–9), as an extension of the upper and lower orthant orders, having important applications in the research...

Notions of positive dependence and copulas play important roles in modeling dependent risks. The invariant properties of notions of positive dependence and copulas under increasing transformations are often used in the studies of economics, finance, insurance and many other fields. In this...

This paper analyzes ruin-like risk models in Insurance, which are variants of the Cramer–Lundberg (C–L) model with a barrier or a threshold. We consider three model variants, which have different portfolio strategies when the risk reserve reaches the barrier or exceeds the threshold. In...

The goal of this paper is to investigate (locally) risk-minimizing hedging strategies under the benchmark approach in a financial semimartingale market model where there are restrictions on the available information. More precisely, we characterize the optimal strategy as the integrand appearing...

Consider a renewal risk model in which claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure described via the conditional distribution of the inter-arrival time given the...

In this paper, we consider an extension of the classical risk model in which the premium rate policy is adaptive to claim experience. We assume that the premium rate is reviewed each time the surplus reaches a new descending ladder height. A choice between a finite number m of rates is then made...