We study the optimal insurance design problem. This is a risk sharing problem between an insured and an insurer. The main novelty in this paper is that we study this optimization problem under a risk-adjusted premium calculation principle for the insurance cover. This risk-adjusted premium...

We consider a spectrally-negative Markov additive process as a model of a risk process in a random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process as negative, where the observation rate may...

We study the recursive moments of aggregate discounted claims, where the dependence between the inter-claim time and the subsequent claim size is considered. Using the general expression for the<em> m-th</em> order moment proposed by Léveillé and Garrido (Scand. Actuar. J. <strong>2001</strong>, 2, 98–110), which...

“What is complicated is not necessarily insightful and what is insightful is not necessarily complicated: <i>Risks</i> welcomes simple manuscripts that contribute with <b>in</b>sight, <b>out</b>look, <b>under</b>standing and <b>over</b>view”—a quote from the first editorial of this journal [1]. Good articles are not...

In a randomized trial of two interventions on employer health benefit decision-making, 156 employers in the evidence-based (EB) condition attended a two hour presentation reviewing scientific evidence demonstrating depression products that increase high quality treatment of depression in the...

A spectrum of upper bounds (<i>Q</i>_<i>α</i>(<i>X</i><i> </i>; <i>p) </i> _{<i>α</i>ε[0<i>,</i>∞]} on the (largest)  (1-p)-quantile <i>Q</i>(<i>X</i>;<i>p</i>)  of an arbitrary random variable  <i>X </i>is introduced and shown to be stable and monotonic in <i>α</i>, <i>p</i>, and <i>X </i>, with <i>Q</i>₀(<i>X</i><i> </i>;p) = <i>Q</i>(<i>X</i>;<i>p</i>).    If <i>p </i>is small enough and the distribution of <i>X </i>is regular enough,...

Evaluating risk measures, premiums, and capital allocation based on dependent multi-losses is a notoriously difficult task. In this paper, we demonstrate how this can be successfully accomplished when losses follow the multivariate Pareto distribution of the second kind, which is an attractive...

Random shifting typically appears in credibility models whereas random scaling is often encountered in stochastic models for claim sizes reflecting the time-value property of money. In this article we discuss some aspects of random shifting and random scaling of insurance risks focusing in...

This paper proposes a new method to introduce coherent risk measures for risks with infinite expectation, such as those characterized by some Pareto distributions. Extensions of the conditional value at risk, the weighted conditional value at risk and other examples are given. Actuarial...

We present the optimal consumption and investment strategy for an investor, endowed with labor income, searching to maximize utility from consumption and terminal wealth when facing a binding capital constraint of a European (constraint on terminal wealth) or an American (constraint on the...