The safest dependence structure among risks.

In this paper, we investigate the dependence in Frechet spaces containing mutually exclusive risks. It is shown that, under some reasonable assumptions, the safest dependence structure, in the sense of the minimal stop-loss premiums for the aggregate claims involved, is obtained with the Frechet lower bound and precisely corresponds to the mutually exclusive risk of the Frechet space. In that respect, the present paper complements some previous studies by Heilmann (1986), Dhaene & Goovaerts (1996, 1997), Müller (1997) and Taizhong & Zhiqiang (1998). A couple of actuarial applications enhance the interest of the results derived.Dependence; Risk; Structure;

Correlated risks, bivariate utility and optimal choices

In this paper, we consider a décision-maker facing a financial risk flanked by a background risk, possibly non-financial, such as health or environmental risk. A decision has to be made about the amount of an investment (in the financial dimension) resulting in a future benefit either in the same dimension (savings) or in the order dimension (environmental quality or health improvement). In the first case, we show that the optimal amount of savings decreases as the pair of risks increases in the bivariate increasing concave dominance rules of higher degrees which express the common preferences of all the decision-makers whose two-argument utility function possesses direct and cross derivatives fulfilling some specific requirements. Roughly speaking, the optimal amount of savings decreases as the two risks become "less positively correlated" or marginally improve in univariate stochastic dominance. In the second case, a similar conclusion on optimal investment is reached under alternative conditions on the derivatives of the utility function.bivariate higher order increasing concave stochastic dominance, precautionary savings, background risk, dependence

A Kolmogorov-Smirnov type test for shortfall dominance against parametric alternatives

This paper proposes a Kolmogorov-type test for the shortfall order (also known in the literature as the right-spread or excess-wealth order) against parametric alternatives. In the case of the null hypothesis corresponding to the Negative Exponential distribution, this provides a test for the new better than used in expectation (NBUE) property. Such a test is particularly useful in reliability applications as well as duration and income distribution analysis. The theoretical properties of the testing procedure are established. Simulation studies reveal that the test proposed in this paper performs well, even with moderate sample sizes. Applications to real data, namely chief executive officer (CEO) compensation data and flight delay data, illustrate the empirical relevance of the techniques described in this paper.Right-spread order; Excess-wealth order; New better than used in expectation; Bootstrap; Reliability; CEO compensation; Flight delay

Towards the Synthesis Dual-Inhibitors of Fatty Acid Synthase and the Human 20S Proteasome as Anticancer Agents

Human fatty acid synthase (FAS) and the human 20S proteasome are useful targets for anticancer chemotherapy, and the latter target has been validated as a target for treatment of various forms of cancer. Belactosin C, cinnabaramide A, and orlistat are three β-lactone containing compounds that have been shown to inhibit either FAS or the human 20S proteasome, leading to tumor cell death via apoptosis. This project describes the design and synthesis of novel dual inhibitors of these two enzyme targets premised on these three β-lactone containing compounds with the goal of finding a more potent and “druggable” inhibitor. The key step in this synthesis of the described synthetic strategy toward these dual inhibitors is a nucleophile catalyzed aldol lactonization (NCAL) process to form the γ-lactam fused β-lactone core

Risk and saving contracts.

Abstract: Following the ''time-capital'' approach of De Vylder (1997) it is shown that a fair life insurance contract can uniquely be separated into a fair savings and a fair pure risk contract. It is also shown that a fair life insurance contract can be separated into a fair associated stochastic savings contract and a fair associated pure risk contract.Risk;

Multivariate concave and convex stochastic dominance

Stochastic dominance permits a partial ordering of alternatives (probability distributions on consequences) based only on partial information about a decision maker’s utility function. Univariate stochastic dominance has been widely studied and applied, with general agreement on classes of utility functions for dominance of different degrees. Extensions to the multivariate case have received less attention and have used different classes of utility functions, some of which require strong assumptions about utility. We investigate multivariate stochastic dominance using a class of utility functions that is consistent with a basic preference assumption, can be related to well-known characteristics of utility, and is a natural extension of the stochastic order typically used in the univariate case. These utility functions are multivariate risk averse, and reversing the preference assumption allows us to investigate stochastic dominance for utility functions that are multivariate risk seeking. We provide insight into these two contrasting forms of stochastic dominance, develop some criteria to compare probability distributions (hence alternatives) via multivariate stochastic dominance, and illustrate how this dominance could be used in practice to identify inferior alternatives. Connections between our approach and dominance using different stochastic orders are discussed.decision analysis: multiple criteria, risk; group decisions; utility/preference: multiattribute utility, stochastic dominance, stochastic orders

The concept of comonotonicity in actuarial science and finance : theory.

n an insurance context, one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. It also appears when considering discounted payments related to a single policy or a portfolio at different future points in time. The assumption of mutual independence between the components of the sum is very convenient from a computational point of view, but sometimes not realistic. We will determine approximations for sums of random variables, when the distributions of the terms are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with. In this paper, the theoretical aspects are considered. Applications of this theory are considered in a subsequent paper. Both papers are to a large extent an overview of recent research results obtained by the authors, but also new theoretical and practical results are presented.Risk; Actuarial; Science; Theory;