Supporting ALARP decision making by cost benefit analysis and multiattribute utility theory

Current guidance in the UK and elsewhere indicate upper and target risk limits for the operation of nuclear plant in terms of individual risk per annum. ‘As low as reasonably practicable’ (ALARP) arguments are used to justify the acceptance or rejection of policies that lead to risk changes between these limits. The suitability of cost‐benefit analysis (CBA) and multiattribute utility theory (MAUT) are assessed for performing ALARP (‘as low as reasonably possible’) assessments, in particular within the nuclear industry. Four problems stand out in current CBA applications to ALARP, concerning the determination of prices of safety gains or detriments, the valuation of group and individual risk, calculations using ‘disproportionality’, and the use of discounting to trade‐off risks through time. This last point has received less attention in the past but is important because of the growing interest in risk‐informed regulation in which policies extend over several timeframes and distribute the risk unevenly over these, or in policies that lead to a nonuniform risk within a single timeframe (such as maintenance policies). The problems associated with giving quantitative support to such decisions are discussed. It is argued that multiattribute utility methods (MAUT) provide an alternative methodology to CBA which enable the four problems described above to be addressed in a more satisfactory way. Through sensitivity analysis MAUT can address the perceptions of all stakeholder groups, facilitating constructive discussion and elucidating the key points of disagreement. It is also argued that by being explicitly subjective it provides an open, auditable and clear analysis in contrast to the illusory objectivity of CBA. CBA seeks to justify a decision by using a common basis for weights (prices), while MAUT recognizes that different parties may want to give different valuations. It then allows the analyst to explore the ways in which different parties might (or might not) come to the same conclusion even when weighting items differently.     

Risk Preferences Regarding Multiple Fatalities and Some Implications for Societal Risk Decision Making—An Empirical Study

Risk preferences related to accidents or other situations involving the possibility of multiple fatalities were studied in 87 persons in Sweden belonging to two separate groups with professional or educational knowledge of risk‐ and crisis‐management issues. Use was made of a tradeoff method, the results obtained consisting of von Neuman–Morgenstern utility functions over the range of 0–1000 fatalities. Most of the utility curves for the number of fatalities were found to be convex, implying the majority of subjects to display risk‐seeking behaviour. Implications of the findings for societal risk decision making are discussed, along with prospective areas of application and the possibilities of considering other dimensions than the number of fatalities.     

Portfolio optimization under model uncertainty and BSDE games

We consider robust optimal portfolio problems for markets modeled by (possibly non-Markovian) Itô–Lévy processes. Mathematically, the situation can be described as a stochastic differential game, where one of the players (the agent) is trying to find the portfolio that maximizes the utility of her terminal wealth, while the other player (“the market”) is controlling some of the unknown parameters of the market (e.g., the underlying probability measure, representing a model uncertainty problem) and is trying to minimize this maximal utility of the agent. This leads to a worst case scenario control problem for the agent. In the Markovian case, such problems can be studied using the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation, but these methods do not work in the non-Markovian case. We approach the problem by transforming it into a stochastic differential game for backward stochastic differential equations (a BSDE game). Using comparison theorems for BSDEs with jumps we arrive at criteria for the solution of such games in the form of a kind of non-Markovian analogue of the HJBI equation. The results are illustrated by examples.     

Ruin probabilities in models with a Markov chain dependence structure

In this paper we derive explicit expressions for the probability of ruin in a renewal risk model with dependence among the increments (Z _k ) _k>0. We study the case where the dependence structure among (Z _k ) _k>0 is driven by a Markov chain with a transition kernel that can be described via ordinary differential equations with constant coefficients.     

Option Pricing in Discrete‐Time Incomplete Market Models

Various aspects of pricing of contingent claims in discrete time for incomplete market models are studied. Formulas for prices with proportional transaction costs are obtained. Some results concerning pricing with concave transaction costs are shown. Pricing by the expected utility of terminal wealth is also considered.     

Finite-dimensional utilities

Summary. Sufficient axioms are identified for the existence of a finite- dimensional quasilinear utility function whose lexicographically ordered vectors preserve a decision maker's preference order on a mixture set . It is shown that those axioms are also necessary for the linear lexicographic representation when the underlying set is a mixture space. Received: August 20, 1998; revised version: December 14, 1998     

RISK MEASURES FOR NON-INTEGRABLE RANDOM VARIABLES

We show that when a real-valued risk measure is defined on a solid, rearrangement invariant space of random variables, then necessarily it satisfies a weak compactness, also called continuity from below, property, and the space necessarily consists of integrable random variables. As a result we see that a risk measure defined for, say, Cauchy-distributed random variable, must take infinite values for some of the random variables.     

CB – Time Dependent Markov Model for Pricing Convertible Bonds

In this paper, we propose what we call the convertible bond (CB) – timedependent Markov model, which prices N given individual convertible bondssimultaneously, and apply it to Japanese convertible bond data. One of themain features of the model is that it makes full use of the correlationstructure of convertible bond prices. The empirical results show that themodel well describes individual prices in the market.     

随机仓库布局问题模型与算法研究

通过讨论随机条件下仓库布局问题．建立了随机仓库布局问题机会约束规划模型，并设计出基于随机模拟的禁忌搜索算法求解模型，最后利用算例来验证算法的有效性。     

Gibbsian and non-Gibbsian states at Eurandom

We review some of the work on non-Gibbsian states of the last 10 years, emphasizing the developments in which Eurandom played a role.