Risk Apportionment Research Articles

Knock-for-knock clauses

English Court of Appeal lends further support to the contractual freedom of parties to agree broad exclusions of liability, including consequential loss In a recent judgment of real importance to offshore oil and gas exploration, the English court has rejected a challenge to the ‘knock-for-knock’ principle on which the drilling contractor business model is founded. Wide-ranging indemnities are common in offshore drilling contracts and are a way of creating certainty in respect of apportionment of risk. Under the ‘knock-for-knock’ principle, the basic premise is that each party bears its own risk. Therefore, although drilling contractors can incur reduced or zero day rates and be exposed to termination, they are otherwise often not thought to be liable for any delays and losses suffered by the oil company. In recent years, there have been a number of attempts to challenge that principle. In the main, those challenges were resolved through negotiation, but now in Transocean v Providence1 the Court of Appeal has decisively upheld the principle. Where the wording of exclusions of liability is clear, English courts will enforce ‘knock-for-knock’ clauses.

Precautionary self-insurance-cum-protection

Precautionary self-insurance-cum-protection (SICP) arises when an individual spends more on SICP when background risk is introduced. We develop a two-period model wherein additive/multiplicative background risk prevails in the second period. Using the theory of monotone comparative statics and risk apportionment, we derive necessary and sufficient conditions under which the individual spends more on SICP when the background risk deteriorates via higher-order stochastic dominance. Prudence is called for to create a precautionary motive that induces the individual to shift his wealth in a way to reduce the loss of expected utility caused by the addition of background risk, thereby giving rise to the precautionary SICP.

Source apportionment of mass concentration and inhalation risk with long-term ambient PCDD/Fs measurements in an urban area

This study applies a receptor model to quantify source contributions to ambient concentration of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) and inhalation cancer risk in Taipei from 2003 through 2009. Seventeen PCDD/F congeners were used in the effective variance solution to the Chemical Mass Balance equations to estimate source-specific mass contributions and inhalation risks. The average total PCDD/F concentration was 0.611pg/Nm3 (0.036pg I-TEQ/Nm3). Traffic emissions contributed the most to the PCDD/F concentration (55.7%), followed by waste incinerators (18.6%) and joss stick burning (9.6%). For the inhalation cancer risk, the average was 1.1×10−6 with traffic, waste incinerators, and joss paper burning as the main contributors (67.3%, 19.4%, and 6.3%, respectively). The mass and risk contributions of waste incinerators decreased significantly from 2003 to 2009 and were higher at downwind sites than at upwind sites. Reducing PCDD/F emissions from traffic and waste incinerators would provide the greatest health benefit. Policies that reduce the uncontrolled burning of joss stick and joss paper also need to be implemented.

Polycyclic aromatic hydrocarbons (PAHs) at traffic and urban background sites of northern Greece: source apportionment of ambient PAH levels and PAH-induced lung cancer risk.

Thirteen particle-phase PAHs, including nine >4-ring congeners [Benz[a]anthracene (BaAn), Chrysene (Chry), Benzo[b]fluoranthene (BbF), Benzo[k]fluoranthene (BkF), Benzo[e]pyrene (BeP), Benzo[a]pyrene (BaP), Dibenzo[a,h]anthracene (dBaAn), Benzo[g,h,i]perylene (BghiPe), Indeno(1,2,3-c,d)pyrene (IP)], listed by IARC (International Agency for Research on Cancer) as class 1, class 2A, and 2B carcinogens, plus four ≤ 4-ring congeners [Phenanthrene (Ph), Anthracene (An), Fluoranthene (Fl), Pyrene (Py)], were concurrently measured in inhalable and respirable particle fractions (PM10 and PM2.5) at a heavy-traffic and an urban background site in Thessaloniki, northern Greece, during the warm and the cold period of the year. Carcinogenic and mutagenic potencies of the PAH-bearing particles were calculated, and the inhalation cancer risk (ICR) for local population was estimated. Finally, Chemical Mass Balance (CMB) modeling was employed for the source apportionment of ambient PAH levels and the estimated lung cancer risk. Resulted inhalation cancer risk during winter was found to be equivalent in the city center and the urban background area suggesting that residential wood burning may offset the benefits from minor traffic emissions.

Characterization and source apportionment of health risks from ambient PM10 in Hong Kong over 2000–2011

Atmospheric particulate matter (PM) pollution is a major public health concern in Hong Kong. In this study, the spatiotemporal variations of health risks from ambient PM10 from seven air quality monitoring stations between 2000 and 2011 were analyzed. Positive matrix factorization (PMF) was adopted to identify major source categories of ambient PM10 and quantify their contributions. Afterwards, a point-estimated risk model was used to identify the inhalation cancer and non-cancer risks of PM10 sources. The long-term trends of the health risks from classified local and non-local sources were explored. Furthermore, the reason for the increase of health risks during high PM10 days was discussed. Results show that vehicle exhaust source was the dominant inhalation cancer risk (ICR) contributor (72%), whereas trace metals and vehicle exhaust sources contributed approximately 27% and 21% of PM10 inhalation non-cancer risk (INCR), respectively. The identified local sources accounted for approximately 80% of the ICR in Hong Kong, while contribution percentages of the non-local and local sources for INCR are comparable. The clear increase of ICR at high PM days was mainly attributed to the increase of contributions from coal combustion/biomass burning and secondary sulfate, while the increase of INCR at high PM days was attributed to the increase of contributions from the sources coal combustion/biomass burning, secondary nitrate, and trace metals. This study highlights the importance of health risk-based source apportionment in air quality management with protecting human health as the ultimate target.

Source and risk apportionment of selected VOCs and PM2.5 species using partially constrained receptor models with multiple time resolution data

This study was conducted to identify and quantify the sources of selected volatile organic compounds (VOCs) and fine particulate matter (PM2.5) by using a partially constrained source apportionment model suitable for multiple time resolution data. Hourly VOC, 12-h and 24-h PM2.5 speciation data were collected during three seasons in 2013. Eight factors were retrieved from the Positive Matrix Factorization solutions and adding source profile constraints enhanced the interpretability of source profiles. Results showed that the evaporative emission factor was the largest contributor (25%) to VOC mass concentration, while the largest contributor to PM2.5 mass concentration was soil dust/regional transport related factor (26%). In terms of risk prioritization, traffic/industry related factor was the major cause for benzene, ethylbenzene, Cr, and polycyclic aromatic hydrocarbons (29–69%) while petrochemical related factor contributed most to the Ni risk (36%). This indicated that a larger contributor to mass concentration may not correspond to a higher risk.

Risk aversion, prudence, and asset allocation: a review and some new developments

In this paper, we consider the composition of an optimal portfolio made of two dependent risky assets. The investor is first assumed to be a risk-averse expected utility maximizer, and we recover the existing conditions under which all these investors hold at least some percentage of their portfolio in one of the assets. Then, we assume that the decision maker is not only risk-averse, but also prudent and we obtain new minimum demand conditions as well as intuitively appealing interpretations for them. Finally, we consider the general case of investor’s preferences exhibiting risk apportionment of any order and we derive the corresponding minimum demand conditions. As a byproduct, we obtain conditions such that an investor holds either a positive quantity of one of the assets (positive demand condition) or a proportion greater than 50 % (i.e., the “50 % rule”).

Analyses of local dose distributions in the lungs for the determination of risk apportionment factors.

For radiation protection purposes, the relative contributions of bronchial (BB), bronchiolar (bb) and alveolar-interstitial (AI) doses to lung cancer risk are represented by their corresponding apportionment factors. The current assumption of equal apportionment factors can be tested by comparing different radon and thoron progeny exposures, which produce different regional dose distributions, with the pathologically observed regional cancer distributions: (1) radon progeny inhalation, (2) thoron progeny inhalation, (3) thoron and thoron progeny exhalation (Thorotrast patients) and (4) RP inhalation in rats, and cigarette smoke inhalation as smoking is the dominant cause of lung cancer. Comparison with the pathologically observed regional cancer distributions suggests (1) a smaller apportionment factor for the AI region as compared with BB and bb regions and (2) a higher value for the BB region relative to that for the bb region.

Robust Comparative Statics of Risk Changes

The standard method for establishing the comparative statics of risk changes in optimization problems has been confined to comparing unique interior solutions, relying on strong assumptions about payoff functions and decision variables. We propose a simple and intuitive approach that hinges on considerably weaker assumptions. Merging insights from the monotone comparative statics literature with insights from the risk apportionment literature, we show that the ranking of simple lottery pairs is all that is needed for establishing the comparative statics of risk changes. We use this approach to analyze the comparative statics of Nth-degree stochastic dominance shifts in a general setting with one and with multiple decision variables, and we show how these results can be applied to generalize the classical theories of precautionary saving, self-protection, and others. This paper was accepted by James Smith, decision analysis.

Preserving Risk Aversion Under a Background Risk

We identify new conditions ensuring risk aversion in the sense of Arrow-Pratt in a two-argument utility framework where a financial risk is accompanied by a background risk. The results generalize the findings by Finkenstal et al (1999), by considering the case of high-order expectation dependence and of high-order two-variable risk apportionment. We also provide three empirical applications to exhibit high-order expectation dependence are quiet important in determining risk aversion with two risks.

Multiple Interacting Risk Factors: On Methods for Allocating Risk Factor Interactions

A persistent problem in health risk analysis where it is known that a disease may occur as a consequence of multiple risk factors with interactions is allocating the total risk of the disease among the individual risk factors. This problem, referred to here as risk apportionment, arises in various venues, including: (i) public health management, (ii) government programs for compensating injured individuals, and (iii) litigation. Two methods have been described in the risk analysis and epidemiology literature for allocating total risk among individual risk factors. One method uses weights to allocate interactions among the individual risk factors. The other method is based on risk accounting axioms and finding an optimal and unique allocation that satisfies the axioms using a procedure borrowed from game theory. Where relative risk or attributable risk is the risk measure, we find that the game-theory-determined allocation is the same as the allocation where risk factor interactions are apportioned to individual risk factors using equal weights. Therefore, the apportionment problem becomes one of selecting a meaningful set of weights for allocating interactions among the individual risk factors. Equal weights and weights proportional to the risks of the individual risk factors are discussed.

Another look at risk apportionment

This paper presents a general result on the random selection of an element from an ordered sequence of risks and uses this result to derive additive and cross risk apportionment. Preferences favoring an improvement of the sampling distribution in univariate or bivariate first-order stochastic dominance are those exhibiting additive or cross risk apportionment. The univariate additive and multiplicative risk apportionment concepts are then related to the notion of bivariate cross risk apportionment by viewing the single-attribute utility function of an aggregate position (sum or product of attributes) as a 2-attribute utility function. The results derived in the present paper allow one to further explore the connections between the different concepts of risk apportionment proposed so far in the literature.

Appraisal of the Concept of 'Proximate Cause of Loss' under the Marine Insurance Cover

Marine Insurance is a very important aspect of international trade, it is the practice that safe-guards the apportionment of marine transportation risk between the parties engaged in an international transaction that involves sea or marine voyage. Many times, it is impossible to come to consensus on the liability or non-liability of the insurers and the insured, this is often the case where the causation of the marine peril is in issue. This paper therefore critically examines the doctrine of ‘proximate cause’ under the Marine Insurance, its meanings, connotations, applications and present relevance in the area of Marine Insurance.

Skewed Background Risks

Left-skewed risks imply large losses with low probability. Thus they resemble many of the most significant risks that people face in their lives, such as the unlikely event of a job loss. We derive a general result on decisions in the presence of left-skewed background risks and point out a sufficient condition on preferences that ensures that agents take these risks particularly seriously. This condition implies, for example, the accumulation of particularly large precautionary savings for left-skewed background risks. Our mathematical approach borrows from rather new results in the theory of higher-order risk preferences, notably from the risk apportionment idea of Eeckhoudt and Schlesinger (2006). Moreover, our theoretical results have important consequences for experiments on higher-order risk preferences.

Carcinogenic and mutagenic risk associated to airborne particle-phase polycyclic aromatic hydrocarbons: A source apportionment

Conventional risk assessment studies provide no detailed information about the role of specific sources determining the total carcinogenic and mutagenic potencies of PAH mixtures on humans health. In this study, the main emission sources of 11 particle-phase PAHs listed as carcinogenic and mutagenic agents by the IARC were identified by a risk apportionment method. The contribution of sources to the total concentration of PAHs in the study area was also quantified. A receptor model based on factor and multiple linear regression analyses was applied to estimate the source-specific risk associated to PAH inhalation in an urban background area of a large city (Venice-Mestre, Northern Italy). The proposed approach has discriminated the sources of mutagenic and carcinogenic congeners and their role in determining a serious hazard for human health. Results, interpreted on the basis of seasonal variations and atmospheric conditions, have shown that even though domestic heating is the main source of total PAHs in winter, a background pollution including traffic mainly accounts for the carcinogenic and mutagenic risk during the whole year. The findings of this work and the approach used can be easily applied to other geographic areas and provide useful information for local and regional air pollution control strategies.

Risk apportionment via bivariate stochastic dominance

This paper extends to bivariate utility functions, Eeckhoudt et al.’s (2009) result for the combination of ‘bad’ and ‘good’. The decision-maker prefers to get some of the ‘good’ and some of the ‘bad’ to taking a chance on all the ‘good’ or all the ‘bad’ where ‘bad’ is defined via (N,M)-increasing concave order. We generalize the concept of bivariate risk aversion introduced by Richard (1975) to higher orders. Importantly, in the bivariate framework, preference for the lottery [(X̃,T̃);(Ỹ,Z̃)] to the lottery [(X̃,Z̃);(Ỹ,T̃)] when (X̃,Z̃) dominates (Ỹ,T̃) via (N,M)-increasing concave order allows us to assert bivariate risk apportionment of order (N,M) and to extend the concept of risk apportionment defined by Eeckhoudt and Schlesinger (2006).

Risk and Price in the Bidding Process of Contractors

Formal and analytical risk models prescribe how risk should be incorporated into construction bids. However, the actual process of how contractors and their clients negotiate and agree to price is complex and not clearly articulated in the literature. With participant observation, the entire tender process was shadowed in two leading U.K. construction firms. This was compared with propositions in analytical models, and significant differences were found. A total of 670 h of work observed in both firms revealed three stages of the bidding process. Bidding activities were categorized and their extent estimated as deskwork (32%), calculations (19%), meetings (14%), documents (13%), off-days (11%), conversations (7%), correspondence (3%), and travel (1%). Risk allowances of 1–2% were priced in some bids, and three tiers of risk apportionment in bids were identified. However, priced risks may be excluded from the final bid to enhance competitiveness. Although risk apportionment affects a contractor’s pricing s...

Prudence probability premium

Prudence probability premium is defined in the risk apportionment model (Eeckhoudt and Schlesinger, 2006). For an increase in downside risk, we show sufficient conditions for comparing the probability premiums between two individuals when the apportioned risk is small and large.

Prudence, temperance, edginess, and risk apportionment as decreasing sensitivity to detrimental changes

This paper shows that the notions of prudence, temperance, edginess, and, more generally, risk apportionment of any degree are the consequences of the natural idea that the sensitivity to detrimental changes should decrease with initial wealth. In the setting of Epstein and Tanny (1980), this turns out to be equivalent to the supermodularity of the expected utility for some specific 4-state lotteries.

On Higher-Order Risk Preferences, Skewness and Diversification

All of the commonly used utility functions exhibit mixed risk aversion. We show that the utility of downside risk diversification is maximal if and only if the decision maker is mixed risk averse. This intuitive result supports the commonly made assumption of mixed risk aversion in many areas of economics and finance and is particularly interesting for portfolio choice. The proof relies on an investigation of all moments of the proper risk apportionment lotteries of Eeckhoudt and Schlesinger (2006), thereby generalizing results of Ekern (1980) and Roger (forthcoming). These computations also give a better understanding of the relationships between proper risk apportionment, in particular, prudence and temperance, expected utility, statistical moments, preference for skewness and kurtosis aversion.