The Risk Margin under Solvency II is determined as the cost of holding capital over the lifetime of liabilities, whereby future costs are discounted to the valuation date at risk-free rates. An implicit assumption of the current method is that the Risk Margin should allow for new capital to be raised after the occurrence of losses no larger than required capital. Using “Cost of Capital” as general valuation method, various approaches are discussed, giving rise to several alternative calculation methods of the Risk Margin. A comparison is made with the adjustment proposed by EIOPA in 2020 and also an approach is explored where future capital raisings are treated as contingent commitments. Each of the approaches discussed can be justified on its own merits in the context of Solvency II legislation, and leads to substantially different results for liabilities with long durations. Therefore, a more precise specification of the function of the Risk Margin and underlying assumptions is desirable.

Intertemporal choices involve tradeoffs between outcomes that occur at different times. Most of the research has used pure gains tasks and the discount rates yielding from those tasks to explain and predict real-world behaviors and consequences. However, real decisions are often more complex and involve mixed outcomes (e.g., sooner-gain and later-loss or sooner-loss and later-gain). No study has used mixed gain-loss intertemporal tradeoff tasks to explain and predict real-world behaviors and consequences, and studies involving such tasks are also scarce. Considering that tasks involving a combination of gains and losses may yield different discount rates and that existing pure gains tasks do not explain or predict real-world outcomes well, this study conducted two experiments to compare the discount rates of mixed gain-loss intertemporal tradeoffs with those of pure gains or pure losses (Experiment 1) and to examine whether these tasks predicted different real-world behaviors and consequences (Experiment 2). Experiment 1 suggests that the discount rate ordering of the four tasks was, from highest to lowest, pure gains, sooner-loss and later-gain, pure losses, and sooner-gain and later-loss. Experiment 2 indicates that the evidence supporting the claim that the discount rates of the four tasks were related to different real-world behaviors and consequences was insufficient.

This article surveys the debate over the social discount rate. The focus is on the economics rather than the philosophy literature, but the survey emphasizes foundations in ethical theory rather than highly technical details. I begin by locating the standard approach to discounting within the overall landscape of ethical theory. The article then covers the Ramsey equation and its relationship to observed interest rates, arguments for and against a positive rate of pure time preference, the consumption elasticity of utility, and the effect of various sorts of uncertainty on the discount rate. Climate change is discussed as an application.

I argue that the use of a social discount rate to assess the consequences of climate policy is unhelpful and misleading. I consider two lines of justification for discounting: (i) ethical arguments for a ‘pure rate of time preference’ and (ii) economic arguments that take time as a proxy for economic growth and the diminishing marginal utility of consumption. In both cases I conclude that, given the long time horizons, distinctive uncertainties, and particular costs and benefits at stake in the climate context, discount rates are at best a poor proxy for the normative considerations they are meant to represent.

Investment decision rules in risk situations have been extensively analyzed for firms. Most research focus on financial options and the wide range of methods based on dynamic programming currently used by firms to decide on whether and when to implement an irreversible investment under uncertainty. The situation is quite different for public investments, which are decided and largely funded by public authorities. These investments are assessed by public authorities, not through market criteria, but through public Cost-Benefit Analysis (CBA) procedures. Strangely enough, these procedures pay little attention to risk and uncertainty. The present text aims at filling this gap. We address the classic problem of whether and when an investment should be implemented. This stopping time problem is established in a framework where the discount rate is typically linked to GDP, which follows a Brownian motion, and where the benefits and cost of implementation follow linked Brownian motions. We find that the decision rule depends on a threshold value of the First Year Advantage/Cost ratio. This threshold can be expressed in a closed form including the means, standard deviations and correlations of the stochastic variables. Simulations with sensible current values of these parameters show that the systemic risk, coming from the correlation between the benefits of the investment and economic growth, is not that high, and that more attention should be paid to risks relating to the construction cost of the investment; furthermore, simple rules of thumb are designed for estimating the above-mentioned threshold. Some extensions are explored. Others are suggested for further research.

We argue that the appropriate discount rate for pension liabilities depends on the objective. In particular, if the objective is to measure pension under- or overfunding, a default-free discount rate should always be used, even if the liabilities are themselves not default-free. If, instead, the objective is to determine the market value of pension benefits, then it is appropriate that discount rates incorporate default risk. We also discuss the choice of a default-free discount rate. Finally, we show how cost-of-living adjustments that are common in public pensions can be accounted for and valued in this framework.

This is a comment on a paper by David F. Burgess and Richard O. Zerbe. It derives a different set of conclusions than the cited authors do from the customary premises underlying benefit-cost analysis. It concludes that capital should be shadow priced, and that the appropriate discount rate to use in benefit-cost analysis is the interest rate of the capital market to which the public sector has access. It proposes that a plausible source of the great divergence in approaches to discounting stems from different answers being given to the question of whether present day consumption has a future consumption opportunity cost.

The Pension Benefit Guaranty Corporation's (PBGC) Pension Insurance Modeling System model has taken on the Herculean task of modeling in detail and under many scenarios the cash outflows associated with the pension obligations, they have assumed. This paper's comments are focused almost entirely upon the PBGC's termination liabilities, and address four pressing issues: (1) the need to discount the liability stream by current riskless interest rates instead of using corporate bond rates that reflect credit risk, call risk, and other risks, or using some ad hoc prescribed average of past rates; (2) the need to use a term structure of interest rates; (3) the need to employ more useful investment management benchmarks; and (4) how to implement a relevant and rigorous liability benchmark.

The objective of this study is to identify experimental economic tools that can be employed to explain the role of economic behavior in overweight and obesity in the household. We identify three economic experiments that can be used to understand how parent-child economic relationships relate to obesity. Loss aversion experiments are discussed as a tool to understand challenges some individuals face in achieving a healthy diet. Finally, testbed experiments are introduced as a means to test and understand new policies and incentives for better health at the household level.

Two comments in this issue of the Journal address our recent article in Volume 2, Issue 2. The fundamental issue with both comments is that they confuse the financial rate of return with the opportunity cost rate of return and therefore advocate for an inappropriate basis on which to calculate the government discount rate. That is, both comments confuse the financial cost of funds, or the borrowing rate, with the economic opportunity cost of funds. We hope that this exchange advances the subject by reducing confusion.

In order to be sensible about what discount rate to use one must be clear about its purpose. We suggest that its purpose is to help select those projects that will contribute more net benefits than some other discount rate. This approach, which is after all the foundation for benefit-cost analysis, helps to reconcile different suggested procedures for determining the discount rate. We suggest that the social opportunity cost of capital (SOC) is superior to other suggested approaches in its generality and its ease of use. We use the SOC to determine a range of real rates that vary between 6% and 8%. We suggest that approaches based on determination of preferences, which result in hyperbolic discounting, are less appropriate and less useful.

This paper reviews the developments in reporting of traditional embedded value and summarises some of the reasons why this is now undergoing change. It considers the purpose of an embedded value calculation and the effect of differing attitudes to risk. It comments on the recently developed European Embedded Value Principles and sets out the main areas where scope remains to apply judgement.

The paper proposes the market-consistent embedded value framework as a way forward to help provide guidance in some of these areas, in particular on the choice of discount rate and on calibration of stochastic techniques used to value embedded options and guarantees. The paper recognises that market-consistent embedded values are in relative infancy and sets out areas for possible future development.

For two independent principles of intergenerational equity, the implied discount rate equals the growth rate of real per capita income, say, 2%, thus falling right into the range suggested by the U.S. Office of Management and Budget. To prove this, we develop a simple tool to evaluate small policy changes affecting several generations, by reducing the dynamic problem to a static one. A necessary condition is time invariance, which is satisfied by any common solution concept in an overlapping-generations model with exogenous growth. This tool is applied to derive the discount rate for cost–benefit analysis under two different utilitarian welfare functions: classical and relative. It is only with relative utilitarianism, and assuming time-invariance of the set of alternatives (policies), that the discount rate is well defined for a heterogeneous society at a balanced growth equilibrium, is corroborated by an independent principle equating values of human lives, and equals the growth rate of real per-capita income.

Eric Posner’s signaling theory of social norms holds that individuals adopt social norms in order to signal that they have a low discount rate (that is, they value the future more than the present), and are therefore reliable long-term cooperative partners. This paper radically expands Posner’s theory by incorporating internalization into his model (the sense that norms possess some sort of binding quality, an “ought to”). I do this by tethering Posner’s theory to an evolutionary model. I argue that internalization is an adaptive quality that enhances the individual’s ability to play Posner’s signaling game and was thus selected for. The idea that internalization is evolutionarily conditioned is not new; however, linking this to Posner’s theory of discount rate signals is, and doing so offers tremendous explanatory potential.

Part I identifies the limitations of Posner’s purely rational choice approach, argues for the necessity of including internalization, and then proposes a model that does so – what I call the Expanded Signaling Model of Norms (ESM). Part II examines the problems that arise when we embrace such a model. How this model answers some key criticisms plaguing sociobiology is also briefly explored. Part III then examines existing criticisms of Posner’s theory, demonstrating how the Expanded Signaling Model clearly resolves these issues. The paper concludes that incorporating internalization into Posner’s signaling model greatly broadens the explanatory reach of Posner’s theory, providing a measure of clarity and predictability regarding how and why norms are internalized – an important insight, as these beliefs form the normative underpinning to law.