Comparative statics under multiple sources of risk with applications to insurance demand

In this paper we propose an answer to the following problem of comparative statics in models with multiple sources of risk: How a risk averse agent will change his coinsurance demand when the distribution of the insurable loss is shifted? To answer the question, we first comment on Jack Meyer's results and then we show how an alternate approach leads to more definitive comparative statics.     

On Viable Diffusion Price Processes of the Market Portfolio

The assumption that the market portfolio follows a specified diffusion process implies, in a simple equilibrium framework, that the representative individual must have a certain utility function which is identified in the paper. Not every diffusion process is viable, i.e., can be “endogenized” to be the market portfolio's price process in such an equilibrium model. The paper provides necessary and sufficient conditions for viability which imply that viable diffusion processes constitute a rather restricted family.     

The Relationship between Arbitrage and First Order Stochastic Dominance

This paper joins together two fields of research in financial economics. The first field studies stochastic dominance, while the second field studies arbitrage pricing. The two fields are linked together through the derivation and the proof of a characterization theorem. The characterization theorem gives necessary and sufficient conditions for the existence of arbitrage opportunities in terms of the existence of two assets, one of which first order stochastically dominates the other and the price of a particular contingent claim. Examples are provided to demonstrate the theorem's content.     

Mossin's Theorem Given Random Initial Wealth

The purpose of this article is to reexamine Mossin's Theorem under random initial wealth. Conditions necessary and sufficient for Mossin's Theorem depend on the stochastic dependence between risks. The correlation coefficient, however, is not an adequate measure of stochastic dependence in the general expected‐utility model, and so other notions of dependence are used to investigate Mossin's Theorem. The inadequacy of the correlation coefficient is illustrated with two counterexamples. Then, using notions of positive and negative dependence measures, we provide necessary and sufficient conditions for a generalized Mossin Theorem to hold. In addition, a generalized Mossin Theorem is interpreted using the notion of a mean preserving spread made popular by Rothschild and Stiglitz (1970) . Given a fair premium and dependent stochastic conditions, we show that an individual can obtain a final wealth distribution with less weight in its tails by selecting less than or more than full insurance.     

The social risk–rent thesis: A reply to Harney

The paper responds to Stefano Harney's critique, ‘Accounting, Risk and Revolution’ and in doing so offers a further extension of Toms, 2006, Toms, 2010 perspective on labour rents and capitalist risk. Harney's challenge, to ask what is left out of critical accounting's account of risk, is an important one. Therefore the social rent–risk (SRR) hypothesis extends the analysis of critical accounting from systematic risk to include firm specific risk and primitive accumulation risk. It is argued that the SRR approach provides a generalised method of accounting for social relations of production and the necessary conditions of social transformation.     

On Testing the Assumptions of the Cash Recovery Rate Approach to the Estimation of Economic Performance

The first purpose of this paper is to investigate the necessary (as opposed to sufficient) assumptions underlying the CRR approach to the estimation of corporate economic performance. By so doing, the general circumstances in which an estimate of corporate economic performance based on CRRs will exactly equal a firm's IRR are identified. It is pointed out that these necessary assumptions are related to the concept of corporate economic performance being invoked (within the general idea that we are trying to estimate a firm's internal rate of return). Second, there is a drawing out of the empirical implications, as to the behaviour of corporate cash flows and CRRs, of the necessary assumptions for the CRR approach to produce an estimate of economic performance equal to a firm's IRR for each of these definitions of corporate economic performance. In particular, it is argued that these empirical implications depend upon the specific manner in which the CRR approach is applied in practice. A third purpose of the paper is to provide some empirical evidence as to whether an example of the practice of using the CRR approach employs data consistent with the necessary assumptions for this particular approach to be valid outlined in the paper. In fact, it turns out that this might not be the case. The evidence casts light on the extent to which CRR-based estimates of corporate economic performance are likely to be reasonable proxies of firms' IRRs.     

Investment Management and Risk Sharing with Multiple Managers

This paper addresses the investor's decision to employ multiple managers for the management of investment funds. Under conditions such that specialization of managers and diversification among managers are not motives for the use of multiple managers, the paper shows that risk sharing considerations may be sufficient. A model is developed in which the decision to use multiple managers is explicitly treated, and conditions are studied such that an increase or decrease in the number of managers would be desirable. Under some conditions, a multiple manager solution is preferred over a single manager solution.     

When Is a Coinsurance‐Type Insurance Policy Inferior or Even Giffen?

This article derives the necessary and sufficient conditions for a coinsurance‐type insurance policy covering a particular risk to be inferior and to be Giffen. Mossin's decreasing absolute risk aversion assumption for insurance to be inferior is avoided. The result generalizes Hoy and Robson and Briys, Dionne, and Eeckhoudt's results to the case with a continuum of states and relaxes their assumption of constant relative risk aversion. It is shown that knowledge about the distribution of risk can be used to relax assumptions on an utility function for a coinsurance‐type insurance policy to be inferior and to be Giffen.     

Encouraging savings through the life cycle

This paper discusses management of an individual's savings over the life cycle. It introduces the concept of a ‘Lifetime Savings Account’, to provide a coherent framework for organising investments: a ‘one-stop shop’ for all financial needs, encompassing cash, medium- and long-term investments, managing credit card debt, accessing loans, life insurance and keeping an individual's pension entitlements in one place. The paper proposes replacing tax relief with matching saving incentives, which could be administered by the account, and recommends introduction of a fixed-term Individual Savings Account (ISA) with incentives to keep invested for five years and extra incentives to renew or transfer to a pension. Finally, the paper introduces the concept of a ‘Minimum Lifetime Annuity’ which would be sufficient to ensure no need for meanstested benefits, also suggesting it might be sufficient if an individual has adequate capital in the Lifetime Savings Account to be able to purchase such an annuity if necessary, without having actually to effect the transaction.     

Group Welfare and the Formation of a Common Labor Market: Some Global Results

Consider a collection of isolated or autarkic regions. The original residents or natives of each region are by assumption a group with a welfare function defined over group members' consumption. Now suppose the regions form a common labor market and a federal government, and one type from each group can freely migrate to other regions. Under what circumstances is this change even potentially beneficial to all groups? We derive a necessary and sufficient condition that depends only on the exogenous parameters of our model. Earlier treatments of these issues focus on relationships among endogenous variables. Our condition underlies those relationships. We also show that there is nothing pathological about the conditions under which federalism must make some or all groups worse off. When it is possible to make all groups better off, we show that the change can be supported by Wildasin's (1991) corrected Nash equilibrium in redistributive transfers.     

Extremes on the discounted aggregate claims in a time dependent risk model

This paper presents an extension of the classical compound Poisson risk model for which the inter-claim time and the forthcoming claim amount are no longer independent random variables (rv's). Asymptotic tail probabilities for the discounted aggregate claims are presented when the force of interest is constant and the claim amounts are heavy tail distributed rv's. Furthermore, we derive asymptotic finite time ruin probabilities, as well as asymptotic approximations for some common risk measures associated with the discounted aggregate claims. A simulation study is performed in order to validate the results obtained in the free interest risk model.     

Evaluating Competitive Strategies

In this paper we introduce a conception of learning which is a natural extension of economists' representations of learning and which is natural to develop using KBS technology. In the particular form of KBS we use, rule conditions and actions are well-formulated formulae of first-order predicate logic (FOPL). As a result, the simulation results obtained from these models are no less analytical than those of pure analytic models. Our results are further strengthened by an experimental design for simulations of competitive behaviour which eliminates implicit bias in the selection of possible behaviours. The system is applied to the Cournot duopoly model. We find that modest intelligence on the part of at least one duopolist systematically increases the profits of both.     

Stock Market Return Expectations: Some General Properties

This paper examines how and how well do leading economists forecast stock market returns. This question is fundamental in finance, since the Capital Asset Pricing foundation rests upon assumptions about the properties of investors' expectations for stock market returns. The results reveal that economists' expectations of market returns as exemplified in Livingston's data do not meet the necessary conditions of efficiency. It should be noted however, that in later period some improvement in the quality of economists' forecasts was observed.     

First-Order Approach to Principal-Agent Problems: A Generalization

The first-order approach (FOA) to principal agent problems is very convenient and mathematically tractable. However, existing results show that the FOA is valid only for additively separable utility functions. This is somewhat limiting. In this article sufficient conditions are identified that extend the validity of the FOA to nonseparable cases. The additional conditions involve restrictions on the agent's preferences, particularly interactions between action and the wage contract. These conditions imply that leisure is normal and the agent's absolute risk aversion increases with action. Comparative static results regarding the wage contract and its gradient are also discussed.     

Consumption Externality and Equilibrium Underinsurance

Relative consumption has been found to be crucial in many areas, such as asset pricing, the design of taxation, and economic growth. This article extends this line of research to the individual's insurance decision. We first define “keeping up with the Joneses” in the purchase of insurance and find that jealousy does not necessarily give rise to “keeping up with the Joneses.” We also identify several sufficient conditions that cause the optimal coverage in the private market to be less than the social optimum (equilibrium underinsurance). Jealousy is found to be neither a sufficient nor a necessary condition for equilibrium underinsurance. We further show that a social welfare maximizing government could adopt a tax system to correct for the consumption externality and make individuals better off.     

Skewness Preference,Risk Taking and Expected Utility Maximisation

Available empirical evidence suggests that skewness preference plays an important role in understanding asset pricing and gambling. This paper establishes a skewness-comparability condition on probability distributions that is necessary and sufficient for any decision-maker's preferences over the distributions to depend on their means, variances, and third moments only. Under the condition, an Expected Utility maximizer's preferences for a larger mean, a smaller variance, and a larger third moment are shown to parallel, respectively, his preferences for a first-degree stochastic dominant improvement, a mean-preserving contraction, and a downside risk decrease and are characterized in terms of the von Neumann-Morgenstern utility function in exactly the same way. By showing that all Bernoulli distributions are mutually skewness comparable, we further show that in the wide range of economic models where these distributions are used individuals’ decisions under risk can be understood as trade-offs between mean, variance, and skewness. Our results on skewness-inducing transformations of random variables can also be applied to analyze the effects of progressive tax reforms on the incentive to make risky investments.     

Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for the existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.     

Literatur

1. A simplified method for the deduction of Sheppard's correction formulae for ordinary and factorial moments, and for semi-invariants, together with more general results than those previously known, especially with regard to the remainder term, has recently been given ¹ H. Wold: Sulla correzione di Sheppard. Giornale dell' Istituto Italiano degli Attuari IV 1934, pp. 304–314. The methods used in the note referred to are similar to those used by W. F. Sheppard in his paper “The Calculation of Moments of a Frequency Distribution”, Biometrika V 1907, pp. 450–459. However, Sheppard's results are not valid under equally general conditions. . The method is based upon a very simple application of Euler—MacLaurin's formula, and the usual corrections are thereby shown to be valid for very general frequency curves, even for those without high contact in one or both directions. The note referred to deals with the case of one variable; the use of the method employed there can, however, easily be extended to an arbitrary number of variables, which extension it is the purpose of this paper to carry through. For the sake of formal simplicity the deductions are performed with two variables; the results can then immediately be generalized.     

Determining Meaningful Sales Relational (Mix) Variances

Further separation of the volume variance component of a multi-product firm's revenue variance into mix and quantity variances is regularly advocated by management accounting educators. Techniques used to achieve this separation are generally an extension of the analytical techniques used in the traditional flexible budget step-down? approach to variance determination. The analysis in this paper suggests that such an extension in most multi-product situations is inappropriate and generates useless and misleading results. Specific situations in which relational (in lieu of mix) variances may be appropriate do exist and applicable techniques are developed.