Diversification Preferences in the Theory of Choice

Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von-Neumann-Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper studies axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. Implications of these notions on portfolio choice are discussed. We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion

Estimating Risk Preferences in the Field

We survey the literature on estimating risk preferences using field data. We concentrate our attention on studies in which risk preferences are the focal object and estimating their structure is the core enterprise. We review a number of models of risk preferences—including both expected utility (EU) theory and non-EU models—that have been estimated using field data, and we highlight issues related to identification and estimation of such models using field data. We then survey the literature, giving separate treatment to research that uses individual-level data (e.g., property insurance data) and research that uses aggregate data (e.g., betting market data). We conclude by discussing directions for future research

Aversion to ambiguity and model misspecification in dynamic stochastic environments

Preferences that accommodate aversion to subjective uncertainty and its potential misspecification in dynamic settings are a valuable tool of analysis in many disciplines. By generalizing previous analyses, we propose a tractable approach to incorporating broadly conceived responses to uncertainty. We illustrate our approach on some stylized stochastic environments. By design, these discrete time environments have revealing continuous time limits. Drawing on these illustrations, we construct recursive representations of intertemporal preferences that allow for penalized and smooth ambiguity aversion to subjective uncertainty. These recursive representations imply continuous time limiting Hamilton–Jacobi–Bellman equations for solving control problems in the presence of uncertainty.Published versio

On the cost of misperceived travel time variability

Recent studies show that traveler’s scheduling preferences compose a willingness-to-pay function directly corresponding to aggregate measurement of travel time variability under some assumptions. This property makes valuation on travel time variability transferable from context to context, which is ideal for extensive policy evaluation. However, if respondents do not exactly maximizing expected utility as assumed, such transferability might not hold because two types of potential errors: (i) scheduling preference elicited from stated preference experiment involving risk might be biased due to misspecification and (ii) ignoring the cost of misperceiving travel time distribution might result in undervaluation. To find out to what extent these errors matter, we reformulate a general scheduling model under rank-dependent utility theory, and derive reduced-form expected cost functions of choosing suboptimal departure time under two special cases. We estimate these two models and calculate the empirical cost due to misperceived travel time variability. We find that (i) travelers are mostly pessimistic and thus tend to choose departure time too earlier to bring optimal cost, (ii) scheduling preference elicited from stated choice method could be quite biased if probability weight- ing is not considered and (iii) the extra cost of misperceiving travel time distribution contributes trivial amount to the discrepancy between scheduling model and its reduced form

Mean-Variance and Expected Utility: The Borch Paradox

The model of rational decision-making in most of economics and statistics is expected utility theory (EU) axiomatised by von Neumann and Morgenstern, Savage and others. This is less the case, however, in financial economics and mathematical finance, where investment decisions are commonly based on the methods of mean-variance (MV) introduced in the 1950s by Markowitz. Under the MV framework, each available investment opportunity ("asset") or portfolio is represented in just two dimensions by the ex ante mean and standard deviation $(\mu,\sigma)$ of the financial return anticipated from that investment. Utility adherents consider that in general MV methods are logically incoherent. Most famously, Norwegian insurance theorist Borch presented a proof suggesting that two-dimensional MV indifference curves cannot represent the preferences of a rational investor (he claimed that MV indifference curves "do not exist"). This is known as Borch's paradox and gave rise to an important but generally little-known philosophical literature relating MV to EU. We examine the main early contributions to this literature, focussing on Borch's logic and the arguments by which it has been set aside.Comment: Published in at http://dx.doi.org/10.1214/12-STS408 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Equity Premia with Benchmark Levels of Consumption: Closed-Form Results

I calculate exact expressions for risk premia, term premia, and the premium on levered equity in a framework that includes habit formation, keeping/catching up with the Joneses, and possible departures from rational expectations. Closed-form expressions for the first and second moments of returns and for the R2 of a regression of stock returns on the dividend-price ratio are derived under lognormality for the case that includes keeping/catching up with the Joneses. Linear approximations illustrate how these moments of returns are affected by parameter values and illustrate quantitatively how well the model can account for values of the equity premium, the term premium, and the standard deviations of the riskless return and the rate of return on levered equity. For empirically relevant parameter values, the linear approximations yield values of the various moments that are close to those obtained from the exact solutions.

Background Uuncertainty and the Demand for Insurance against Insurable Risks

Theory suggests that people facing higher uninsurable background risk buy more insurance against other risks that are insurable. This proposition is supported by Italian cross-sectional data. It is shown that the probability of purchasing casualty insurance increases with earnings uncertainty. This finding is consistent with consumer preferences being characterised by decreasing absolute prudenceInsurance, background risk, prudence