Correspondence between lifetime minimum wealth and utility of consumption

We establish when the two problems of minimizing a function of lifetime minimum wealth and of maximizing utility of lifetime consumption result in the same optimal investment strategy on a given open interval O in wealth space. To answer this question, we equate the two investment strategies and show that if the individual consumes at the same rate in both problems—the consumption rate is a control in the problem of maximizing utility—then the investment strategies are equal only when the consumption function is linear in wealth on O, a rather surprising result. It then follows that the corresponding investment strategy is also linear in wealth and the implied utility function exhibits hyperbolic absolute risk aversion.      

Multiperiod Optimal Investment-Consumption Strategies with Mortality Risk and Environment Uncertainty

Abstract

In this article we investigate three related investment-consumption problems for a risk-averse investor: (1) an investment-only problem that involves utility from only terminal wealth, (2) an investment-consumption problem that involves utility from only consumption, and (3) an extended investment-consumption problem that involves utility from both consumption and terminal wealth. Although these problems have been studied quite extensively in continuous-time frameworks, we focus on discrete time. Our contributions are (1) to model these investmentconsumption problems using a discrete model that incorporates the environment risk and mortality risk, in addition to the market risk that is typically considered, and (2) to derive explicit expressions of the optimal investment-consumption strategies to these modeled problems. Furthermore, economic implications of our results are presented. It is reassuring that many of our findings are consistent with the well-known results from the continuous-time models, even though our models have the additional features of modeling the environment uncertainty and the uncertain exit time.     

Optimal capital and risk allocations for law- and cash-invariant convex functions

In this paper we provide a complete solution to the existence and characterization problem of optimal capital and risk allocations for not necessarily monotone, law-invariant convex risk measures on the model space L ^p for any p∈[1,∞]. Our main result says that the capital and risk allocation problem always admits a solution via contracts whose payoffs are defined as increasing Lipschitz-continuous functions of the aggregate risk. Filipović is supported by WWTF (Vienna Science and Technology Fund). Svindland gratefully acknowledges financial support from Munich Re Grant for doctoral students and hospitality of the Research Unit of Financial and Actuarial Mathematics, Vienna University of Technology. We thank Beatrice Acciaio and Walter Schachermayer for fruitful discussions and an anonymous referee for helpful remarks.     

Robust utility maximization for complete and incomplete market models

We investigate the problem of maximizing the robust utility functional . We give the dual characterization for its solution for both a complete and an incomplete market model. To this end, we introduce the new notion of reverse f-projections and use techniques developed for f-divergences. This is a suitable tool to reduce the robust problem to the classical problem of utility maximization under a certain measure: the reverse f-projection. Furthermore, we give the dual characterization for a closely related problem, the minimization of expenditures given a minimum level of expected utility in a robust setting and for an incomplete market.Received: September 2004, Mathematics Subject Classification (2000): 62C20, 62O05, 91B16, 91B28JEL Classification: D81, G11I thank Hans Föllmer for his help when writing this paper. Furthermore, I thank Alexander Schied for discussing the topic with me and Michael Kupper and the referees for their helpful remarks.     

Asymmetric Information in Fads Models

Fads models were introduced by Shiller (Am Econ Rev 71:421–436, 1981) and Summers (J Finance 41:591–601, 1986) as plausible alternatives to the efficient markets/constant expected returns assumptions. Under these models, logarithms of asset prices embody both a martingale component, with permanent shocks, and a stationary component, with temporary shocks. We study a continuous-time version of these models both from the point of view of informed agents, who observe both fundamental and market values, and from that of uninformed agents, who only observe market prices. We specify the asset price in the larger filtration of the informed agent, and then derive its decomposition in the smaller filtration of the uninformed agent using the Hitsuda representation of Gaussian processes. For uninformed agents we obtain a non-Markovian dynamics, which justifies the use of technical analysis in optimal trading strategies. For both types of agents, we solve the problem of maximization of expected logarithmic utility from terminal wealth, and obtain an explicit formula for the additional logarithmic utility of informed agents. Finally, we apply the decomposition result to the problem of testing the presence of fads from market data. An application to the NYSE-AMEX indices from the CRSP database shows that, if the fads component prevails, then the mean-reversion speed must be slow.     

Multivariate geometric expectiles

A generalization of expectiles for d-dimensional multivariate distribution functions is introduced. The resulting geometric expectiles are unique solutions to a convex risk minimization problem and are given by d-dimensional vectors. They are well behaved under common data transformations and the corresponding sample version is shown to be a consistent estimator. We exemplify their usage as risk measures in a number of multivariate settings, highlighting the influence of varying margins and dependence structures.     

Recovering the market risk premium from higher-order moment risks

We propose a consistent approach for the estimation of the market risk premium. As a first step, we define the broadest possible set of ex ante estimators from the viewpoint of a power utility optimiser holding the market portfolio. We then employ an evaluation framework to optimise the parametrisation of the methodology. We show that this theoretical framework can still produce reasonable market risk premium estimates, even when the representative agent is not a power utility optimiser. Our results show that the inclusion of higher-order moment risk premia improves the accuracy of the method.     

Managing risk through the veil of ignorance

Background. We view overconfidence within risk management as a problem likely to manifest within philosophical preferences for anticipationism over resilienism, and in assumptions that risks are objectively real external powers or potentialities rather than subjective knowledge propositions. Methods. We argue that the realist tradition within Italian social theory, first crystallised by Niccolò Machiavelli and later elaborated by the sociologist Vilfredo Pareto, offers valuable lessons for corporate risk management praxis by demanding that we map out the complex relations between the risk subjectivities of risk managers, and their objective risk environments, from a standpoint of psychological and sociological realism which stresses the risk ignorance of practitioners. We caution that risk management efforts to improve risk subjectivities to achieve perfect veridicality to objective risk environments might often amount to a wishful bildungsroman of epistemological growth, reflecting the common aspirations of risk managers to demonstrate professional competence. We suggest that the profession should control this overconfidence problem by stressing the corrigibility of risk subjectivities with reference to sociological understandings that reflect on the widespread risk ignorance that can persist and even intensify where risk management effort is made. Results. Following the macrosociological framework sketched by Pareto, we show how two common ‘modes of uncertainty’ can be scrutinised for their adaptive fitness to two common types of risk environment. Conclusions. It can be helpful to think sociologically of organisations as engaging with some highly significant strategic risks blindly through a veil of ignorance.