Life insurance decisions under recursive utility

In this paper, we generalize recursive utility to include lifetime uncertainty and utility from bequest. The generalization applies to discrete-time as well as continuous-time recursive utility, and it is an important step forward in the development of recursive utility. We formalize the problem of optimal consumption, investment, and life insurance choice under recursive utility, and we state a verification theorem with a generalized Hamilton-Jacobi-Bellman equation. Our generalization of recursive utility allows us to study optimal consumption, investment, and life insurance choice under separation of (market) risk aversion, elasticity of inter-temporal substitution, and elasticity of substitution between bequest and future utility. The separation gives rise to hump-shaped consumption patterns as observed in realized consumption.     

Borrowing constraints,the cost of precautionary saving and unemployment insurance

When it is costly for individuals to save or to borrow, unemployment insurance (UI) provides an alternative source of liquidity that smooths consumption over time and leads individuals to spend longer unemployed searching for a suitable job. We show in a tractable life-cycle model how the optimal unemployment replacement ratio and the fall in consumption on job loss depend on the cost of self-insurance and the cost of borrowing. This implies that the value of UI depends on age at job loss, consumption needs (such as the presence of children), discount rates, the return on saving, access to credit and the presence of other social insurance programmes. Optimal replacement rates vary substantially with plausible variation in these factors (from less than 20 percent to almost 60 percent).     

Consumption-portfolio optimization with recursive utility in incomplete markets

In an incomplete market, we study the optimal consumption-portfolio decision of an investor with recursive preferences of Epstein?CZin type. Applying a classical dynamic programming approach, we formulate the associated Hamilton?CJacobi?CBellman equation and provide a suitable verification theorem. The proof of this verification theorem is complicated by the fact that the Epstein?CZin aggregator is non-Lipschitz, so standard verification results (e.g. in Duffie and Epstein, Econometrica 60, 393?C394, 1992) are not applicable. We provide new explicit solutions to the Bellman equation with Epstein?CZin preferences in an incomplete market for non-unit elasticity of intertemporal substitution (EIS) and apply our verification result to prove that they solve the consumption-investment problem. We also compare our exact solutions to the Campbell?CShiller approximation and assess its accuracy.     

From precautionary inadequacy to participatory risk management

This paper examines the case of mobile telephone infrastructure as an example of a contemporary risk defined by a lack of scientific evidence and consensus as regards potential or future harm. This uncertainty has led to recourse to the precautionary principle at the European, national, regional and local level of EMF risk management. Local risk governance of mobile telephone infrastructures in Catalonia can be seen as an example of a socio-technical complex system linked to risk perception which highlights the limitations of the precautionary principle in a scientifically uncertain context. Active participation of stakeholders and the public in risk management arenas is required if current technocratic risk management strategies are to be superseded by transparent processes of decision-making in risk management spheres.     

Technocratic precautionary principle: Korean risk governance of mad cow disease

This study investigates the multiplicity of sciences and the assemblage of technocracy with the precautionary principle (PP) in the Korean risk governance of mad cow disease (Bovine Spongiform Encephalopathy [BSE]). It conducts a policy typological analysis and a sociocultural analysis of the PP. Korean BSE policies are built on the technocratic PP. This principle emphasizes the scientific evidence of risk, although taking precautionary policy actions against BSE. This principle led to the absence of a total BSE inspection, a specified risk material policy for Korean cattle, a Hazard Analysis and Critical Control Point policy for beef processing and circulation, and an animal feed ban on nonruminants. Moreover, the BSE debate is not one about a unified science vs. a unified PP, but rather it concerns complex struggles between PPs in alliance with different sciences.     

Changes in risk and the demand for saving

How does risk affect saving? Empirical work typically examines the effects of detectible differences in risk within the data. How these differences affect saving in theoretical models depends on the metric one uses for risk. For labor-income risk, second-degree increases in risk require prudence to induce increased saving demand. However, prudence is not necessary for first-degree risk increases and not sufficient for higher-degree risk increases. For increases in interest-rate risk, a precautionary effect and a substitution effect need to be compared. This paper provides necessary and sufficient conditions on preferences for an Nth-degree change in risk to increase saving.     

Pricing innovations in consumption growth: A re-evaluation of the recursive utility model

We re-evaluate the cross-sectional asset pricing implications of the recursive utility function of  and , using innovations in future consumption growth in our tests. Our empirical specification helps explain the size, value and momentum effects. Specifically, we find that (?) the beta associated with news about consumption growth has a systematic pattern: beta decreases along the size dimension and increases along the book-to-market and momentum dimensions, (??) innovation in consumption growth is significantly priced in asset returns using both the Fama and MacBeth (1973) and the stochastic discount factor approaches, and (???) the model performs better than both the CAPM and Fama–French model.     

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.     

Pricing jump risk with utility indifference

This paper is concerned with option pricing in an incomplete market driven by a jump-diffusion process. We price options according to the principle of utility indifference. Our main contribution is an efficient multi-nomial tree method for computing the utility indifference prices for both European and American options. Moreover, we conduct an extensive numerical study to examine how the indifference prices vary in response to changes in the major model parameters. It is shown that the model reproduces ‘crash-o-phobia’ and other features of market prices of options. In addition, we find that the volatility smile generated by the model corresponds to a zero mean jump size, while the volatility skew corresponds to a negative mean jump size.     

Convertibility risk: the precautionary demand for foreign currency in a crisis

This paper presents theoretical work linking money demand to the perceptions of households about the risk that domestic currency may become inconvertible or that it may be devalued. An empirical investigation of the size of this effect is carried out using monthly data for Korea to estimate an augmented demand-for-money equation. It is found that the fear of inconvertibility arising from the 1997 Korean currency crisis may have caused broad money demand to fall by 4–5% points,equivalent to the loss of reserves of $6–7.5 billion (or about 30% of reserves as measured at end-November 1997). This is a revised version of IMF Working paper WP/2001/210; it was written while Professor Black was Senior Policy Advisor at the IMF Institute and Christofides and Mourmouras were staff members in the IMF’s Policy Development and Review Department. The views expressed are those of the authors and should not be attributed to the IMF, its Executive Board, or its management. For useful comments and suggestions we thank an anonymous referee, Tim Lane, Ydahlia Metzgen, Roberto Perelli, Tony Richards, Christian Mulder, Steve Russell, as well as seminar participants at the IMF Institute, the IMF’s Asia and Pacific Department, Federal Reserve Board, and Bank of Indonesia. We would also like to note similar (unpublished) empirical results using our approach by Dr. Rino Effendi for Indonesia and Angana Banerji for Russia     

Optimal insurance under maxmin expected utility

We examine a problem of demand for insurance indemnification, when the insured is sensitive to ambiguity and behaves according to the maxmin expected utility model of Gilboa and Schmeidler (J. Math. Econ. 18:141–153, 1989), whereas the insurer is a (risk-averse or risk-neutral) expected-utility maximiser. We characterise optimal indemnity functions both with and without the customary ex ante no-sabotage requirement on feasible indemnities, and for both concave and linear utility functions for the two agents. This allows us to provide a unifying framework in which we examine the effects of the no-sabotage condition, of marginal utility of wealth, of belief heterogeneity, as well as of ambiguity (multiplicity of priors) on the structure of optimal indemnity functions. In particular, we show how a singularity in beliefs leads to an optimal indemnity function that involves full insurance on an event to which the insurer assigns zero probability, while the decision maker assigns a positive probability. We examine several illustrative examples, and we provide numerical studies for the case of a Wasserstein and a Rényi ambiguity set.

     

Exponential utility maximization under partial information

We consider the exponential utility maximization problem under partial information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available. We show that this problem is equivalent to a new exponential optimization problem which is formulated in terms of observable processes. We prove that the value process of the reduced problem is the unique solution of a backward stochastic differential equation (BSDE) which characterizes the optimal strategy. We examine two particular cases of diffusion market models for which an explicit solution has been provided. Finally, we study the issue of sufficiency of partial information.     

Asset pricing under quantile utility maximization

“Focus on the downside, and the upside will take care of itself” is a famous quote among professional investors. By considering an agent who follows this advice, we reproduce the first and second moments of stock returns, risk-free rate and consumption growth. The agent's behavior toward risk is analogous to a relative risk aversion of about 3 under expected utility, the elasticity of intertemporal substitution is about 0.5 and the time discount factor is below 1. In particular, the proposed model separates time and risk preferences in an innovative way.     

CVP under uncertainty and the manager's utility function

Cost-volume-profit analysis has focused on the firm's short-run output decision assuming that the manager maximizes the firm's objective function rather than his or her own. This study argues that the decision problem facing the manager is to determine not only the level of output, but also the level of investment in risky assets in such a way that the expected utility of the manager's own end-of-period wealth can be maximized when the manager's wealth function is dependent on vested interests both within and outside of the firm, possibly in competition with the firm. Through analytical work, it is demonstrated that a change in fixed costs of the firm affects not only the production decision of a manager, but also his orher decision to invest in risky assets. The direction of this fixed cost effect depends on the particular type of risk aversion displayed by the manager. From the analytical work, five propositions are developed for empirical investigation in the future.The most helpful comments of Professor Cheng-few Lee are greatly acknowledged. We wish to thank anonymous referees who's comments have improved the paper. Furthermore, participants at the seminar at the University of Massachusetts Lowell also provided helpful comments.     

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.     

Genetically modified plants and the precautionary principle

The European regulation of genetically modified plants is a particular example of technological risk management that has become an essential part of the management of change. The role of regulators in this management process, when there are demands for regulatory action concerning unquantified (and sometimes unquantifiable) technological risks – with regulation under conditions of uncertainty – is explored. Where the retrospective evidence concerning a postulated risk scenario is sparse, the precautionary principle (PP) may be invoked. The origins of the European regulatory system, which applied until 17 October 2002 (Directive 90/220), why this has been revised (Directive 2001/18) and the probable impact of this revision are described. This is illustrated with risk assessments that have accompanied submissions for marketing approval for genetically modified plants under Directive 90/220. Some of the problems associated with the PP and the regulation of GM plants are discussed.     

A note on wealth effect under CARA utility

There is a simple but overlooked way of capturing the wealth effect under CARA utility via making the absolute-risk aversion parameter wealth-dependent. We implement this approach in the asymmetric information setting of Verrecchia (1982), and compare it with the alternative approach of changing the utility function (Peress, 2004). Ours is a straightforward tractable extension of Verrecchia, while Peress has to resort to approximate methods. Importantly, our closed-form solution reveals that the relation between wealth and wealth share invested in a risky asset can be negative, while Peress’s main result is that this relation is uniquely positive.