Who would invest only in the risk-free asset?

Within the setup of continuous-time semimartingale financial markets, we show that a multiprior Gilboa–Schmeidler minimax expected utility maximizer forms a portfolio consisting only of the riskless asset if and only if among the investor’s priors there exists a probability measure under which all admissible wealth processes are supermartingales. Furthermore, we show that under a certain attainability condition (which is always valid in finite or complete markets) this is also equivalent to the existence of an equivalent (local) martingale measure among the investor’s priors. As an example, we generalize a no betting result due to Dow and Werlang.

OPTIMAL PORTFOLIO UNDER STATE-DEPENDENT EXPECTED UTILITY

We derive the optimal portfolio for an expected utility maximizer whose utility does not only depend on terminal wealth but also on some random benchmark (state-dependent utility). We then apply this result to obtain the optimal portfolio of a loss-averse investor with a random reference point (extending a result of Berkelaar et al. (2004) Optimal portfolio choice under loss aversion, The Review of Economics and Statistics 86 (4), 973–987). Clearly, the optimal portfolio has some joint distribution with the benchmark and we show that it is the cheapest possible in having this distribution. This characterization result allows us to infer the state-dependent utility function that explains the demand for a given (joint) distribution.

COMMENTS ON 'REVERSE AUCTION: THE LOWEST UNIQUE POSITIVE INTEGER GAME'

In Zeng et al. [Fluct. Noise Lett. 7 (2007) L439–L447] the analysis of the lowest unique positive integer game is simplified by some reasonable assumptions that make the problem tractable for arbitrary numbers of players. However, here we show that the solution obtained for rational players is not a Nash equilibrium and that a rational utility maximizer with full computational capability would arrive at a solution with a superior expected payoff. An exact solution is presented for the three- and four-player cases and an approximate solution for an arbitrary number of players.

Choice under Limited Uncertainty

This paper considers the problem of an agent's choice under uncertainty in a new framework. The agent does not know the true probability distribution over the state space but is objectively informed that it belongs to a specified set of probabilities. Maintaining the hypothesis that this agent is a subjective expected utility maximizer, we address the question of how the objective information influences her subjective prior.Three plausible rules are proposed. The first, named state independence, states that the subjective probability should not depend on how the uncertain states are `labeled'. Location-consistency, the second property, assumes that `similar' objective sets of probabilities result in `similar' subjective priors. The third rule is an `update-consistency' rule. Suppose the agent selects some probability p. She is then told that the likelihood assigned by p to some event A is in fact correct; then this should not cause her to revise her choice of p.Another property, alternative to update-consistency, is also proposed. When an agent forms her subjective prior assigning subjective probabilities to events in some ordered sequence, this property requires that the resulting prior be independent of that order. This last property, named order independence, is shown to be equivalent to update-consistency.A class of sets of probabilities is found on which state independence, location-consistency and update consistency (order independence) uniquely determine a selection rule. Some intuition is given regarding why these properties work in this collection of problems.

Reason, Egoism, and the Prisoners' Dilemma

In this essay I shall try to show that the egoist's inability to avoid the Prisoners’ Dilemma is not a reason for rejecting egoism. In the first section I shall outline the Prisoners’ Dilemma and indicate why the egoist cannot avoid the dilemma. In the next section I shall consider an argument against egoism based upon an appeal to our intuitions as to what is rational. And in the final section I shall consider the argument that egoism is not self-supporting and so is not an adequate conception of rationality.But first a few words should be said about what is meant by egoism here. The egoist is commonly thought of as someone who acts from selfinterest. This is in keeping with the present use of the term as long as ‘self-interest’ is not understood in a too narrow a fashion. Perhaps a Jess misleading way of characterizing the egoist, though, is as someone who tries to maximize his happiness - i.e., he is an individual utility maximizer.

The Appeal of the Political Entrepreneur

In its purest form a collective good is said to possess the characteristics of non-rivalness in consumption and non-price exclusion. Non-rivalness implies that consumption to the full by one person in no way impedes the consumption of that same quantity by others. This does not mean that the same subjective benefit is derived by each individual, but simply that consumption by one individual does not interfere with the benefits derived by another. The characteristic of non-exclusion requires that if the good is provided to one then it is provided to all. It is this attribute in particular which casts doubt on the likelihood that, in a large group, individuals will voluntarily reveal their preferences for the good. Goods which are not perfectly rival but which are price exclusive may be provided in the market by clubs. However, when an individual's consumption of a good is not dependent on his making a contribution to its provision the individual utility maximizer may be inclined to ‘free ride’, in the hope of enjoying the good at no personal expense. It is clear that if all individuals act in the same manner this good is not likely to be provided in the private market.