Utility Maximization under Model Uncertainty in Discrete Time

We give a general formulation of the utility maximization problem under nondominated model uncertainty in discrete time and show that an optimal portfolio exists for any utility function that is bounded from above. In the unbounded case, integrability conditions are needed as nonexistence may arise even if the value function is finite.Comment: 18 page

RISK BALANCING USING FARM LEVEL DATA: AN ECONOMETRIC ANALYSIS

In the paper, an econometric model is proposed to test the risk balancing hypothesis using farm level data. For the purpose, a constraint on expected utility maximization with respect to farm financial structure is given. Cluster method is applied to pick out the farms on the efficient frontier under expected utility maximization given risk attitude and actual interest rate. Regression results are given and compared to previous findings. Farm characteristics associated with the risk behaviors of farms with optimal utility are identified and compared with other farms.Risk and Uncertainty,

Intergenerational justice when future worlds are uncertain

Let there be a positive (exogenous) probability that, at each date, the human species will disappear. We postulate an Ethical Observer (EO) who maximizes intertemporal welfare under this uncertainty, with expected-utility preferences. Various social welfare criteria entail alternative von Neumann- Morgenstern utility functions for the EO: utilitarian, Rawlsian, and an extension of the latter that corrects for the size of population. Our analysis covers, first, a cake-eating economy (without production), where the utilitarian and Rawlsian recommend the same allocation. Second, a productive economy with education and capital, where it turns out that the recommendations of the two EOs are in general different. But when the utilitarian program diverges, then we prove it is optimal for the extended Rawlsian to ignore the uncertainty concerning the possible disappearance of the human species in the future. We conclude by discussing the implications for intergenerational welfare maximization in the presence of global warming.Discounted utilitarianism, Rawlsian, sustainability, maximin, uncertainty, expected utility, von Neumann-Morgenstern, dynamic welfare maximization.

The Effects of Foreign Price Uncertainty on Australian Production and Trade

This paper provides a framework for the empirical analysis of the role of uncertain international prices for the Australian economy’s production sector and its international trade. We model the movement of traded goods prices via a bivariate GARCH model and embed this within an expected utility maximizing model of the production sector. We find that the empirical results are consistent with expected utility maximization and that the hypothesis of risk neutrality is soundly rejected. Estimates of the effects of changes in expected prices and volatility of traded goods prices upon production decisions and the return to capital are presented and discussed, as are the impacts of changes in output growth of Australia’s major trading partners. The overall conclusion is that price uncertainty matters for the Australian production sector.Price uncertainty, production under risk, expected utility maximization, international trade

Robust utility maximization with nonlinear continuous semimartingales

In this paper we study a robust utility maximization problem in continuous time under model uncertainty. The model uncertainty is governed by a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued function that depends on time and path. We show that the robust utility maximization problem is in duality with a conjugate problem, and we study the existence of optimal portfolios for logarithmic, exponential and power utilities.Comment: To appear in "Mathematics and Financial Economics