Nonconcave Utility Maximization with Portfolio Bounds

The problems of nonconcave utility maximization appear in many areas of finance and economics, such as in behavioral economics, incentive schemes, aspiration utility, and goal-reaching problems. Existing literature solves these problems using the concavification principle. We provide a framework for solving nonconcave utility maximization problems, where the concavification principle may not hold, and the utility functions can be discontinuous. We find that adding portfolio bounds can offer distinct economic insights and implications consistent with existing empirical findings. Theoretically, by introducing a new definition of viscosity solution, we show that a monotone, stable, and consistent finite difference scheme converges to the value functions of the nonconcave utility maximization problems. This paper was accepted by Agostino Capponi, finance.

An investigation of private public partnerships using real options analysis

<p>This thesis develops a model that investigates aspects of New Zealand’s largest public-private partnership project, the rollout of Ultra Fast Broadband. The model features four cities with different demand and construction-cost characteristics. It is used to study the different choices of the private party (Chorus) and the public party (Crown Fibre Holdings (CFH)). Using a real options approach, we identify two sorts of potential conflicts between the two parties: a timing conflict about the number of cities the two parties would like to develop in each period and a sequencing conflict about the order in which the UFB network is rolled out in different cities. Inspired by the incomplete contracting and information asymmetry literatures, we introduce several incentive schemes (including four subsidy schemes and two fine schemes) that help manage the possible conflicts. We compare both their ability to reduce the conflicts and their sensitivity to the model’s underlying parameters. Overall, there are four main findings. First, the magnitude of the conflict is a non-monotonic function of the inter-city demand differences and the inter-city construction-cost differences; it is an increasing function of the ratio of consumer surplus to producer surplus and of demand volatility. Second, a demand-dependent lump sum subsidy has the best performance among all included incentive schemes in controlling the possible conflicts. Third, the conflict level becomes quite sensitive to the subsidy scheme in two cases. A) When either the inter-city demand differences or the inter-city construction-cost differences turn out to be modest; B) When either the ratio of consumer surplus to producer surplus or demand volatility turns out to be large. The above result may provide some suggestions in managing the optimal subsidy. Last but not least, the requirement that Chorus is willing to participate in the partnership means that the fine schemes are generally outperformed by the subsidy schemes. Relating our findings to the undertaking UFB project, we provide CFH with several practical suggestions that may improve its management of possible conflicts.</p>

An investigation of private public partnerships using real options analysis

<p>This thesis develops a model that investigates aspects of New Zealand’s largest public-private partnership project, the rollout of Ultra Fast Broadband. The model features four cities with different demand and construction-cost characteristics. It is used to study the different choices of the private party (Chorus) and the public party (Crown Fibre Holdings (CFH)). Using a real options approach, we identify two sorts of potential conflicts between the two parties: a timing conflict about the number of cities the two parties would like to develop in each period and a sequencing conflict about the order in which the UFB network is rolled out in different cities. Inspired by the incomplete contracting and information asymmetry literatures, we introduce several incentive schemes (including four subsidy schemes and two fine schemes) that help manage the possible conflicts. We compare both their ability to reduce the conflicts and their sensitivity to the model’s underlying parameters. Overall, there are four main findings. First, the magnitude of the conflict is a non-monotonic function of the inter-city demand differences and the inter-city construction-cost differences; it is an increasing function of the ratio of consumer surplus to producer surplus and of demand volatility. Second, a demand-dependent lump sum subsidy has the best performance among all included incentive schemes in controlling the possible conflicts. Third, the conflict level becomes quite sensitive to the subsidy scheme in two cases. A) When either the inter-city demand differences or the inter-city construction-cost differences turn out to be modest; B) When either the ratio of consumer surplus to producer surplus or demand volatility turns out to be large. The above result may provide some suggestions in managing the optimal subsidy. Last but not least, the requirement that Chorus is willing to participate in the partnership means that the fine schemes are generally outperformed by the subsidy schemes. Relating our findings to the undertaking UFB project, we provide CFH with several practical suggestions that may improve its management of possible conflicts.</p>