Multi-dimensional Virtual Values and Second-degree Price Discrimination

We consider a multi-dimensional screening problem of selling a product with multiple quality levels and design virtual value functions to derive conditions that imply optimality of only selling highest quality. A challenge of designing virtual values for multi-dimensional agents is that a mechanism that pointwise optimizes virtual values resulting from a general application of integration by parts is not incentive compatible, and no general methodology is known for selecting the right paths for integration by parts. We resolve this issue by first uniquely solving for paths that satisfy certain necessary conditions that the pointwise optimality of the mechanism imposes on virtual values, and then identifying distributions that ensure the resulting virtual surplus is indeed pointwise optimized by the mechanism. Our method of solving for virtual values is general, and as a second application we use it to derive conditions of optimality for selling only the grand bundle of items to an agent with additive preferences

Content-Specific Broadcast Cellular Networks based on User Demand Prediction: A Revenue Perspective

The Long Term Evolution (LTE) broadcast is a promising solution to cope with exponentially increasing user traffic by broadcasting common user requests over the same frequency channels. In this paper, we propose a novel network framework provisioning broadcast and unicast services simultaneously. For each serving file to users, a cellular base station determines either to broadcast or unicast the file based on user demand prediction examining the file's content specific characteristics such as: file size, delay tolerance, price sensitivity. In a network operator's revenue maximization perspective while not inflicting any user payoff degradation, we jointly optimize resource allocation, pricing, and file scheduling. In accordance with the state of the art LTE specifications, the proposed network demonstrates up to 32% increase in revenue for a single cell and more than a 7-fold increase for a 7 cell coordinated LTE broadcast network, compared to the conventional unicast cellular networks.Comment: 6 pages; This paper will appear in the Proc. of IEEE WCNC 201

Asset pricing implications of Pareto optimality with private information

In this paper, we consider a dynamic economy in which the agents in the economy are privately informed about their skills, which evolve stochastically over time in an arbitrary fashion. We consider an asset pricing equilibrium in which equilibrium quantities are constrained Pareto optimal. Under the assumption that agents have constant relative risk aversion, we derive a novel asset pricing kernel for financial asset returns. The kernel equals the reciprocal of the gross growth of the γth moment of the consumption distribution, where – is the coefficient of relative risk aversion. We use data from the consumer expenditure survey (CEX) and show that the new stochastic discount factor performs better than existing stochastic discount factors at rationalizing the equity premium. However, its ability to simultaneously explain the equity premium and the expected return to the Treasury bill is about the same as existing discount factors. --

Joint Optimal Pricing and Electrical Efficiency Enforcement for Rational Agents in Micro Grids

In electrical distribution grids, the constantly increasing number of power generation devices based on renewables demands a transition from a centralized to a distributed generation paradigm. In fact, power injection from Distributed Energy Resources (DERs) can be selectively controlled to achieve other objectives beyond supporting loads, such as the minimization of the power losses along the distribution lines and the subsequent increase of the grid hosting capacity. However, these technical achievements are only possible if alongside electrical optimization schemes, a suitable market model is set up to promote cooperation from the end users. In contrast with the existing literature, where energy trading and electrical optimization of the grid are often treated separately or the trading strategy is tailored to a specific electrical optimization objective, in this work we consider their joint optimization. Specifically, we present a multi-objective optimization problem accounting for energy trading, where: 1) DERs try to maximize their profit, resulting from selling their surplus energy, 2) the loads try to minimize their expense, and 3) the main power supplier aims at maximizing the electrical grid efficiency through a suitable discount policy. This optimization problem is proved to be non convex, and an equivalent convex formulation is derived. Centralized solutions are discussed first, and are subsequently distributed. Numerical results to demonstrate the effectiveness of the so obtained optimal policies are then presented

Optimal funding and investment strategies in defined contribution pension plans under Epstein-Zin utility

A defined contribution pension plan allows consumption to be redistributed from the plan member’s working life to retirement in a manner that is consistent with the member’s personal preferences. The plan’s optimal funding and investment strategies therefore depend on the desired pattern of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member has an Epstein-Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution, and we also take into account the member’s human capital. We show that a stochastic lifestyling approach, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches is an optimal investment strategy. In addition, the optimal contribution rate each year is not constant over the life of the plan but reflects trade-offs between the desire for current consumption, bequest and retirement savings motives at different stages in the life cycle, changes in human capital over the life cycle, and attitude to risk