Stability of Radner Equilibria with respect to small frictions

We study risk-sharing equilibria with trading subject to small proportional transaction costs. We show that the frictionless equilibrium prices also form an "asymptotic equilibrium" in the small-cost limit. To wit, there exist asymptotically optimal policies for all agents and a split of the trading cost according to their risk aversions for which the frictionless equilibrium prices still clear the market. Starting from a frictionless equilibrium, this allows to study the interplay of volatility, liquidity, and trading volume

A General Equilibrium Financial Asset Economy with Transaction Costs and Trading Constraints

This paper presents a unified framework for examining the general equilibrium effects of transactions costs and trading constraints on security market trades and prices. The model uses a discrete time/state framework and Kuhn-Tucker theory to characterize the optimal decisions of consumers and financial intermediaries. Transaction costs and constraints give rise to regions of no trade and to bid-ask spreads: their existence frustrate the derivation of standard results in arbitrage-based pricing. Nevertheless, we are able to obtain as dual characterizations of our primal problems, one-sided arbitrage pricing results and a personalized martingale representation of asset pricing. These pricing results are identical to those derived by Jouini and Kallal (1995) using arbitrage arguments. The paper's framework incorporates a number of specialized existing models and results, proves new results and discusses new directions for research. In particular, we include characterizations of intermediaries who hold optimal portfolios; brokers who do not hold portfolios, and consumer-specific transactions costs and trading constraints. Furthermore we show that in the special case of equiproportional transaction costs and a sufficient number of assets, there is an analogue of the arbitrage pricing result for European derivatives where prices are interpreted as mid-prices between the bid-ask spread. We discuss the effects of non-convex transaction technologies on prices and trades.Financial Markets, Transaction Costs, Trading Constraints, Asset Pricing, General Equilibrium, Incomplete Markets

Cross-border congestion management in the electricity market

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Equilibrium models for the carbon leakage problem

Carbon leakage in this pape ris the phenomenon whereby Electricity Intensive Industries subject to harsh environmental standards move their activity or part of it to more environmentally lenient regions. Carbon leakage has been mentioned as a possible outcome of the EU Emission Trading Scheme. Different studies are underway to assess the reality of the phenomenon and to devise policies to mitigate its possible impact. One remedy, proposed by the Energy Intensive Industries is to combine free emission allowances with a pricing of electricity whereby energy emissions and transmission costs are bundled and sold on an average cost basis. The paper attempts to model this proposal. We cast the problem in a spatial model of the power sector where generators can develop new capacities, the transmission system is organized on a flowgate basis, emission allowances are auctioned, except possibly for industries, and traded. The consumer market is decomposed in two segments. Industries purchase electricity according to some form of average cost price, the rest of the market is supplied at marginal cost. These equilibrium models are non convex. We present the models and discuss their properties. Companion papers report policy implications.carbon leakage, emission trading scheme, electricity, energy policies, equilibrum, complementarity.

Illiquid Assets and Optimal Portfolio Choice

The presence of illiquid assets, such as human wealth or a family owned business, complicates the problem of portfolio choice. This paper is concerned with the problem of optimal asset allocation and consumption in a continuous time model when one asset cannot be traded. This illiquid asset, which depends on an uninsurable source of risk, provides a liquid dividend. In the case of human capital we can think about this dividend as labor income. The agent is endowed with a given amount of the illiquid asset and with some liquid wealth which can be allocated in a market where there is a risky and a riskless asset. The main point of the paper is that the optimal allocations to the two liquid assets and consumption will critically depend on the endowment and characteristics of the illiquid asset, in addition to the preferences and to the liquid holdings held by the agent. We provide what we believe to be the first analytical solution to this problem when the agent has power utility of consumption and terminal wealth. We also derive the value that the agent assigns to the illiquid asset. The risk adjusted valuation procedure we develop can be used to value both liquid and illiquid assets, as well as contingent claims on those assets.

Portfolio optimization in arbitrary dimensions in the presence of small bid-ask spreads

This thesis deals with the problem of maximizing the expected utility of terminal wealth in financial markets with an arbitrary number of risky assets in the presence of small bid-ask spreads. The goal is to determine an asymptotically optimal trading strategy and to quantify the asymptotic welfare impact of small proportional fees levied on investor's transactions. The approach taken in this study relies on the concept of a shadow price transforming the problem of portfolio optimization with proportional costs into a frictionless one. With the help of the shadow price, an asymptotically optimal trading strategy is shown to be a solution to a reflecting stochastic differential equation. The (stochastic) reflecting boundary is characterized as solution to a free-boundary problem. The boundary constrains the motion of the trading strategy to a domain known as the no-trade region. Instead of attempting to find exact solutions, we propose several simple domains as candidates for the no-trade region. Trading strategy to each of the domains is defined as solution to a stochastic Skorohod problem. By adapting the notion of the shadow price, we establish a duality relation between trading strategies and martingale measures for shadow-price processes. This allows us to derive an upper bound on the expected utility generated by each candidate strategy, which provides an estimate of the expected utility of the exact asymptotic optimizer. Expected utility of each trading strategy together with the associated upper bound are evaluated by means of numerical simulations. The simulations are run on the Black-Scholes model for portfolios of up to 30 risky assets

Dynamic portfolio optimization with transaction costs and state-dependent drift

The problem of dynamic portfolio choice with transaction costs is often addressed by constructing a Markov Chain approximation of the continuous time price processes. Using this approximation, we present an efficient numerical method to determine optimal portfolio strategies under time- and state-dependent drift and proportional transaction costs. This scenario arises when investors have behavioral biases or the actual drift is unknown and needs to be estimated. Our numerical method solves dynamic optimal portfolio problems with an exponential utility function for time-horizons of up to 40 years. It is applied to measure the value of information and the loss from transaction costs using the indifference principle