# Abstracts

**Explicit formula for the optimal government debt ceiling**

*Abel Cadenillas (University of Alberta, Canada)*

Wednesday June 4, 14:30-15:00 | session 5.9 | Economics | room H

Motivated by the current debt crisis in the world, we consider a government that wants to control its debt ratio. The debt generates a cost for the country.The government can reduce its debt ratio, but there is a cost associated with this reduction. We obtain a solution for the government debt problem. In particular, we obtain an explicit formula for the optimal debt ceiling.

**Asset pricing with arbitrage activity**

*Julien Hugonnier (EPFL, Switzerland)*

Wednesday June 4, 15:00-15:30 | session 5.9 | Economics | room H

We study an economy populated by three groups of logarithmic agents: Constrained agents subject to a portfolio constraint that limits their risk-taking, unconstrained agents subject to a standard nonnegative wealth constraint, and arbitrageurs with access to uncollateralized credit. Such credit is valuable as it allows arbitrageurs to exploit the limited arbitrage opportunities that emerge endogenously in reaction to the portfolio imbalance generated by constrained agents. The model is solved in closed-form and we show that, in contrast to most equilibrium models with frictions and logarithmic agents, arbitrage activity has an impact on the price level and generates both excess volatility and the leverage effect. We show that these results are due to the fact that arbitrageurs lever up in good times and delever in bad times, and also investigate the effects of an unexpected tightening of the funding liquidity conditions of arbitrageurs.

**Equilibrium with imbalance of the derivative market**

*Yavor Stoev (London School of Economics, UK)*

Wednesday June 4, 15:30-16:00 | session 5.9 | Economics | room H

This presentation investigates the impact of imbalanced derivative markets - markets in which not all agents hedge - on the underlying stock market. The availability of a closed-form representation for the equilibrium stock price in the context of a complete (imbalanced) market with terminal consumption allows us to study how this equilibrium outcome is affected by the risk aversion of agents and the degree of imbalance. In particular, it will be shown that the derivatives imbalance leads to significant changes in the equilibrium stock price process: volatility changes from constant to local, while risk premia decrease and become stochastic processes. Moreover the model produces implied volatility skew consistent with empirical observations.