In the modern theory of finance, the valuation of derivative assets is commonly based on a replication argument. When there are transaction costs, this argument is no longer valid. In this paper, we try to address the general problem of finding the optimal portfolio among those which dominate a given derivative asset at maturity. We derive an interval for its price. the upper bound is the minimum amount one has to invest initially in order to obtain proceeds at least as valuable as the derivative asset. the lower bound is the maximum amount one can borrow initially against the proceeds of the derivative asset. We show that, in some instances, this interval may be strictly bounded above by the price of the replicating strategy. Prima facie, the cost of a dominating strategy should appear to be higher than that of the replicating one. But because trading is costly, it may pay to weigh the benefits of replication against those of potential savings on transaction costs. Copyright 1992 Blackwell Publishers.

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We provide sufficient conditions for the existence of a solution to a consumption and portfolio problem in continuous time under uncertainty with an infinite horizon. \N'hen the price processes for securities are diffusion processes, optimal policies can be computed by solving a linear partial differential equation. We also provide conditions under which the solution to an infinite horizon problem is the limit of the solutions to finite horizon problems when the horizon increases to infinity.'The authors would like to thank conversations with Robert Merton.

am indebted to Bruno Biais for pointing out a flaw in an early version and to Denis Gromb and Jean-Charles Rochet for their invaluable guidance and support. I would like to thank two anonymous referees, Hendrik Hakenes, Christian Hellwig and George Pennacchi for insightful comments and suggestions, Monique Jeanblanc and Dylan Possamaï for their help with the mathematics and simulations, as well as discussants and participants in many seminars and conferences over the last three years. All errors are mine. The usual disclaimer applies.

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In this paper, we take up the analysis of a principal/agent model with moral hazard introduced in [17], with optimal contracting between competitive investors and an impatient bank monitoring a pool of long-term loans subject to Markovian contagion. We provide here a comprehensive mathematical formulation of the model and show using martingale arguments in the spirit of Sannikov [18] how the maximization problem with implicit constraints faced by investors can be reduced to a classical stochastic control problem. The approach has the advantage of avoiding the more general techniques based on forward-backward stochastic differential equations described in [6] and leads to a simple recursive system of Hamilton-Jacobi-Bellman equations. We provide a solution to our problem by a verification argument and give an explicit description of both the value function and the optimal contract. Finally, we study the limit case where the bank is no longer impatient.

am indebted to Bruno Biais for pointing out a flaw in an early version and to Denis Gromb and Jean-Charles Rochet for their invaluable guidance and support. I would like to thank two anonymous referees, Hendrik Hakenes, Christian Hellwig and George Pennacchi for insightful comments and suggestions, Monique Jeanblanc and Dylan Possamaï for their help with the mathematics and simulations, as well as discussants and participants in many seminars and conferences over the last three years. All errors are mine. The usual disclaimer applies.

The paper applies a reduced-form model to uncover from secondary market's Brady bond prices, together with Libor interest rates, how the risk of sovereign default is perceived to depend upon time. The methodology is implemented on a particular issue, a discount bond issued by Brazil and maturing in April 2024. It is shown that subsuming liquidity risk in default risk may result in a misspecified model that, while generating the desired negative correlation between credit spreads and default-free interest rates, also generates negative probabilities of default at long horizons. BIS WorkingPapers are written by members of the Monetary and Economic Department of the Bank for International Settlements, and from time to time by other economists, and are published by the Bank. The papers are on subjects of topical interest and are technical in character. The views expressed in them are those of their authors and not necessarily the views of the BIS.