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35
Overconfidence and speculative bubbles
 Journal of Political Economy
, 2003
"... Motivated by the behavior of asset prices, trading volume and price volatility during historical episodes of asset price bubbles, we present a continuous time equilibrium model where overconfidence generates disagreements among agents regarding asset fundamentals. With shortsale constraints, an ass ..."
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Cited by 282 (18 self)
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Motivated by the behavior of asset prices, trading volume and price volatility during historical episodes of asset price bubbles, we present a continuous time equilibrium model where overconfidence generates disagreements among agents regarding asset fundamentals. With shortsale constraints, an asset owner has an option to sell the asset to other overconfident agents when they have more optimistic beliefs. As in Harrison and Kreps (1978), this resale option has a recursive structure, that is, a buyer of the asset gets the option to resell it. Agents pay prices that exceed their own valuation of future dividends because they believe that in the future they will find a buyer willing to pay even more. This causes a significant bubble component in asset prices even when small differences of beliefs are sufficient to generate a trade. In equilibrium, large bubbles are accompanied by large trading volume and high price volatility. Our model has an explicit solution, which allows for several comparative statics exercises. Our analysis shows that while Tobin’s tax can substantially reduce speculative trading when transaction costs are small, it has only a limited impact on the size of the bubble or on price volatility. We also give an example where the price of a subsidiary is larger than its parent firm. This paper was previously circulated under the title “Overconfidence, ShortSale Constraints and Bubbles.”
Optimal Control under a Dynamic Fuel Constraint
 SIAM Journal on Control and Optimization
, 2005
"... We present a new approach to solve optimal control problems of the monotone follower type. The key feature of our approach is that it allows to include an arbitrary dynamic fuel constraint. Instead of dynamic programming, we use the convexity of our cost functional to derive a first order characteri ..."
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Cited by 22 (0 self)
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We present a new approach to solve optimal control problems of the monotone follower type. The key feature of our approach is that it allows to include an arbitrary dynamic fuel constraint. Instead of dynamic programming, we use the convexity of our cost functional to derive a first order characterization of optimal policies based on the Snell envelope of the objective functional’s gradient at the optimum. The optimal control policy is constructed explicitly in terms of the solution to a representation theorem for stochastic processes obtained in Bank and El Karoui (2004). As an illustration, we show how our methodology allows to extend the scope of the explicit solutions obtained for the classical monotone follower problem and for an irreversible investment problem arising in economics.
Overconfidence, ShortSale Constraints, and Bubbles
 JOURNAL OF POLITICAL ECONOMY
, 2001
"... Motivated by the behavior of internet stock prices in 19982000, we present a continuous time equilibrium model of bubbles where overconfidence generates agreements to disagree among agents about asset fundamentals. With a shortsale constraint, an asset owner has an option to sell the asset to othe ..."
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Cited by 13 (0 self)
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Motivated by the behavior of internet stock prices in 19982000, we present a continuous time equilibrium model of bubbles where overconfidence generates agreements to disagree among agents about asset fundamentals. With a shortsale constraint, an asset owner has an option to sell the asset to other agents when they have more optimistic beliefs. This resale option has a recursive structure, that is a buyer of the asset gets the option to resell it, causing a significant bubble component in asset prices even when small differences of beliefs are sufficient to generate a trade. The model generates prices that are above fundamentals, excessive trading, and excess volatility. We also give an example where the price of a subsidiary is larger than its parent firm. Our analysis shows that while Tobin's tax can substantially reduce speculative trading when transaction costs are small, it has only a limited impact on the size of the bubble or on price volatility.
Connections between singular control and optimal switching
 SIAM J. on Control and Optimization
, 2008
"... Abstract. This paper builds a new theoretical connection between singular control of finite variation and optimal switching problems. This correspondence provides a novel method for solving highdimensional singular control problems and enables us to extend the theory of reversible investment: Suffi ..."
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Cited by 13 (4 self)
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Abstract. This paper builds a new theoretical connection between singular control of finite variation and optimal switching problems. This correspondence provides a novel method for solving highdimensional singular control problems and enables us to extend the theory of reversible investment: Sufficient conditions are derived for the existence of optimal controls and for the regularity of value functions. Consequently, our regularity result links singular controls and Dynkin games through sequential optimal stopping problems.
VALUATION OF INVESTMENTS IN REAL ASSETS WITH IMPLICATIONS FOR THE STOCK PRICES ∗
"... Abstract. A general model for the valuation of natural resource investments is formulated and analyzed within a stochastic control theoretic framework. Using dynamic programming, the value of such an investment with a general payoff function is determined under the assumption that the commodity pric ..."
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Cited by 11 (0 self)
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Abstract. A general model for the valuation of natural resource investments is formulated and analyzed within a stochastic control theoretic framework. Using dynamic programming, the value of such an investment with a general payoff function is determined under the assumption that the commodity price process is given by a stochastic differential equation. The analysis results in closed form analytic solutions which can easily be computed and exhibits qualitatively different optimal behaviors, depending on parameter values. Implications for stocks and options are also considered.
On an Integral Equation for the FreeBoundary of Stochastic
 Irreversible Investment Problems, arXiv:1211.0412. Fothcoming on
"... Abstract. In this paper we derive a new handy integral equation for the freeboundary of infinite time horizon, continuous time, stochastic, irreversible investment problems with uncertainty modeled as a onedimensional, regular diffusion X. The new integral equation allows to explicitly find the ..."
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Cited by 9 (6 self)
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Abstract. In this paper we derive a new handy integral equation for the freeboundary of infinite time horizon, continuous time, stochastic, irreversible investment problems with uncertainty modeled as a onedimensional, regular diffusion X. The new integral equation allows to explicitly find the freeboundary b(·) in some so far unsolved cases, as when the operating profit function is not multiplicatively separable and X is a threedimensional Bessel process or a CEV process. Our result follows from purely probabilistic arguments. Indeed, we first show that b(X(t)) = l∗(t), with l ∗ the unique optional solution of a representation problem in the spirit of BankEl Karoui [5]; then, thanks to such identification and the fact that l ∗ uniquely solves a backward stochastic equation, we find the integral problem for the freeboundary. Key words: integral equation, freeboundary, irreversible investment, singular stochastic
Optimal environmental management in the presence of irreversibilities
 Journal of Economic Theory
, 2001
"... We consider an environment of a fixed size that can be converted to another use. This conversion can be made in steps, but it is irreversible. The future benefits (per unit) from the original use, and from the alternative use, follow a diffusion process. For a fairly general case, we show that the v ..."
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Cited by 9 (2 self)
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We consider an environment of a fixed size that can be converted to another use. This conversion can be made in steps, but it is irreversible. The future benefits (per unit) from the original use, and from the alternative use, follow a diffusion process. For a fairly general case, we show that the value function must be the unique (viscosity) solution to the associated HamiltonJacobiBellman equation. We also exhibit several properties of the solution for the case of constant relative risk aversion between 0 and 1, and a loglinear diffusion for the benefits. Journal of
2010a, “Optimal taxation in the presence of bailouts
 Journal of Monetary Economics
"... The termination of a representative financial firm due to excessive leverage may lead to substantial bankruptcy costs. A government in the tradition of Ramsey (1927) may be inclined to provide transfers to the firm so as to prevent its liquidation and the associated deadweight costs. It is shown tha ..."
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Cited by 6 (1 self)
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The termination of a representative financial firm due to excessive leverage may lead to substantial bankruptcy costs. A government in the tradition of Ramsey (1927) may be inclined to provide transfers to the firm so as to prevent its liquidation and the associated deadweight costs. It is shown that the optimal taxation policy to finance such transfers exhibits countercyclicality and history dependence, even in a complete market. These results are in contrast with preexisting literature on optimal fiscal policy, and are driven by the endogeneity of the transfer payments that are required to salvage the financial firm.
Irreversible Investment under Interest Rate Variability: Some Generalizations
 SPEC JVM98 Benchmarks
, 2003
"... The current literature on irreversible investment decisions usually makes the assumption of constant interest rate. We study the impact of interest rate and revenue variability on the decision to carry out an irreversible investment project. Given the generality of the considered valuation problem, ..."
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Cited by 5 (2 self)
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The current literature on irreversible investment decisions usually makes the assumption of constant interest rate. We study the impact of interest rate and revenue variability on the decision to carry out an irreversible investment project. Given the generality of the considered valuation problem, we first provide a thorough mathematical characterization of the twodimensional optimal stopping problem and develop some new results. We establish that interest rate variability has a profound decelerating or accelerating impact on investment demand depending on whether the current interest rate is below or above the long run steady state interest rate and that its quantitative size may be very large. Allowing for interest rate uncertainty is shown to decelerate rational investment demand by raising both the required exercise premium of the irreversible investment opportunity and the value of waiting. Finally, we demonstrate that increased revenue volatility strengthens the negative impact of interest rate uncertainty and vice versa.
A Stochastic Reversible Investment Problem on a FiniteTime Horizon: FreeBoundary Analysis, ArXiv: 1303.6189
, 2013
"... Abstract. We study a continuoustime, finite horizon optimal stochastic reversible investment problem for a firm producing a single good. The production capacity is modeled as a onedimensional, timehomogeneous, linear diffusion controlled by a bounded variation process which represents the cumula ..."
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Cited by 5 (3 self)
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Abstract. We study a continuoustime, finite horizon optimal stochastic reversible investment problem for a firm producing a single good. The production capacity is modeled as a onedimensional, timehomogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investmentdisinvestment strategy. We associate to the investmentdisinvestment problem a zerosum optimal stopping game and characterize its value function through a freeboundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solve a system of nonlinear integral equations of Volterra type. The optimal investmentdisinvestment strategy is then shown to be a diffusion reflected at the two boundaries. Key words: reversible investment; singular stochastic control; zerosum optimal stopping games; freeboundary problems; Skorokhod reflection problem. MSC2010 subsject classification: 93E20, 60G40, 35R35, 91A15, 91B70. JEL classification: C02, C73, E22, D92.