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36
Default Risk, Asset Pricing, and Debt Control
 Journal of Financial Econometrics
, 2005
"... The pricing and control of firms ’ debt has become a major issue since Merton’s (1974) seminal paper. Yet, Merton as well as other recent theories presume that the asset value of the firm is independent of the debt of the firm. However, when using debt finance firms may have to pay a premium for an ..."
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Cited by 10 (9 self)
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The pricing and control of firms ’ debt has become a major issue since Merton’s (1974) seminal paper. Yet, Merton as well as other recent theories presume that the asset value of the firm is independent of the debt of the firm. However, when using debt finance firms may have to pay a premium for an idiosyncratic default risk and may face debt constraints. We demonstrate that firm specific debt constraints and endogenous risk premia, based on collateralized borrowing, affect the asset value of the firm and, in turn, the collateral value of the firm. In order to explore the interdependence of debt finance and asset pricing of firms we endogenize default premia and borrowing constraints in a production based asset pricing model. In this context then the dynamic decision problem of maximizing the present value of the firm faces an additional constraint giving rise to the debt dependent firm value. We solve for the asset value of the firm with debt finance by the use of numerical dynamic programming. This allows us to solve the debt control problem and to compute sustainable debt as well as firm’s debt value. We want to thank John Donaldson, Martin Lettau and Buz Brock for helpful suggestions and discussions. We also want to thank participants
2010): “Computing Equilibria in Dynamic Models with Occasionally Binding Constraints,” Working paper
"... We propose a method to compute equilibria in dynamic models with several continuous state variables and occasionally binding constraints. These constraints induce nondifferentiabilities in policy functions. We develop an interpolation technique that addresses this problem directly: It locates the n ..."
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Cited by 9 (4 self)
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We propose a method to compute equilibria in dynamic models with several continuous state variables and occasionally binding constraints. These constraints induce nondifferentiabilities in policy functions. We develop an interpolation technique that addresses this problem directly: It locates the nondifferentiabilities, and adds interpolation nodes there. To handle this flexible grid, it uses simplicial interpolation. Hence, we call this method Adaptive Simplicial Interpolation (ASI). We embed ASI into a time iteration algorithm to compute recursive equilibria in an infinite horizon endowment economy where heterogeneous agents trade in a bond and a stock subject to various trading constraints. We show that this method computes equilibria accurately and outperforms equidistant grid schemes by far.
Solving Asset Pricing Models with Stochastic Dynamic Programming
 BIELEFELD UNIVERSITY
, 2004
"... The study of asset price characteristics of stochastic growth models such as the riskfree interest rate, equity premium and the Sharpe ratio has been limited by the lack of global and accurate methods to solve dynamic optimization models. In this paper a stochastic version of a dynamic programming m ..."
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Cited by 7 (7 self)
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The study of asset price characteristics of stochastic growth models such as the riskfree interest rate, equity premium and the Sharpe ratio has been limited by the lack of global and accurate methods to solve dynamic optimization models. In this paper a stochastic version of a dynamic programming method with adaptive grid scheme is applied to compute the above mentioned asset price characteristics of a stochastic growth model. The stochastic growth model is of the type as developed by Brock and Mirman (1972) and Brock (1979, 1982). In order to test our method it is applied to a basic stochastic growth model for which the optimal consumption and asset prices can analytical be computed. Since, as shown, our method produces only negligible errors as compared to the analytical solution it is recommended to be used for more elaborate stochastic growth models with different preferences and technology shocks, adjustment costs, and heterogenous agents.
2012, `BoomBust Cycles: Leveraging, Complex Securities, and Asset Prices
 Journal of Economic Behavior & Organization
"... Recent history suggests that many boombust cycles are naturally driven by linkages between the credit market and asset prices. Additionally, new structured securities have been developed, e.g., MBS, CDOs, and CDS, which have acted as instruments of risk transfer. We show that there is a certain non ..."
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Cited by 6 (1 self)
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Recent history suggests that many boombust cycles are naturally driven by linkages between the credit market and asset prices. Additionally, new structured securities have been developed, e.g., MBS, CDOs, and CDS, which have acted as instruments of risk transfer. We show that there is a certain nonrobustness in the pricing of these instruments and we create a model in which their role in the recent nancial market meltdown, and in which the mechanism by which they exacerbate leverage cycles, is explicit. We rst discuss the extent to which complex securities can amplify boombust cycles. Then, we propose a model in which distinct nancial market boombust cycles emerge naturally. We demonstrate the interaction of leveraging and asset pricing in a dynamical model and spell out some implications for monetary policy.
Selecting concise sets of samples for a reinforcement learning agent
 In Proceedings of the Third International Conference on Computational Intelligence, Robotics and Autonomous Systems (CIRAS 2005
, 2005
"... We derive an algorithm for selecting from the set of samples gathered by a reinforcement learning agent interacting with a deterministic environment, a concise set from which the agent can extract a good policy. The reinforcement learning agent is assumed to extract policies from sets of samples by ..."
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Cited by 5 (3 self)
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We derive an algorithm for selecting from the set of samples gathered by a reinforcement learning agent interacting with a deterministic environment, a concise set from which the agent can extract a good policy. The reinforcement learning agent is assumed to extract policies from sets of samples by solving a sequence of standard supervised learning regression problems. To identify concise sets, we adopt a criterion based on an error function defined from the sequence of models produced by the supervised learning algorithm. We evaluate our approach on twodimensional maze problems and show its good performances when problems are continuous. 1
Monetary Policy with Nonlinear Phillips Curve and Endogenous NAIRU.” Center for Empirical Macroeconomics
, 2004
"... The recent literature on monetary policy has questioned the shape of the Phillips curve and the assumption of a constant NAIRU. In this paper we explore monetary policy considering nonlinear Phillips curves and an endogenous NAIRU which can be aected by the monetary policy. We rst study monetary pol ..."
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Cited by 4 (2 self)
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The recent literature on monetary policy has questioned the shape of the Phillips curve and the assumption of a constant NAIRU. In this paper we explore monetary policy considering nonlinear Phillips curves and an endogenous NAIRU which can be aected by the monetary policy. We rst study monetary policy with dierent shapes of the Phillips curve: Linear, convex and convexconcave. We nd that the optimal monetary policy changes with the shape of the Phillips curve, but there exists a unique equilibrium no matter whether the Phillips curve is linear or nonlinear. We also explore monetary policy with an endogenous NAIRU, since some researchers, Blanchard (2003) for example, have proposed that the NAIRU may be in
uenced by monetary policy. Based on some empirical evidence and assuming that monetary policy can in
uence the NAIRU, we nd that there may exist multiple equilibria in the economy, dierent from the results of models presuming a constant NAIRU.
Currency Crises Monetary Policy Rules.” Working paper 82
, 2005
"... This paper studies optimal monetary policy rules by the central bank confronted by foreign investors ' statedependent reactions and selfful lling expectations. We extend Taylor type monetary policy rules by allowing the central bank to give some weight to the level of precautionary foreign re ..."
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Cited by 4 (4 self)
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This paper studies optimal monetary policy rules by the central bank confronted by foreign investors ' statedependent reactions and selfful lling expectations. We extend Taylor type monetary policy rules by allowing the central bank to give some weight to the level of precautionary foreign reserve balances as one of its targets. We show that a currency crisis scenario can easily be created when the weight is zero, and it can be avoided when the weight is positive. The impacts of the central bank's monetary control on the output level, the in
ation rate, the exchange rate, and the foreign reserve level are investigated as well. In solving our model variants we apply both the Hamiltonian as well as the HamiltonJacobiBellman (HJB) equation, the latter leading to a dynamic programming formulation of the problem. The
exible use of both the Hamiltonian as well as dynamic programming allows us to explore safe domains of attractions in a variety of complicated model variants. Given the uncertainties the central banks face, we also show of how central banks can enlarge safe domains of attraction.
Firm Value, Diversified Capital Assets, and Credit Risk: Towards a Theory of Default Correlation
, 2007
"... Following the lead of Merton (1974), recent research has focused on the relationship of credit risk to firm value. Although this has usually been done for a single firm, the growth of structured finance, which necessarily involves the correlation between included securities, has spurred interest in ..."
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Cited by 4 (3 self)
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Following the lead of Merton (1974), recent research has focused on the relationship of credit risk to firm value. Although this has usually been done for a single firm, the growth of structured finance, which necessarily involves the correlation between included securities, has spurred interest in the connection between creditdefault risk and the dependencies and crosscorrelations arising in families of firms. Previous work by Grüne and Semmler (2005), focusing on a single firm, has shown that firmvalue models, incorporating companyspecific endogenous risk premia, imply that exposure to risk does impact asset value. In this paper, we extend these results to study the effects of random shocks to diversified capital assets wherein the shocks are correlated to varying degrees. Thus, we construct a framework within which the effects of correlated shocks to capital assets can be related to the probability of default for the company. The dynamic decision problem of maximizing the present value of a firm faced with stochastic shocks is solved using numerical techniques. Further, the impact of varying dependency structures on the overall default rate is also explored.
Skiba points for small discount rates
 Journal of Optimization Theory and Applications
, 2006
"... The present article uses perturbation techniques to approximate the value function of a economic minimisation problem for small values of the discount rate. This can be used to obtain the approximate location of Skiba states (or indifference thresholds) in the problem; these are states for which the ..."
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Cited by 3 (0 self)
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The present article uses perturbation techniques to approximate the value function of a economic minimisation problem for small values of the discount rate. This can be used to obtain the approximate location of Skiba states (or indifference thresholds) in the problem; these are states for which there are two distinct optimal state trajectories, converging to different optimal steady states. It is shown that the sets of indifference thresholds are locally smooth manifolds. For a simple example, all relevant quantities are computed explicitely. Moreover, the approximation can be used to obtain parameterdependent approximations to indifference manifolds.
The Premium of Marine Protected Areas: A Simple Valuation Model
"... Abstract The article addresses the induced cost, the premium, from establishing a marine protected area in a deterministic model of a fishery. Outside the protected area, the fishery is managed optimally through total allowable catch quotas. The premium is found to be increasing and convex along th ..."
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Cited by 3 (3 self)
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Abstract The article addresses the induced cost, the premium, from establishing a marine protected area in a deterministic model of a fishery. Outside the protected area, the fishery is managed optimally through total allowable catch quotas. The premium is found to be increasing and convex along the protection parameter. Biological measures are introduced to increase the understanding of the mechanisms in the bioeconomic system. Timeseries solutions show that the net return per unit of fish increases after the protected area is established. Key words Bioeconomics, dynamic programming, fisheries management, marine protected areas, migration, modeling, optimization, renewable resources. JEL Classification Codes C61, Q22, Q57.