Results 1  10
of
1,685
Term structures of credit spreads with incomplete accounting information
 ECONOMETRICA
, 2001
"... We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer’s assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of the firm ..."
Abstract

Cited by 307 (18 self)
 Add to MetaCart
We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuer’s assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of the firm are a geometric Brownian motion until informed equityholders optimally liquidate, we derive the conditional distribution of the assets, given accounting data and survivorship. Contrary to the perfectinformation case, there exists a defaultarrival intensity process. That intensity is calculated in terms of the conditional distribution of assets. Credit yield spreads are characterized in terms of accounting information. Generalizations are provided.
The Asymptotic Elasticity of Utility Functions and Optimal Investment in Incomplete Markets
 Annals of Applied Probability
, 1997
"... . The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theor ..."
Abstract

Cited by 258 (17 self)
 Add to MetaCart
(Show Context)
. The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less then one. 1. Introduction A basic problem of mathematical finance is the problem of an economic agent, who invests in a financial market so as to maximize the expected utility of his terminal wealth. In the framework of a continuoustime model the problem was studied for the first time by R. Merton in two seminal papers [27] and [28] (see also [29] as well as [32] for a treatment of the discrete time case). Using the methods of stochastic optimal control Merton derived a nonlinear partial differential equation (Bellman equation) for the value function of the optimization problem. He al...
Solving ForwardBackward Stochastic Differential Equations Explicitly – a Four Step Scheme
 Prob. Th. Rel. Fields
, 1994
"... Abstract. The problem of nding adapted solutions to systems of coupled linear forwardbackward stochastic di erential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability ..."
Abstract

Cited by 245 (17 self)
 Add to MetaCart
(Show Context)
Abstract. The problem of nding adapted solutions to systems of coupled linear forwardbackward stochastic di erential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and su cient condition for the solvability of the linear FBSDEs with the processes Z (serves as a correction, see x1) being absent in the drift. Then a Riccati type equation for matrixvalued (not necessarily square) functions is derived using the idea of the FourStepScheme (introduced in [11] for general FBSDEs). The solvability of such a Riccati type equation is studied which leads to a representation of adapted solutions to linear FBSDEs. Keywords. Linear forwardbackward stochastic di erential equations, adapted solution, Riccati type equation. AMS Mathematics subject classi cation. 60H10.
Meanfield backward stochastic differential equations and related patial differential equations
, 2007
"... In [5] the authors obtained MeanField backward stochastic differential equations (BSDE) associated with a Meanfield stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward SDEs, corresponding to a large number of “particles” (or “a ..."
Abstract

Cited by 195 (13 self)
 Add to MetaCart
(Show Context)
In [5] the authors obtained MeanField backward stochastic differential equations (BSDE) associated with a Meanfield stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward SDEs, corresponding to a large number of “particles” (or “agents”). The objective of the present paper is to deepen the investigation of such MeanField BSDEs by studying them in a more general framework, with general driver, and to discuss comparison results for them. In a second step we are interested in partial differential equations (PDE) whose solutions can be stochastically interpreted in terms of MeanField BSDEs. For this we study a MeanField BSDE in a Markovian framework, associated with a MeanField forward equation. By combining classical BSDE methods, in particular that of “backward semigroups” introduced by Peng [14], with specific arguments for MeanField BSDEs we prove that this MeanField BSDE describes the viscosity solution of a nonlocal PDE. The uniqueness of this viscosity solution is obtained for the space of continuous functions with polynomial growth. With the help of an example it is shown that for the nonlocal PDEs associated to MeanField BSDEs
HighOrder Collocation Methods for Differential Equations with Random Inputs
 SIAM Journal on Scientific Computing
"... Abstract. Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling met ..."
Abstract

Cited by 180 (9 self)
 Add to MetaCart
(Show Context)
Abstract. Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods. However, when the governing equations take complicated forms, numerical implementations of stochastic Galerkin methods can become nontrivial and care is needed to design robust and efficient solvers for the resulting equations. On the other hand, the traditional sampling methods, e.g., Monte Carlo methods, are straightforward to implement, but they do not offer convergence as fast as stochastic Galerkin methods. In this paper, a highorder stochastic collocation approach is proposed. Similar to stochastic Galerkin methods, the collocation methods take advantage of an assumption of smoothness of the solution in random space to achieve fast convergence. However, the numerical implementation of stochastic collocation is trivial, as it requires only repetitive runs of an existing deterministic solver, similar to Monte Carlo methods. The computational cost of the collocation methods depends on the choice of the collocation points, and we present several feasible constructions. One particular choice, based on sparse grids, depends weakly on the dimensionality of the random space and is more suitable for highly accurate computations of practical applications with large dimensional random inputs. Numerical examples are presented to demonstrate the accuracy and efficiency of the stochastic collocation methods. Key words. collocation methods, stochastic inputs, differential equations, uncertainty quantification
An equilibrium model with restricted stock market participation
 Review of Financial Studies
, 1998
"... This article solves the equilibrium problem in a pureexchange, continuoustime economy in which some agents face information costs or other types of frictions effectively preventing them from investing in the stock market. Under the assumption that the restricted agents have logarithmic utilities, ..."
Abstract

Cited by 156 (6 self)
 Add to MetaCart
This article solves the equilibrium problem in a pureexchange, continuoustime economy in which some agents face information costs or other types of frictions effectively preventing them from investing in the stock market. Under the assumption that the restricted agents have logarithmic utilities, a complete characterization of equilibrium prices and consumption/ investment policies is provided. A simple calibration shows that the model can help resolve some of the empirical asset pricing puzzles. It is well documented that even in welldeveloped capital markets, a large fraction of households does not participate in the stock market. For example, Mankiw and Zeldes (1991) report that 72.4 % of the households in a representative sample from the 1984 Panel Study of Income Dynamics held no stocks at all. 1 These households earned 62 % of the aggregate disposable income and accounted for 68 % of aggreWe thank Steve Shreve for several conversations on this topic and Kerry