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AN EQUILIBRIUM CHARACTERIZATION OF THE TERM STRUCTURE
, 1977
"... The paper derives a general form of the term structure of interest rates. The following assumptions are made: (A.l) The instantaneous (spot) interest rate follows a diffusion process; (A.2) the price of a discount bond depends only on the spot rate over its term; and (A.3) the market is efficient. U ..."
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Cited by 1004 (0 self)
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The paper derives a general form of the term structure of interest rates. The following assumptions are made: (A.l) The instantaneous (spot) interest rate follows a diffusion process; (A.2) the price of a discount bond depends only on the spot rate over its term; and (A.3) the market is efficient. Under these assumptions, it is shown by means of an arbitrage argument that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation. This property is then used to derive a partial differential equation for bond prices. The solution to that equation is given in the form of a stochastic integral representation. An interpretation of the bond pricing formula is provided. The model is illustrated on a specific case.
Exponential Stability of Stochastic Differential Delay Equations
, 1994
"... : In this paper we study both pth moment and almost sure exponential stability of the stochastic differential delay equation dx(t)=f(t;x(t);x(t\Gammaø))dt+g(t;x(t);x(t\Gammaø))dw(t). Introduce the corresponding stochastic differential equation (without delay) dx(t)=f(t;x(t);x(t))dt+ g(t;x(t);x(t))dw ..."
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Cited by 112 (46 self)
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: In this paper we study both pth moment and almost sure exponential stability of the stochastic differential delay equation dx(t)=f(t;x(t);x(t\Gammaø))dt+g(t;x(t);x(t\Gammaø))dw(t). Introduce the corresponding stochastic differential equation (without delay) dx(t)=f(t;x(t);x(t))dt+ g(t;x(t);x(t))dw(t) and assume it is exponentially stable which is guaranteed by the existence of the Lyapunov function. We shall show that the original stochastic differential delay equation remains exponentially stable provided the time lag ø is sufficiently small, and a bound for such ø is obtained. Key Words: stochastic differential delay equations, Lyapunov function, Lyapunov exponent, BorelCantelli lemma. AMS 1991 Classifications: 60H10, 34K30 1. Introduction In many branches of science and industry stochastic differential delay equations have been used to model the evolution phenomena because the measurements of timeinvolving variables and their dynamics usually contain some delays (cf. Kolmanov...
Stochastic differential systems with memory. theory, examples and applications
 Stochastic Analysis and Related Topics VI. The Geilo Workshop, 1996., Progress in Probability. Birkhauser
, 1998
"... This Article is brought to you for free and open access by the Department of Mathematics at OpenSIUC. It has been accepted for inclusion in Miscellaneous (presentations, translations, interviews, etc) by an authorized administrator of OpenSIUC. For more information, please contact ..."
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Cited by 42 (11 self)
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This Article is brought to you for free and open access by the Department of Mathematics at OpenSIUC. It has been accepted for inclusion in Miscellaneous (presentations, translations, interviews, etc) by an authorized administrator of OpenSIUC. For more information, please contact
Inflation, asset prices and the term structure of interest rates in monetary economies
 Review of Financial Studies 9
, 1996
"... This article offers a tractable monetary asset pricing model. In monetary economies, the price level, inflation, asset prices, and the real and nominal interest rates have to be determined simultaneously and in relation to each other. This link allows us to relate in closed form each of the dependen ..."
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Cited by 34 (2 self)
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This article offers a tractable monetary asset pricing model. In monetary economies, the price level, inflation, asset prices, and the real and nominal interest rates have to be determined simultaneously and in relation to each other. This link allows us to relate in closed form each of the dependent entities to the underlying real and monetary variables. Among other features of such economies, inflation can be partially nonmonetary and the real and nominal term structures can depend on fundamentally different risk factors. In one extreme, the process followed by the real term structure is independent of that followed by its nominal counterpart. This article studies the endogenous and simultaneous determination of the price level, inflation, asset prices, and the term structure of interest rates, both real and nominal. The setup is an intertemporal monetary economy where there is fiat money for transaction purposes and where investors find it useful to hold cash balances. The objective is to relate, in the spirit of Cox, Ingersoll, and Ross (1985b) (henceforth, The authors would like to thank Franklin Allen (the editor) and the anonymous referee for helpful comments and suggestions. Any remaining errors
A stochastic particle method for the McKeanVlasov and the Burgers equation
 Math. Comp
, 1997
"... Abstract. In this paper we introduce and analyze a stochastic particle method for the McKeanVlasov and the Burgers equation; the construction and error analysis are based upon the theory of the propagation of chaos for interacting particle systems. Our objective is threefold. First, we consider a ..."
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Cited by 30 (4 self)
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Abstract. In this paper we introduce and analyze a stochastic particle method for the McKeanVlasov and the Burgers equation; the construction and error analysis are based upon the theory of the propagation of chaos for interacting particle systems. Our objective is threefold. First, we consider a McKeanVlasov equation in [0,T]×R with sufficiently smooth kernels, and the PDEs giving the distribution function and the density of the measure µt, the solution to the McKeanVlasov equation. The simulation of the stochastic system with N particles provides a discrete measure which approximates µk∆t for each time k∆t (where ∆t is a discretization step of the time interval [0,T]). An integration (resp. smoothing) of this discrete measure provides approximations of the distribution function (resp. density) of µk∆t. We show that the convergence rate is O 1 / √ N + √) ∆t for the approximation in L1 (Ω × R) ofthecumulative distribution function at time T, and of order O ε2 + 1
An Evaluation of MultiFactor CIR Models Using LIBOR, Swap Rates, and Cap and Swaption Prices
, 2001
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Statistical Aspects of the fractional stochastic calculus
 ANN. STAT
, 2007
"... We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equati ..."
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Cited by 23 (6 self)
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We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by fractional Brownian motion with any level of Holderregularity (any Hurst parameter). We prove existence and strong consistency of the MLE for linear and nonlinear equations. We also prove that a version of the MLE using only discrete observations is still a strongly consistent estimator.
Invariant Sets for Controlled Degenerate Diffusions: a Viscosity Solutions Approach
 in Stochastic analysis, control, optimization and applications, 191–208, Birkhäuser
, 1999
"... : We study invariance and viability properties of a closed set for the trajectories of either a controlled diffusion process or a controlled deterministic system with disturbances. We use the value functions associated to suitable optimal control problems or differential games and analyze the relate ..."
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Cited by 21 (3 self)
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: We study invariance and viability properties of a closed set for the trajectories of either a controlled diffusion process or a controlled deterministic system with disturbances. We use the value functions associated to suitable optimal control problems or differential games and analyze the related Dynamic Programming equation within the theory of viscosity solutions. KEYWORDS: degenerate diffusion; invariance; viability; stochastic control; differential games; viscosity solutions; HamiltonJacobiBellman equations; nonsmooth analysis. 1 Introduction Consider the controlled Ito stochastic differential equation in IR N (SDE) ae dX t = oe ff t (X t )dB t + f ff t (X t )dt; t ? 0; X 0 = x: (1.1) where B t is an Mdimensional Brownian motion and ff t is the control taking values in a given set A. A set K is invariant for (SDE) if for all initial points x 2 K and all admissible controls ff, the trajectory X t of (SDE) remains in K for all t ? 0 almost surely. One of the main re...
Weighted Stochastic Sobolev Spaces and Bilinear SPDE's Driven by Spacetime White Noise
"... In this paper we develop basic elements of Malliavin calculus on a weighted L 2(\Omega\Gamma2 This class of generalized Wiener functionals is a Hilbert space. It turns out to be substantially smaller than the space of Hida distributions while large enough to accommodate solutions of bilinear stoch ..."
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Cited by 20 (5 self)
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In this paper we develop basic elements of Malliavin calculus on a weighted L 2(\Omega\Gamma2 This class of generalized Wiener functionals is a Hilbert space. It turns out to be substantially smaller than the space of Hida distributions while large enough to accommodate solutions of bilinear stochastic PDE's. As an example, we consider a stochastic advectiondiffusion equation driven by spacetime white noise in IR d . It is known that for d ? 1, this equation has no solutions in L 2(\Omega\Gamma4 In contrast, it is shown in the paper that in an appropriately weighted L 2(\Omega\Gamma there is a unique solution to the stochastic advectiondiffusion equation for any d 1. In addition we present explicit formulas for the HermiteFourier coefficients in the Wiener chaos expansion of the solution.