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86
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 603 (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.
Option pricing when underlying stock returns are discontinuous
 Journal of Financial Economics
, 1976
"... The validity of the classic BlackScholes option pricing formula dcpcnds on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying ..."
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Cited by 507 (1 self)
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The validity of the classic BlackScholes option pricing formula dcpcnds on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying stock return dynamics can be described by a stochastic process with a continuous sample path. In this paper, an option pricing formula is derived for the moregeneral cast when the underlying stock returns are gcncrated by a mixture of both continuous and jump processes. The derived formula has most of the attractive features of the original Black&holes formula in that it does not dcpcnd on investor prcfcrenccs or knowledge of the expcctsd return on the underlying stock. Morcovcr, the same analysis applied to the options can bc extcndcd to the pricingofcorporatc liabilities. 1. Intruduction In their classic paper on the theory of option pricing, Black and Scholcs (1973) prcscnt a mode of an:llysis that has rcvolutionizcd the theory of corporate liability pricing. In part, their approach was a breakthrough because it leads to pricing formulas using. for the most part, only obscrvablc variables. In particular,
The Surprise Element: Jumps in Interest Rates
 Journal of Econometrics
, 2002
"... Abstract. That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of PoissonGaussian models of the Fed Funds rate to capture surprise effects, and show that these models offer a good statistical description of short ra ..."
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Cited by 61 (2 self)
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Abstract. That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of PoissonGaussian models of the Fed Funds rate to capture surprise effects, and show that these models offer a good statistical description of short rate behavior, and are useful in understanding many empirical phenomena. Estimators are used based on analytical derivations of the characteristic functions and moments of jumpdiffusion stochastic processes for a range of jump distributions, and are extended to discretetime models. Jump (Poisson) processes capture empirical features of the data which would not be captured by Gaussian models, and there is strong evidence that existing models would be wellenhanced by jump and ARCHtype processes. The analytical and empirical methods in the paper support many applications, such as testing for Fed intervention effects, which are shown to be an important source of surprise jumps in interest rates. The jump model is shown to mitigate the nonlinearity of interest rate drifts, so prevalent in purediffusion models. Dayofweek effects are modelled explicitly, and the jump model provides evidence of bond market overreaction, rejecting the martingale hypothesis for interest rates. Jump models mixed with Markov switching processes predicate that conditioning on regime is important in determining short rate behavior.
A JumpDiffusion Approach to Modeling Credit Risk and Valuing Defaultable Securities
, 1997
"... ..."
On the Stability of InputQueued Switches with SpeedUp
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 2001
"... We consider cellbased switch and router architectures whose internal switching matrix does not provide enough speed to avoid input buffering. These architectures require a scheduling algorithm to select at each slot a subset of input buffered cells which can be transferred toward output ports. In t ..."
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Cited by 50 (4 self)
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We consider cellbased switch and router architectures whose internal switching matrix does not provide enough speed to avoid input buffering. These architectures require a scheduling algorithm to select at each slot a subset of input buffered cells which can be transferred toward output ports. In this paper, we propose several classes of scheduling algorithms whose stability properties are studied using analytical techniques mainly based upon Lyapunov functions. Original stability conditions are also derived for scheduling algorithms that are being used today in highperformance switch and router architectures.
A Lyapunov Bound for Solutions of Poisson's Equation
 Ann. Probab
, 1996
"... In this paper we consider /irreducible Markov processes evolving in discrete or continuous time, on a general state space. We develop a Lyapunov function criterion that permits one to obtain explicit bounds on the solution to Poisson's equation and, in particular, obtain conditions under which the ..."
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Cited by 43 (25 self)
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In this paper we consider /irreducible Markov processes evolving in discrete or continuous time, on a general state space. We develop a Lyapunov function criterion that permits one to obtain explicit bounds on the solution to Poisson's equation and, in particular, obtain conditions under which the solution is square integrable. These results are applied to obtain sufficient conditions that guarantee the validity of a functional central limit theorem for the Markov process. As a second consequence of the bounds obtained, a perturbation theory for Markov processes is developed which gives conditions under which both the solution to Poisson's equation and the invariant probability for the process are continuous functions of its transition kernel. The techniques are illustrated with applications to queueing theory and autoregressive processes. AMS subject classifications: 68M20, 60J10 Running head: Poisson's Equation Keywords: Markov chain, Markov process, Poisson's equation, Lyapunov f...
Feedback Control of Quantum State Reduction
, 2004
"... Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for th ..."
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Cited by 32 (2 self)
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Feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement. We formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter. We explore the use of stochastic Lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability.
Practical Algorithms for Performance Guarantees in Buffered Crossbars
, 2005
"... Network operators would like high capacity routers that give guaranteed throughput, rate and delay guarantees. Because they want high capacity, the trend has been towards input queued or combined input and output queued (CIOQ) routers using crossbar switching fabrics. But these routers require impra ..."
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Cited by 29 (1 self)
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Network operators would like high capacity routers that give guaranteed throughput, rate and delay guarantees. Because they want high capacity, the trend has been towards input queued or combined input and output queued (CIOQ) routers using crossbar switching fabrics. But these routers require impractically complex scheduling algorithms to provide the desired guarantees. In this paper, we explore how a buffered crossbar  a crossbar switch with a packet buffer at each crosspoint  can provide guaranteed performance (throughput, rate, and delay), with less complex, practical scheduling algorithms. We describe scheduling algorithms that operate in parallel on each input and output port, and hence are scalable. With these algorithms, buffered crossbars with a speedup of two can provide 100% throughput, rate, and delay guarantees. Index Terms system design, combinatorics, packet switching, buffered crossbar, scheduling algorithm, performance guarantees, throughput, mimic, quality of service. I. BACKGROUND Network operators would like high capacity routers that give guaranteed performance. First, they prefer routers that guarantee throughput so they can maximize the utilization of their expensive longhaul links. Second, they want routers that can allocate to each flow a guaranteed rate. Third, they want the capability to control the delay for packets of individual flows for realtime applications. Because they want high capacity, the trend has been towards input queued or combined input and output queued (CIOQ) routers. Most of these routers use a crossbar switching fabric with a centralized scheduler. While it is theoretically possible to build crossbar schedulers that give 100% throughput [1] or rate and delay guarantees [2][3] they are considered too complex to b...
A framework for worstcase and stochastic safety verification using barrier certificates
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2007
"... This paper presents a methodology for safety verification of continuous and hybrid systems in the worstcase and stochastic settings. In the worstcase setting, a function of state termed barrier certificate is used to certify that all trajectories of the system starting from a given initial set do ..."
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Cited by 28 (1 self)
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This paper presents a methodology for safety verification of continuous and hybrid systems in the worstcase and stochastic settings. In the worstcase setting, a function of state termed barrier certificate is used to certify that all trajectories of the system starting from a given initial set do not enter an unsafe region. No explicit computation of reachable sets is required in the construction of barrier certificates, which makes it possible to handle nonlinearity, uncertainty, and constraints directly within this framework. In the stochastic setting, our method computes an upper bound on the probability that a trajectory of the system reaches the unsafe set, a bound whose validity is proven by the existence of a barrier certificate. For polynomial systems, barrier certificates can be constructed using convex optimization, and hence the method is computationally tractable. Some examples are provided to illustrate the use of the method.