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26
Backward Stochastic Dierential Equations and Stochastic Controls: A New Perspective
, 1999
"... It is well known that backward stochastic dierential equations (BSDEs) stem from the study on the Pontryagin type maximum principle for optimal stochastic controls. A solution of a BSDE hits a given terminal value (which is a random variable) by virtue of an additional martingale term and an indenit ..."
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It is well known that backward stochastic dierential equations (BSDEs) stem from the study on the Pontryagin type maximum principle for optimal stochastic controls. A solution of a BSDE hits a given terminal value (which is a random variable) by virtue of an additional martingale term
STOCHASTIC MODELS OF COMPLEX NETWORKS
, 2008
"... Stochastic models of complex networks arise in a wide variety of applications in science and engineering. Specic instances include hightech manufacturing, telecommunications, computer systems, service systems and biochemical reaction networks. There are challenging mathematical problems stemming f ..."
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from the need to analyse and control such networks. This course will describe some general mathematical techniques for modeling stochastic networks, for deriving approximations at various scales (especially deterministic dierential equation and diusion approximations), and for analyzing the behavior
Hierarchical sparsity in multistage convex stochastic programs
 Uryasev & P.M. Pardalos, Stochastic Optimization: Algorithms and Applications
, 2000
"... Interior point methods for multistage stochastic programs involve KKT systems with a characteristic global block structure induced by dynamic equations on the scenario tree. We generalize the recursive solution algorithm proposed in an earlier paper so that its linear complexity extends to a rened ..."
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Cited by 13 (4 self)
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Interior point methods for multistage stochastic programs involve KKT systems with a characteristic global block structure induced by dynamic equations on the scenario tree. We generalize the recursive solution algorithm proposed in an earlier paper so that its linear complexity extends to a
Beliefs and Stochastic Modelling of Interest Rate Scenario Risk
"... . We present a framework that allows for a systematic assessment of risk given a specic model and belief on the market. Within this framework the time evolution of risk is modeled in a twofold way. On the one hand, risk is modeled by the time discrete and nonlinear garch(1,1) process, which allows ..."
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. We present a framework that allows for a systematic assessment of risk given a specic model and belief on the market. Within this framework the time evolution of risk is modeled in a twofold way. On the one hand, risk is modeled by the time discrete and nonlinear garch(1,1) process, which
A Stochastic Discount Factor Approach to Asset Pricing Using Panel Data
"... Using the Pricing Equation, in a paneldata framework, we construct a novel consistent estimator of the stochastic discount factor (SDF) mimicking portfolio which relies on the fact that its logarithm is the “common feature”in every asset return of the economy. Our estimator is a simple function of ..."
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Cited by 1 (1 self)
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Using the Pricing Equation, in a paneldata framework, we construct a novel consistent estimator of the stochastic discount factor (SDF) mimicking portfolio which relies on the fact that its logarithm is the “common feature”in every asset return of the economy. Our estimator is a simple function
Global Analysis of NavierStokes and Boussinesq Stochastic Flows using
, 2012
"... We provide a new framework for the study of uid ows presenting complex uncertain behavior. Our approach is based on the stochastic reduction and analysis of the governing equations using the dynamically orthogonal
eld equations. By numerically solving these equations we evolve in a fully coupled wa ..."
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We provide a new framework for the study of uid ows presenting complex uncertain behavior. Our approach is based on the stochastic reduction and analysis of the governing equations using the dynamically orthogonal
eld equations. By numerically solving these equations we evolve in a fully coupled
A Stochastic Evaluation Of The Spatial Moments Of A Contaminant Plume In Porous Media
"... In a previous report (cf. Dean[6]), a method of deriving statistical moment information was developed using a Hilbert space version of It^o's formula. This approach was used to develop a system of partial dierential equations in which the rst and second moments of the concentration distribution ..."
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Cited by 1 (1 self)
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In a previous report (cf. Dean[6]), a method of deriving statistical moment information was developed using a Hilbert space version of It^o's formula. This approach was used to develop a system of partial dierential equations in which the rst and second moments of the concentration
unknown title
"... We present derivative pricing and estimation tools for a class of stochastic volatility models that exploit the observed bursty or persistent nature of stock price volatility An empirical analysis of highfrequency SP index data conrms that volatility reverts slowly to its mean in comparison to th ..."
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to the tickbytick uctuations of the index value but it is fast meanreverting when looked at over the time scale of a derivative contract many months This motivates an asymptotic analysis of the partial dieren tial equation satised by derivative prices utilizing the distinction between these time scales
A Theoretical Study of The Response of Vascular Tumours to Dierent Types of Chemotherapy, (in preparation
"... In this paper we formulate and explore a mathematical model to study continuous infusion of a vascular tumour with isolated and combined bloodborne chemotherapies. The mathematical model comprises a system of nonlinear partial dierential equations that describe the evolution of the healthy (host ..."
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Cited by 2 (1 self)
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In this paper we formulate and explore a mathematical model to study continuous infusion of a vascular tumour with isolated and combined bloodborne chemotherapies. The mathematical model comprises a system of nonlinear partial dierential equations that describe the evolution of the healthy
Fast Numerical Valuation of American, Exotic and Complex Options
 Applied Mathematical Finance
, 1995
"... The purpose of this paper is to present evidence in support of the hypothesis that fast, accurate and parametrically robust numerical valuation of a wide range of derivative securities can be achieved by use of direct numerical methods in the solution of the associated PDE problems. Speci#cally, ..."
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Cited by 13 (1 self)
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maturities and underlying prices, and the parameters required for risk analysis. 1 Introduction This paper brie#y presents evidence accumulated to date in support of the use of direct numerical methods for the solution of partial di#erential equation #PDE# type problems associated with valuation
Results 1  10
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