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1.
Proxy simulation schemes using likelihood ratio weighted Monte Carlo for generic robust MonteCarlo sensitivities and high accuracy drift approximation (with applications to the...
Title:
Proxy simulation schemes using likelihood ratio weighted Monte Carlo for generic robust MonteCarlo sensitivities and high accuracy drift approximation (with applications to the LIBOR Market Model)
Author:
Christian P. Fries
;
Joerg Kampen
Christian P. Fries
;
Joerg Kampen
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Description:
We consider a generic framework for generating likelihood ratio weighted Monte Carlo simulation paths, where we use one simulation scheme K° (proxy scheme) to generate realizations and then reinterpret them as realizations of another scheme K* (target scheme) by adjusting measure (via likelihood ratio) to match the distribution of K° such that E...
We consider a generic framework for generating likelihood ratio weighted Monte Carlo simulation paths, where we use one simulation scheme K° (proxy scheme) to generate realizations and then reinterpret them as realizations of another scheme K* (target scheme) by adjusting measure (via likelihood ratio) to match the distribution of K° such that E( f(K*)  F_t ) = E( f(K°) w  F_t ). This is done numerically in every time step, on every path. This makes the approach independent of the product (the function f) and even of the model, it only depends on the numerical scheme. The approach is essentially a numerical version of the likelihood ratio method [Broadie & Glasserman, 1996] and Malliavin's Calculus [Fournie et al., 1999; Malliavin, 1997] reconsidered on the level of the discrete numerical simulation scheme. Since the numerical scheme represents a time discrete stochastic process sampled on a discrete probability space the essence of the method may be motivated without a deeper mathematical understanding of the time continuous theory (e.g. Malliavin's Calculus). The framework is completely generic and may be used for high accuracy drift approximations and the robust calculation of partial derivatives of expectations w.r.t. model parameters (i.e. sensitivities, aka. Greeks) by applying finite differences by reevaluating the expectation with a model with shifted parameters. We present numerical results using a MonteCarlo simulation of the LIBOR Market Model for benchmarking. ; MonteCarlo, Likelihood Ratio, Malliavin Calculus, Sensitivities, Greeks
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Document Type:
preprint
URL:
http://129.3.20.41/eps/fin/papers/0504/0504010.pdf
http://129.3.20.41/eps/fin/papers/0504/0504010.pdf
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RePEc: Research Papers in Economics
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2.
PERTURBATION STABLE CONDITIONAL ANALYTIC MONTECARLO PRICING SCHEME FOR AUTOCALLABLE PRODUCTS
Title:
PERTURBATION STABLE CONDITIONAL ANALYTIC MONTECARLO PRICING SCHEME FOR AUTOCALLABLE PRODUCTS
Author:
CHRISTIAN P. FRIES
;
MARK S. JOSHI
CHRISTIAN P. FRIES
;
MARK S. JOSHI
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Description:
In this paper, we present a generic method for the MonteCarlo pricing of (generalized) autocallable products (aka. trigger products), i.e., products for which the payout function features a discontinuity with a (possibly) stochastic location (the trigger) and value (the payout).The MonteCarlo pricing of products with discontinuous payout is k...
In this paper, we present a generic method for the MonteCarlo pricing of (generalized) autocallable products (aka. trigger products), i.e., products for which the payout function features a discontinuity with a (possibly) stochastic location (the trigger) and value (the payout).The MonteCarlo pricing of products with discontinuous payout is known to come with a high MonteCarlo error. The numerical calculation of sensitivities (i.e., partial derivatives) of such prices by finite differences gives very noisy results, since the MonteCarlo approximation (being a finite sum of discontinuous functions) is not smooth. Additionally, the MonteCarlo error of the finitedifference approximation explodes as the shift size tends to zero.Our method combines a product specific modification of the underlying numerical scheme, which is to some extent similar to an importance sampling and/or partial proxy simulation scheme and a reformulation of the payoff function into an equivalent smooth payout.From the financial product we merely require that hitting of the stochastic trigger will result in an conditionally analytic value. Many complex derivatives can be written in this form. A class of products where this property is usually encountered are the so called autocallables, where a trigger hit results in cancellation of all future payments except for one redemption payment, which can be valued analytically, conditionally on the trigger hit.From the model we require that its numerical implementation allows for a calculation of the transition probability of survival (i.e., nontrigger hit). Many models allows this, e.g., Euler schemes of Itô processes, where the trigger is a model primitive.The method presented is effective across a large range of cases where other methods fail, e.g. small finite difference shift sizes or short time to trigger reset (approaching maturity); this means that a practitioner can use this method and be confident that it will work consistently.The method itself can be viewed as a generalization of the method proposed by Glasserman and Staum (2001), both with respect to the type (and shape) of the boundaries, as well as, with respect to the class of products considered. In addition we explicitly consider the calculation of sensitivities. ; MonteCarlo simulation, pricing, greeks, variance reduction, autocallable, trigger product, target redemption note
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Document Type:
article
URL:
http://www.worldscinet.com/cgibin/details.cgi?type=pdf&id=pii:S0219024911006334
http://www.worldscinet.com/cgibin/details.cgi?type=html&id=pii:S0219024911006334
http://www.worldscinet.com/cgibin/details.cgi?type=pdf&id=pii:S0219024911006334
http://www.worldscinet.com/cgibin/details.cgi?type=html&id=pii:S0219024911006334
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3.
Markov Functional Modeling of Equity, Commodity and other Assets
Open Access
Title:
Markov Functional Modeling of Equity, Commodity and other Assets
Author:
Christian P. Fries
;
Christian P. Fries
Christian P. Fries
;
Christian P. Fries
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In this short note we show how to setup a one dimensional single asset model, e.g. equity model, which calibrates to a full (two dimensional) implied volatility surface. We show that the efficient calibration procedure used in LIBOR Markov functional models may be applied here too. In a addition to the calibration to a full volatility surface th...
In this short note we show how to setup a one dimensional single asset model, e.g. equity model, which calibrates to a full (two dimensional) implied volatility surface. We show that the efficient calibration procedure used in LIBOR Markov functional models may be applied here too. In a addition to the calibration to a full volatility surface the model allows the calibration of the joint assetinterest rate movement (i.e. local interest rates) and forward volatility. The latter allows the calibration of compound or Bermudan options. The Markov functional modeling approach consists of a Markovian driver process x and a mapping functional representing the asset states S(t) as a function of x(t). It was originally developed in the context of interest rate models, see [7]. Our approach however is similar to the setup of the hybrid Markov functional model in spot measure, as considered in [5]. For equity models it is common to use a deterministic Numéraire, e.g. the bank account with deterministic interest rates. In our approach we will choose the asset itself as Numéraire. This is a subtle, but crucial difference to other approaches considering Markov functional modeling. Choosing the asset itself as Numéraire will allow for a very efficient numerically calibration
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Year of Publication:
20120409
Source:
http://www.christian
fries
.de/finmath/markovfunctionaleqmodel/MarkovFunctionalEQModel.pdf
http://www.christian
fries
.de/finmath/markovfunctionaleqmodel/MarkovFunctionalEQModel.pdf
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Document Type:
text
Language:
en
DDC:
330 Economics
(computed)
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.6512
http://www.christianfries.de/finmath/markovfunctionaleqmodel/MarkovFunctionalEQModel.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.6512
http://www.christianfries.de/finmath/markovfunctionaleqmodel/MarkovFunctionalEQModel.pdf
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4.
A recursive formula for the Kurtosis of an approximation to the distribution of share prices
Open Access
Title:
A recursive formula for the Kurtosis of an approximation to the distribution of share prices
Author:
Christian P. Fries
Christian P. Fries
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Description:
Introduction Given the recursive approximation to the distribution of share prices (see [1, 2]) we will derive a recursive formula for Kurtosis. The Kutosis of a distribution consisting of samples x 1 . . . x N with mean and standard deviation s is given by K = x j . (1) Recursive calculation of Kurtosis We fix notation as follows: Assuming that...
Introduction Given the recursive approximation to the distribution of share prices (see [1, 2]) we will derive a recursive formula for Kurtosis. The Kutosis of a distribution consisting of samples x 1 . . . x N with mean and standard deviation s is given by K = x j . (1) Recursive calculation of Kurtosis We fix notation as follows: Assuming that a distributioin of prices p j ( j = 1, . . . , n) occuring at a volume v j is given (say at time t n ). At later time (say at time t n+1 ) the distribution changed to . one price p n+1 occuring at volume v n+1 . the prices p 1 , . . . , p n occuring at volumes v 1 , . . . , v n , respectively (where N = j=1 v j = j=1 v j +v n+1 is the total volume of shares floating). The Kurtosis of the distribution at time t n is thus given by K n = and the Kurtosis of the distribution at time t n+1 is given by K n+1 = v i where v i = N v i for i = 1, . . . , n a
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20090418
Source:
http://www.christian
fries
.de/evwma/PDF/
fries
_evwma_kurtosis_2001.pdf
http://www.christian
fries
.de/evwma/PDF/
fries
_evwma_kurtosis_2001.pdf
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Document Type:
text
Language:
en
DDC:
519 Probabilities & applied mathematics
(computed)
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.9.8392
http://www.christianfries.de/evwma/PDF/fries_evwma_kurtosis_2001.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.9.8392
http://www.christianfries.de/evwma/PDF/fries_evwma_kurtosis_2001.pdf
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5.
Navigation of Autonomous Robots Using Genetic Algorithms
Open Access
Title:
Navigation of Autonomous Robots Using Genetic Algorithms
Author:
Terrence P. Fries
Terrence P. Fries
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Abstract: Optimal motion planning is critical for the successful operation of an autonomous mobile robot. Many proposed approaches use either fuzzy logic or genetic algorithms (GAs), however, most approaches offer only path planning or only trajectory planning, but not both. In addition, few approaches attempt to address the impact of varying t...
Abstract: Optimal motion planning is critical for the successful operation of an autonomous mobile robot. Many proposed approaches use either fuzzy logic or genetic algorithms (GAs), however, most approaches offer only path planning or only trajectory planning, but not both. In addition, few approaches attempt to address the impact of varying terrain conditions on the optimal path. This paper presents a fuzzygenetic approach that provides both path and trajectory planning, and has the advantage of considering diverse terrain conditions when determining the optimal path. The terrain conditions are modeled using fuzzy linguistic variables to allow for the imprecision and uncertainty of the terrain data. Although a number of methods have been proposed using GAs, few are appropriate for a dynamic environment or provide response in realtime. The method proposed in this paper is robust, allowing the robot to adapt to dynamic conditions in the environment. KeyWords: Motion planning, navigation, robotics, genetic algorithms, fuzzy sets 1
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Year of Publication:
20130818
Source:
http://www.wseas.us/elibrary/conferences/2005miami/papers/501227.pdf
http://www.wseas.us/elibrary/conferences/2005miami/papers/501227.pdf
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text
Language:
en
DDC:
629 Other branches of engineering
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.330.6296
http://www.wseas.us/elibrary/conferences/2005miami/papers/501227.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.330.6296
http://www.wseas.us/elibrary/conferences/2005miami/papers/501227.pdf
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6.
The Foresight Bias in MonteCarlo Pricing of Options with Early Exercise: Classification, Calculation & Removal
Open Access
Title:
The Foresight Bias in MonteCarlo Pricing of Options with Early Exercise: Classification, Calculation & Removal
Author:
Christian P. Fries
Christian P. Fries
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Description:
In this paper we investigate the so called foresight bias that may appear in the MonteCarlo pricing of Bermudan and compound options if the exercise criteria is calculated by the same MonteCarlo simulation as the exercise values. The standard approach to remove the foresight bias is to use two independent MonteCarlo simulations: One simulatio...
In this paper we investigate the so called foresight bias that may appear in the MonteCarlo pricing of Bermudan and compound options if the exercise criteria is calculated by the same MonteCarlo simulation as the exercise values. The standard approach to remove the foresight bias is to use two independent MonteCarlo simulations: One simulation is used to estimate the exercise criteria (as a function of some state variable), the other is used to calculate the exercise price based on this exercise criteria. We shall call this the numerical removal of the foresight bias.
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Year of Publication:
20090419
Source:
http://www.christian
fries
.de/finmath/foresightbias/
Fries
_ForesightBias.pdf
http://www.christian
fries
.de/finmath/foresightbias/
Fries
_ForesightBias.pdf
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text
Language:
en
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.59.7813
http://www.christianfries.de/finmath/foresightbias/Fries_ForesightBias.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.59.7813
http://www.christianfries.de/finmath/foresightbias/Fries_ForesightBias.pdf
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7.
Abstract Localized Proxy Simulation Schemes for Generic and Robust MonteCarlo Greeks
Open Access
Title:
Abstract Localized Proxy Simulation Schemes for Generic and Robust MonteCarlo Greeks
Author:
Christian P. Fries
Christian P. Fries
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Description:
For the numerical calculation of partial derivatives (aka. sensitivites or greeks) from a MonteCarlo simulation there are essentially two possible approaches: The pathwise method and the likelihood ratio method. Both methods have their shortcomings: While the pathwise method works very well for smooth payouts it fails for discontinuous payouts....
For the numerical calculation of partial derivatives (aka. sensitivites or greeks) from a MonteCarlo simulation there are essentially two possible approaches: The pathwise method and the likelihood ratio method. Both methods have their shortcomings: While the pathwise method works very well for smooth payouts it fails for discontinuous payouts. On the other hand, the likelihood ratio gives much better results on discontinuous payouts, but falls short of the pathwise method if smooth payouts are considered. In this paper, we present a modification to the (partial) proxy simulation scheme framework, resulting in a perpath selection of either the pathwise method or the likelihood ratio method. This allows us to chose the optimal simulation method on a pathbypath basis. Since the method is implemented as a proxy simulation scheme as well, the sensitivities can be calculated from simple finite differences applied to the pricing engine.
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Year of Publication:
20080701
Source:
http://www.christian
fries
.de/finmath/proxyscheme/
Fries
LocalizedProxySchemeForGreeks.pdf
http://www.christian
fries
.de/finmath/proxyscheme/
Fries
LocalizedProxySchemeForGreeks.pdf
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Document Type:
text
Language:
en
DDC:
518 Numerical analysis
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.65.1083
http://www.christianfries.de/finmath/proxyscheme/FriesLocalizedProxySchemeForGreeks.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.65.1083
http://www.christianfries.de/finmath/proxyscheme/FriesLocalizedProxySchemeForGreeks.pdf
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8.
A recursive formula for the Kurtosis of an approximation to the distribution of share prices
Open Access
Title:
A recursive formula for the Kurtosis of an approximation to the distribution of share prices
Author:
Christian P. Fries
Christian P. Fries
Minimize authors
Description:
Given the recursive approximation to the distribution of share prices (see [1, 2]) we will derive a recursive formula for Kurtosis. The Kutosis of a distribution consisting of samples x 1 . x N with mean and standard deviation s is given by K = x j . (1) Recursive calculation of Kurtosis We fix notation as follows: Assuming that a distribution o...
Given the recursive approximation to the distribution of share prices (see [1, 2]) we will derive a recursive formula for Kurtosis. The Kutosis of a distribution consisting of samples x 1 . x N with mean and standard deviation s is given by K = x j . (1) Recursive calculation of Kurtosis We fix notation as follows: Assuming that a distribution of prices p j ( j = 1, . . . , n) occuring at a volume v j is given (say at time t n ). At later time (say at time t n+1 ) the distribution changed to . one price p n+1 occuring at volume v n+1 . the prices p 1 , ., p n occuring at volumes v 1 , ., v n , respectively (where N = j=1 v j = j=1 v j +v n+1 is the total volume of shares floating). The Kurtosis of the distribution at time t n is thus given by K n = and the Kurtosis of the distribution at time t n+1 is given by K n+1 = v i where v i = N v i for i = 1, ., n a
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Year of Publication:
20090417
Source:
http://www.spacelike.com/
fries
/evwma/
fries
_evwma_kurtosis_2001.pdf
http://www.spacelike.com/
fries
/evwma/
fries
_evwma_kurtosis_2001.pdf
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Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.8369
http://www.spacelike.com/fries/evwma/fries_evwma_kurtosis_2001.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.8369
http://www.spacelike.com/fries/evwma/fries_evwma_kurtosis_2001.pdf
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9.
The Distribution of Share Prices and Elastic Time and Volume Weighted Moving Averages
Open Access
Title:
The Distribution of Share Prices and Elastic Time and Volume Weighted Moving Averages
Author:
Christian P. Fries
Christian P. Fries
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this article we consider "the distribution of prices paid per share" and derive simple approximation formulas for its mean and other statistical characteristica. The formulas we derive are approximations since the data about the distribution of prices paid by each shareholder for each share is not available. After going through the derivation of...
this article we consider "the distribution of prices paid per share" and derive simple approximation formulas for its mean and other statistical characteristica. The formulas we derive are approximations since the data about the distribution of prices paid by each shareholder for each share is not available. After going through the derivation of the formula we will end up with recursive definitions of time series which could be viewed as random coefficient autoregressive (RCA) time series (see [6, 5])
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Year of Publication:
20090417
Source:
http://www.spacelike.com/
fries
/evwma/
fries
_evwma_preprint_2002.pdf
http://www.spacelike.com/
fries
/evwma/
fries
_evwma_preprint_2002.pdf
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en
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.8639
http://www.spacelike.com/fries/evwma/fries_evwma_preprint_2002.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.8639
http://www.spacelike.com/fries/evwma/fries_evwma_preprint_2002.pdf
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10.
Foresight Bias and Suboptimality Correction in MonteCarlo Pricing of Options with Early Exercise: Classification, Calculation & Removal
Open Access
Title:
Foresight Bias and Suboptimality Correction in MonteCarlo Pricing of Options with Early Exercise: Classification, Calculation & Removal
Author:
Christian P. Fries
Christian P. Fries
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Description:
In this paper we investigate the so called foresight bias that may appear in the MonteCarlo pricing of Bermudan and compound options if the exercise criteria is calculated by the same MonteCarlo simulation as the exercise values. The standard approach to remove the foresight bias is to use two independent MonteCarlo simulations: One simulatio...
In this paper we investigate the so called foresight bias that may appear in the MonteCarlo pricing of Bermudan and compound options if the exercise criteria is calculated by the same MonteCarlo simulation as the exercise values. The standard approach to remove the foresight bias is to use two independent MonteCarlo simulations: One simulation is used to estimate the exercise criteria (as a function of some state variable), the other is used to calculate the exercise price based on this exercise criteria. We shall call this the numerical removal of the foresight bias. In this paper we give an exact definition of the foresight bias in closed form and show how to apply an analytical correction for the foresight bias. Our numerical results show that the analytical removal of the foresight bias gives similar results as the standard numerical removal of the foresight bias. The analytical correction allows for a simpler coding and faster pricing, compared to a numerical removal of the foresight bias. Our analysis may also be used as an indication of when to neglect the foresight bias removal altogether. While this is sometimes possible, neglecting foresight bias will break the possibility
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Year of Publication:
20130725
Source:
http://www.christian
fries
.de/finmath/foresightbias/
Fries
_ForesightBias.pdf
http://www.christian
fries
.de/finmath/foresightbias/
Fries
_ForesightBias.pdf
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Document Type:
text
Language:
en
DDC:
650 Management & auxiliary services
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.9299
http://www.christianfries.de/finmath/foresightbias/Fries_ForesightBias.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.9299
http://www.christianfries.de/finmath/foresightbias/Fries_ForesightBias.pdf
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