E. Platen

发表

Numerical Solution of Stochastic Differential Equations

P. Kloeden, E. Platen, 1992 .

Numerical Solutions of Stochastic Differential Equations

P. Kloeden, E. Platen, 1995 .

Balanced Implicit Methods for Stiff Stochastic Systems

E. Platen, G. Milstein, H. Schurz, 1998 .

An introduction to numerical methods for stochastic differential equations

E. Platen, 1999, Acta Numerica.

Comparison of Some Key Approaches to Hedging in Incomplete Markets

D. Heath, E. Platen, M. Schweizer, 1998 .

Option Pricing under Incompleteness and Stochastic Volatility

E. Platen, M. Schweizer, N. Hofmann, 1992 .

On Smile and Skewness

E. Platen, M. Schweizer, 1994 .

Strong discrete time approximation of stochastic differential equations with time delay

E. Platen, U. Küchler, 2000 .

Option Pricing, Interest Rates and Risk Management: Numerical Comparison of Local Risk-Minimisation and Mean-Variance Hedging

D. Heath, E. Platen, M. Schweizer, 2001 .

Numerical Inversion of Laplace Transforms: A Survey of Techniques with Applications to Derivative Pricing

D. Heath, E. Platen, M. Craddock, 1999 .

Exact and Almost Exact Simulation

E. Platen, Jan Baldeaux, 2013 .

QUANTITATIVE FINANCE RESEARCH CENTRE

E. Platen, 2004 .

Local volatility function models under a benchmark approach

David Heath, Eckhard Platen, D. Heath, 2006 .

Consistent pricing and hedging for a modified constant elasticity of variance model

David Heath, Eckhard Platen, D. Heath, 2002 .

On Feedback Effects from Hedging Derivatives

Eckhard Platen, Martin Schweizer, E. Platen, 1998 .

Detecting Money Market Bubbles

E. Platen, Jan Baldeaux, Katja Ignatieva, 2016 .

Loading Pricing of Catastrophe Bonds and Other Long-Dated, Insurance-Type Contracts

David R. Taylor, E. Platen, D. Taylor, 2016, 1610.09875.

BENCHMARKED RISK MINIMIZATION

E. Platen, Ke Du, 2016 .

Pricing Currency Derivatives Under the Benchmark Approach

E. Platen, Martino Grasselli, Jan Baldeaux, 2013 .

Pricing Currency Derivatives Under the Benchmark Approach

E. Platen, Martino Grasselli, Jan Baldeaux, 2013 .

On the Distributional Characterization of Daily Log‐Returns of a World Stock Index

Eckhard Platen, Kevin Fergusson, E. Platen, 2006 .

Affine Realizations for Levy Driven Interest Rate Models with Real-World Forward Rate Dynamics

E. Platen, Stefan Tappe, 2011 .

Exact Scenario Simulation for Selected Multi-Dimensional Stochastic Processes

E. Platen, Renata Rendek, 2009 .

Exact Scenario Simulation for Selected Multi-dimensional

E. Platen, Renata Rendek, 2009 .

The marginal distributions of returns and volatility

E. Platen, Simon R. Hurst, 1997 .

A tractable model for indices approximating the growth optimal portfolio

E. Platen, Jan Baldeaux, Katja Ignatieva, 2012 .

Laplace transform identities for diffusions, with applications to rebates and barrier options

E. Platen, H. Hulley, 2007 .

A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets

D. Heath, E. Platen, M. Schweizer, 2001 .

The approximation of multiple stochastic integrals

P. Kloeden, E. Platen, I. W. Wright, 1992 .

Numerical Solution of Sde Through Computer Experiments

P. Kloeden, E. Platen, H. Schurz, 1993 .

Recursive marginal quantization of higher-order schemes

E. Platen, Thomas Andrew McWalter, Ralph Rudd, 2017, 1701.02681.

Simulation Methods for Stochastic Differential Equations

E. Platen, 2008 .

Higher-order implicit strong numerical schemes for stochastic differential equations

P. Kloeden, E. Platen, 1992 .

Relations between multiple ito and stratonovich integrals

P. Kloeden, E. Platen, 1991 .

Principles for modelling financial markets

E. Platen, R. Rebolledo, 1996, Journal of Applied Probability.

Investing for the Long Run

Dietmar P. J. Leisen, E. Platen, Jin Sun, 2017, 1705.03929.

A BENCHMARK APPROACH TO FINANCE

Eckhard Platen, E. Platen, 2006 .

Extrapolation methods for the weak approximation of Ito diffusions

Peter E. Kloeden, Eckhard Platen, P. Kloeden, 1995 .

On weak implicit and predictor-corrector methods

Eckhard Platen, E. Platen, 1995 .

Strong Predictor-Corrector Euler Methods for Stochastic Differential Equations

Nicola Bruti-Liberati, Eckhard Platen, E. Platen, 2008 .

CONSISTENT MARKET EXTENSIONS UNDER THE BENCHMARK APPROACH

E. Platen, D. Filipović, 2009 .

Less-Expensive Valuation of Long Term Annuities Linked to Mortality, Cash and Equity

E. Platen, K. Fergusson, 2017, 1711.02808.

THE NUMÉRAIRE PROPERTY AND LONG‐TERM GROWTH OPTIMALITY FOR DRAWDOWN‐CONSTRAINED INVESTMENTS

Eckhard Platen, Constantinos Kardaras, Jan Obloj, 2012, 1206.2305.

Hidden Markov filtering for a mean reverting interest rate model

E. Platen, R. Elliot, P. Fischer, 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

Dynamics of a Well-Diversified Equity Index January 17 , 2019

E. Platen, Renata Rendek, 2019 .

A Benchmark Approach to Investing and Pricing

E. Platen, 2009 .

Modelling Co-movements and Tail Dependency in the International Stock Market via Copulae

E. Platen, Katja Ignatieva, 2009 .

A General Benchmark Model for Stochastic Jump Sizes

E. Platen, M. Christensen, 2004 .

Stochastic Differential Equations

David Heath, Eckhard Platen, D. Heath, 2006 .

On the semimartingale property of discounted asset-price processes

E. Platen, C. Kardaras, 2008, 0803.1890.

On Financial Markets where only Buy-And-Hold Trading is Possible

E. Platen, C. Kardaras, 2008 .

A Discrete Time Benchmark Approach for Insurance and Finance

E. Platen, H. Bühlmann, 2003, ASTIN Bulletin.

Real World Pricing of Long Term Contracts

E. Platen, 2009 .

On Weak Predictor-Corrector Schemes for Jump-Diffusion Processes in Finance

E. Platen, Nicola Bruti-Liberati, 2012 .

A Monte Carlo Method using PDE Expansions for a Diversifed Equity Index Model

D. Heath, E. Platen, 2014 .

Distributional Deviations in Random Number Generation in Finance

E. Platen, S. Chavez, 2008 .

Risken, H.: The Fokker‐Planck Equation. Methods of Solution and Applications. Springer Series in Synergetics, Vol. 18. Springer‐Verlag, Berlin — Heidelberg — New York — Tokyo 1984, XVI, 454 pp., 95 Figs., DM 125,‐. ISBN 3–540–13098–5

E. Platen, 1986 .

Law of the Minimal Price

E. Platen, 2008 .

Stochastic Differential Equations with Jumps: Simulation

E. Platen, Nicola Bruti-Liberati, 2010 .

Approximation of Jump Difiusions in Finance and Economics

E. Platen, Nicola Bruti-Liberati, 2007 .

Benchmarking and Fair Pricing Applied to Two

E. Platen, H. Hulley, Shane Miller, 2005 .

Approximating the numéraire portfolio by naive diversification

E. Platen, Renata Rendek, 2010 .

Real-world jump-diffusion term structure models

E. Platen, Nicola Bruti-Liberati, Christina Nikitopoulos-Sklibosios, 2010 .

A benchmark approach to asset management

E. Platen, 2006 .

Diversified Portfolios with Jumps in a Benchmark Framework

E. Platen, 2004 .

Axiomatic principles for a market model

E. Platen, 1999, Journal of Applied Probability.

Principles for modelling financial markets

E. Platen, R. Rebolledo, 1996, Journal of Applied Probability.

Understanding the Implied Volatility Surface for Options on a Diversified Index

D. Heath, E. Platen, 2004 .

Asset Markets and Monetary Policy

E. Platen, W. Semmler, 2009 .

A Benchmark Approach to Portfolio Optimization under Partial Information

E. Platen, W. Runggaldier, 2007 .

Less-expensive long-term annuities linked to mortality, cash and equity

E. Platen, K. Fergusson, 2022, Annals of Actuarial Science.

No arbitrage and multiplicative special semimartingales

E. Platen, Stefan Tappe, 2020, 2005.05575.

Simulation of Diversified Portfolios in a Continuous Financial Market

E. Platen, Renata Rendek, 2010 .

Real-World Forward Rate Dynamics With Affine Realizations

E. Platen, Stefan Tappe, 2015, 1907.05072.

Alternative Defaultable Term Structure Models

E. Platen, Nicola Bruti-Liberati, Christina Nikitopoulos-Sklibosios, 2009 .

Exploiting arbitrage requires short selling

E. Platen, Stefan Tappe, 2020, 2011.12523.

Using Dynamic Copulae for Modeling Dependency in Currency Denominations of a Diversified World Stock Index

E. Platen, Katja Ignatieva, Renata Rendek, 2011 .

Appendix: Recursive Marginal Quantization of Higher-Order Schemes

E. Platen, Thomas Andrew McWalter, Ralph Rudd, 2017 .

Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods

E. Platen, Jan Baldeaux, 2012, 1204.1126.

Benchmark Model with Intensity Based Jumps

E. Platen, 2002 .

Pricing of long dated equity-linked life insurance contracts

E. Platen, Leunglung Chan, 2016 .

Hedging Long-Dated Interest Rate Derivatives for Australian Pension Funds and Life Insurers

E. Platen, K. Fergusson, 2014 .

Numerical Solution of Sde Through Computer Experiments

P. Kloeden, E. Platen, H. Schurz, 1993 .

2 Incomplete Benchmark Model with Jumps 2 . 1 Modeling Uncertainty

E. Platen, 2003 .

Functionals of Multidimensional Diffusions with Applications to Finance

E. Platen, Jan Baldeaux, 2013 .

On the Strong Approximation of Pure Jump Processes

E. Platen, Nicola Bruti-Liberati, 2005 .

Øksendal, B., Stochastic Differential Equations. An Introduction with Applications. Berlin‐Heidelberg‐New York‐Tokyo, Springer‐Verlag 1985. XIII, 205 S., DM 42,‐. ISBN 3‐540‐15 292‐X (Universitext)

E. Platen, 1987 .

Stochastic Taylor Expansions

E. Platen, 2010 .

Local risk-minimization under the benchmark approach

E. Platen, F. Biagini, A. Cretarola, 2014, Mathematics and Financial Economics.

A Discrete Time Benchmark Approach for Finance and Insurance

E. Platen, H. Bühlmann, 2002 .

A taylor formula for semimartingales solving a stochastic equation

E. Platen, 1981 .

Hedging for the long run

E. Platen, H. Hulley, 2012, Mathematics and Financial Economics.

Credit Derivative Evaluation and CVA Under the Benchmark Approach

E. Platen, Jan Baldeaux, 2015, Asia-Pacific Financial Markets.

A survey of numerical methods for stochastic differential equations

Peter E. Kloeden, Eckhard Platen, P. Kloeden, 1989 .

On Explicit Probability Laws for Classes of Scalar Diffusions

E. Platen, M. Craddock, 2009 .

On the Efficiency of Simplified Weak Taylor Schemes for Monte Carlo Simulation in Finance

Eckhard Platen, Nicola Bruti Liberati, E. Platen, 2004, International Conference on Computational Science.

A variance reduction technique based on integral representations

David Heath, Eckhard Platen, D. Heath, 2002 .

Empirical behavior of a world stock index from intra-day to monthly time scales

E. Platen, W. Breymann, D. Lüthi, 2009 .

On the Distributional Characterization of Log-returns of a World Stock Index

E. Platen, K. Fergusson, 2005 .

Approximating the Growth Optimal Portfolio with a Diversified World Stock Index

E. Platen, Truc Le, 2006 .

Fair Pricing of Weather Derivatives

E. Platen, J. West, 2003 .

Introduction to Stochastic Time Discrete Approximation

Eckhard Platen, Peter E. Kloeden, P. Kloeden, 1992 .

Modelling with Stochastic Differential Equations

P. Kloeden, E. Platen, 1992 .

Applications of Stochastic Differential Equations

Peter E. Kloeden, Eckhard Platen, P. Kloeden, 1992 .

A Unified Framework for Portfolio Optimization and Asset Pricing

E. Platen, 2006 .

Semiparametric diffusion estimation and application to a stock market index

W. Härdle, E. Platen, T. Kleinow, 2008 .

Symmetry group methods for fundamental solutions

Eckhard Platen, Mark Craddock, E. Platen, 2004 .

Hidden Markov Chain Filtering for Generalised Bessel Processes

R. Elliott, E. Platen, 2001 .

Modeling of Oil Prices

E. Platen, Ke Du, Renata Rendek, 2012 .

Computing Functionals of Square Root and Wishart Processes Under the Benchmark Approach via Exact Simulation

E. Platen, Jan Baldeaux, 2013 .

Lie Symmetry Group Methods

Eckhard Platen, Jan Baldeaux, E. Platen, 2013 .

Portfolio selection and asset pricing under a benchmark approach

Eckhard Platen, E. Platen, 2006 .

On the Pricing and Hedging of Long Dated Zero Coupon Bonds

E. Platen, 2006 .

Sharpe Ratio Maximization and Expected Utility when Asset Prices have Jumps

E. Platen, M. Christensen, 2007 .

2 The Jump Diffusion Market Model 2 . 1 The Modeling of Uncertainty

E. Platen, M. Christensen, 2005 .

A reading guide for last passage times with financial applications in view

Ashkan Nikeghbali, Eckhard Platen, E. Platen, 2013, Finance Stochastics.

Probability and Statistics

Peter E. Kloeden, Eckhard Platen, P. Kloeden, 1992 .

Numerical solution of stochastic differential equations in finance

Eckhard Platen, E. Platen, 2014 .

APPLICATION OF MAXIMUM LIKELIHOOD ESTIMATION TO STOCHASTIC SHORT RATE MODELS

E. Platen, K. Fergusson, 2015 .

Approximation of jump diffusions in finance and economics

Nicola Bruti-Liberati, Eckhard Platen, E. Platen, 2007 .

Time Discrete Taylor Approximations for Itǒ Processes with Jump Component

Eckhard Platen, E. Platen, Remigijus Mikulevicius, 1988 .

The Small and Large Time Implied Volatilities in the Minimal Market Model

E. Platen, Zhidong Guo, Zhi Guo, 2011, 1109.6154.

Strong approximations of stochastic differential equations with jumps

Nicola Bruti-Liberati, Eckhard Platen, E. Platen, 2007 .

Loading Pricing of Long-Dated, Insurance-Type Contracts

E. Platen, D. Taylor, 2017 .

The Affine Nature of Aggregate Wealth Dynamics

E. Platen, Renata Rendek, 2012 .

On the Role of the Growth Optimal Portfolio in Finance

Eckhard Platen, E. Platen, 2005 .

A Top-Down Method for Long-Term Investing

Dietmar P. J. Leisen, E. Platen, 2021 .

Valuation of FX barrier options under stochastic volatility

D. Heath, E. Platen, 1996 .

The fundamental theorem of asset pricing for self-financing portfolios

E. Platen, Stefan Tappe, 2020 .

Dynamics of a Well-Diversified Equity Index

E. Platen, Renata Rendek, 2019, SSRN Electronic Journal.

Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees

E. Platen, K. Fergusson, 2013 .

ANALYTIC PRICING OF CONTINGENT CLAIMS UNDER THE REAL-WORLD MEASURE

E. Platen, Shane Miller, Shane M. Miller, 2008 .

Pricing under the Real-World Probability Measure for Jump-Diffusion Term Structure Models

E. Platen, Nicola Bruti-Liberati, Christina Nikitopoulos-Sklibosios, 2007 .

Benchmarking and fair pricing applied to two market models

E. Platen, H. Hulley, Shane Miller, 2005 .

Arbitrage in continuous complete markets

E. Platen, 2002, Advances in Applied Probability.

A Benchmark Model for Financial Markets

E. Platen, 2001 .

Option pricing for a logstable asset price model

Svetlozar T. Rachev, Eckhard Platen, E. Platen, 1999 .

Functionals of Wiener Processes

Eckhard Platen, Jan Baldeaux, E. Platen, 2013 .

Capital Asset Pricing for Markets with Intensity Based Jumps

E. Platen, 2006 .

2 Continuous Benchmark Model 2 . 1 Primary Security Accounts

E. Platen, 2005 .

A Benchmark Framework for Risk Management

E. Platen, 2003 .

Hedging of Options under Discrete Observation on Assets with Stochastic Volatility

Wolfgang J. Runggaldier, Eckhard Platen, G. B. Di Masi, 1995 .

A Benchmark Approach to Quantitative Finance

D. Heath, E. Platen, 2006 .

Modelling the Stochastic Dynamics of Volatility for Equity Indices

D. Heath, E. Platen, Simon R. Hurst, 1999 .

Existence of equivalent local martingale deflators in semimartingale market models

E. Platen, Stefan Tappe, 2020, 2006.01572.

No-arbitrage concepts in topological vector lattices

E. Platen, Stefan Tappe, 2020, Positivity.

Local risk-minimization under the benchmark approach

Eckhard Platen, Francesca Biagini, Alessandra Cretarola, 2012, 1210.2337.

Natural Disasters, Insurance Stocks and the Numeraire Portfolio

E. Platen, J. West, 2014 .

Investments for the Short and Long Run

E. Platen, 2005 .

Various Approaches to Asset Pricing

D. Heath, E. Platen, 2006 .

Stochastic Differential Equations with Jumps

Nicola Bruti-Liberati, Eckhard Platen, E. Platen, 2010 .

On the Strong Approximation of Jump-Diffusion Processes

Nicola Bruti-Liberati, Eckhard Platen, E. Platen, 2005 .

Processes of class Sigma, last passage times and drawdowns

Ashkan Nikeghbali, Patrick Cheridito, Eckhard Platen, 2009, 0910.5493.

Minimizing the Expected Market Time to Reach a Certain Wealth Level

Eckhard Platen, Constantinos Kardaras, E. Platen, 2009, SIAM J. Financial Math..

Exact Simulation of Solutions of SDEs

Eckhard Platen, Nicola Bruti-Liberati, E. Platen, 2010 .

Pricing via anticipative stochastic calculus

E. Platen, R. Rebolledo, 1994, Advances in Applied Probability.

An Intraday Empirical Analysis of Electricity Price Behaviour

E. Platen, W. Breymann, J. West, 2004 .

Comment on "Numerical methods for stochastic differential equations".

Kevin Burrage, Eckhard Platen, Pamela Burrage, 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

On the numerical stability of simulation methods for SDEs under multiplicative noise in finance

Eckhard Platen, E. Platen, Lei Shi, 2008 .

Stability of weak numerical schemes for stochastic differential equations

Eckhard Platen, E. Platen, N. Hofmann, 1994 .

Time Discrete Approximation of Deterministic Differential Equations

P. Kloeden, E. Platen, 1992 .

Monte Carlo and Quasi-Monte Carlo Methods

Eckhard Platen, Jan Baldeaux, E. Platen, 2013 .

About secretary problems

E. Platen, E. Platen, 1980 .

Hedging for the long run

E. Platen, H. Hulley, 2012 .

On the existence of sure profits via flash strategies

Markus Pelger, Eckhard Platen, Claudio Fontana, 2017, Journal of Applied Probability.

Sure profits via flash strategies and the impossibility of predictable jumps

E. Platen, Markus Pelger, Claudio Fontana, 2017 .

Market Efficiency and Growth Optimal Portfolio

E. Platen, Renata Rendek, 2017, 1706.06832.

Real-World Pricing for a Modified Constant Elasticity of Variance Model

E. Platen, Shane Miller, 2010 .

Pollard, D.:Convergence of stochastic processes. (Springer series in statistics). Springer‐Verlag, New York ‐ Berlin ‐ Heidelberg ‐ Tokyo 1984, 216 pp., 36 illustr., DM 82

E. Platen, 1986 .

Intraday Empirical Analysis and Modeling of Diversified World Stock Indices

E. Platen, W. Breymann, Leah A. Kelly, 2005 .

Filtering and Parameter Estimation for a Mean Reverting Interest Rate Model

Robert J. Elliott, Eckhard Platen, R. Elliott, 1999 .

Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices

Eckhard Platen, Renata Rendek, E. Platen, 2007 .

Estimation for discretely observed diffusions using transform functions

Michael Sørensen, Eckhard Platen, E. Platen, 2003, Journal of Applied Probability.

A dynamic portfolio approach to asset markets and monetary policy

E. Platen, W. Semmler, 2012 .

Detecting Money Market Bubbles

E. Platen, Jan Baldeaux, Katja Ignatieva, 2016 .

Alternative Term Structure Models for Reviewing Expectations Puzzles

E. Platen, Christina Sklibosios Nikitopoulos, 2012 .

A Fair Pricing Approach to Weather Derivatives

Jason West, Eckhard Platen, E. Platen, 2004 .

Risk Minimizing Hedging Strategies Under Partial Observation

Wolfgang J. Runggaldier, Eckhard Platen, Paul Fischer, 1999 .

A Benchmark Approach to Filtering in Finance

Wolfgang J. Runggaldier, Eckhard Platen, E. Platen, 2004 .

A hardware generator of multi-point distributed random numbers for Monte Carlo simulation

Massimo Piccardi, Eckhard Platen, Nicola Bruti Liberati, 2008, Math. Comput. Simul..

Pricing of index options under a minimal market model with log-normal scaling

D. Heath, E. Platen, 2003 .

Sure profits via flash strategies and the impossibility of predictable jumps

E. Platen, Markus Pelger, Claudio Fontana, 2017 .

Ito Stochastic Calculus

P. Kloeden, E. Platen, 1992 .

Pricing volatility derivatives under the modified constant elasticity of variance model

Eckhard Platen, Leunglung Chan, E. Platen, 2015, Oper. Res. Lett..

Three-Benchmarked Risk Minimization for Jump Diffusion Markets

E. Platen, Ke Du, 2011 .

On honest times in financial modeling

E. Platen, A. Nikeghbali, 2008, 0808.2892.

Quantitative Finance Research Centre Quantitative Finance Research Centre on Honest times in Financial Modelling on Honest times in Financial Modeling

E. Platen, A. Nikeghbali, 2022 .

Robust Product Markovian Quantization

E. Platen, Thomas Andrew McWalter, Ralph Rudd, 2020, SSRN Electronic Journal.

Fast Quantization of Stochastic Volatility Models

Eckhard Platen, Ralph Rudd, Thomas A. McWalter, 2017, 1704.06388.

2 Quantization of Single-factor Models

E. Platen, Ralph Rudd, A. Thomas, 2017 .

A Visual Classification of Local Martingales

E. Platen, H. Hulley, 2008 .

Numerical Solutions of Stochastic Differential Equations

P. Kloeden, E. Platen, 1995 .

Higher Order Approximate Markov Chain Filters

Peter E. Kloeden, Eckhard Platen, Henri Schurz, 1993 .

WEAK CONVERGENCE OF SEMIMARTINGALES AND DISCRETISATION METHODS

Rolando Rebolledo, Eckhard Platen, E. Platen, 1985 .

Continuous Stochastic Processes

E. Platen, Jan Baldeaux, 2013 .

Probability Theory and Stochastic Processes

Eckhard Platen, Peter E. Kloeden, P. Kloeden, 1992 .

Selected Applications of Strong Approximations

P. Kloeden, E. Platen, 1992 .

ON THE DYBVIG‐INGERSOLL‐ROSS THEOREM

E. Platen, C. Kardaras, 2009, 0901.2080.

Time Delay and Noise Explaining Cyclical Fluctuations in Prices of Commodities

E. Platen, U. Küchler, 2007 .

Probability and Statistics

P. Kloeden, E. Platen, 1992 .

On effects of discretization on estimators of drift parameters for diffusion processes

Peter E. Kloeden, Michael Sørensen, Eckhard Platen, 1996, Journal of Applied Probability.

Modelling Co-movements and Tail Dependency in the International Stock Market via Copulae

E. Platen, Katja Ignatieva, 2009 .