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Position: PhD Position Numerical Methods for Stochastic Differential Equations
Institution: Delft University of Technology
Location: Delft, South Holland, Netherlands
Duties: The focus of the project lies on the numerical approximation of solutions to stochastic differential equations, which due to the form of these equations are not Markov processes. Such stochastic processes "with memory" are of importance in several disciplines, such as for financial and statistical modelling. However, due to the correlation structure their computational simulation is very challenging. The PhD project addresses this challenge. Possible topics are computational methods for stochastic equations driven by fractional Brownian motion and multilevel Monte Carlo methods. Applications include option pricing under rough volatility models in finance and long-range dependencies in statistics
Requirements: Completed Master's degree or diploma in the field of Mathematics or a closely related field (completed or about to be completed); A strong background in Numerical Analysis and/or in Probability Theory; Enthusiasm for abstract mathematical problems and persistance in solving them
   
Text: PhD Position Numerical Methods for Stochastic Differential Equations The focus of the project lies on the numerical approximation of solutions to stochastic differential equations, which due to the form of these equations are not Markov processes. Such stochastic processes "with memory" are of importance in several disciplines, such as for financial and statistical modelling. However, due to the correlation structure their computational simulation is very challenging. The PhD project addresses this challenge. Possible topics are computational methods for stochastic equations driven by fractional Brownian motion and multilevel Monte Carlo methods. Applications include option pricing under rough volatility models in finance and long-range dependencies in statistics Completed Master's degree or diploma in the field of Mathematics or a closely related field (completed or about to be completed); A strong background in Numerical Analysis and/or in Probability Theory; Enthusiasm for abstract mathematical problems and persistance in solving them
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