Research Project 10

RP10. Numerical Solution of High-Dimensional BSDE’s (Kouma Gnameho)

WP 3, Leading Partner: Maastricht University. Supervisor: Prof. Antoon Pelsser

RP10 seeks to find efficient numerical methods to implement the pricing methods for realistic insurance products. In real-life applications, we need to model a high number of risk drivers simultaneously. Therefore, it is most likely that we will have to rely on Monte Carlo simulation methods. In particular, we are interested in the numerical solution of Backward Stochastic Differential Equations (BSDE’s) which arise in the study of the time-consistent pricing operators in RP9. In recent years, some progress has been made in the numerical solution of BSDE’s for low-dimensional problems. We aim to develop numerical methods that also work in high dimensions. The methods outlined in Brandt et al. (2005) [Brandt, M., A. Goyal, P. Santa-Clara, and J. Stroud, 2005, “A simulation approach to dynamic portfolio choice with an application to learning about return predictability,” Review of Financial Studies, 18, 831-873.] have been successfully applied to the problem of finding optimal investment strategies in high-dimensional problems. We feel that a promising research avenue is to apply this methodology to the numerical solution of high-dimensional BSDE’s.

Results

Deliverables

DELIVERABLE 4.4 on project 10 (K. K. Gnameho, Maastricht)

  • Gnameho, K.K., Stadje, M.A. & Pelsser, A. (2015), "Numerical Solution of Backward SDE’s: Regression Later Algorithm" [download]
  • Gnameho, K.K. & Pelsser, A. (2015), "Fourier-Hermite Expansion Algorithm for Backward SDE’s" [download]

Presentations

  • Gnameho, K.K., "Modeling Volatility Risk Premium" with prof. Juho Kanniainen & Ye Yue, Mathematical and Statistical Methods for Actuarial Science and Finance, Paris 30 March - 1 April 2016
  • Gnameho, K.K, "A Numerical Solution of Backward SDEs", The 2015 AMMCS-CAIMS Congres, Waterloo Ontario, Canada 7-12 June 2015
  • Gnameho, K.K. "Numerical Solution of Backward SDEs: Regression Later" Actuarial and Financial Mathematics Conference, Brussels, Belgium, 05-06 February 2015. [download]
  • Gnameho, K.K. "Numerical Solution of BSDE’s" Summer School: Numerical and quantitative methods in finance, Maastricht, Netherlands, 27 August 2013.

Final conference

Kossi Kouma Gnameho (Maastricht University): Numerical Solutions of Backward SDEs