Ongoing projects
- Adding and subtracting Merton: A new approach for the optimal portfolio problem
- Proposed a diffusion-operator-integral-expansion-based method to solve optimal investment and consumption problems under several models.
- Programmed for numerical experiments for the application of the proposed method to the optimal investment problem under several stochastic models, including the CEV, Heston, 4/2, SABR model, and optimal investment-consumption problem under the Heston model.
- Offline simulation of portfolio default risk under stochastic volatility models
- Replicated numerical tests implemented in Jiang et al. (2019) to verify their proposed method to measure the portfolio default risk.
- Combined variance reduction techniques like EMS to the simulation as a modification to the perturbation method.
- Designed and programmed for additional experiments for underlying assets modeled by the 3/2 model, α-hypergeometric model and portfolio including path-dependent products like arithmetic Asian options and lookback options to illustrate the accuracy and efficiency of the proposed method.
- Explicit quantile through Fourier cosine expansion and Lagrange inversion
- Derived an explicit representation of quantile in terms of the specified probability utilizing Fourier cosine expansion and Lagrange inversion theorem.
- Derived an alternative representation of quantile by a direct expansion of the cumulative density function.
- Implemented a numerical test of normal distribution.
