Related papers: Sparse Grid Method for Highly Efficient Computatio…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
In this paper, we introduce a new method called SPSC (Simulation, Partitioning, Selection, Cloning) to estimate efficiently the probability of possible solutions in stochastic simulations. This method can be applied to any type of…
This work studies the dynamic risk management of the risk-neutral value of the potential credit losses on a portfolio of derivatives. Sensitivities-based hedging of such liability is sub-optimal because of bid-ask costs, pricing models…
Optimal execution of a portfolio have been a challenging problem for institutional investors. Traders face the trade-off between average trading price and uncertainty, and traditional methods suffer from the curse of dimensionality. Here,…
We investigate the portfolio selection problem against the systemic risk which is measured by CoVaR. We first demonstrate that the systemic risk of pure stock portfolios is essentially uncontrollable due to the contagion effect and the…
We show how one can actually take advantage of the strongly non-Gaussian nature of the fluctuations of financial assets to simplify the calculation of the Value-at-Risk of complex non linear portfolios. The resulting equations are not hard…
Probabilistic evaluation improves the trade-off between target coverage and OAR sparing in IMPT but remains computationally demanding. This study proposes sparse probabilistic evaluation (SPE), a computationally efficient approach…
This article develops the theory of risk budgeting portfolios, when we would like to impose weight constraints. It appears that the mathematical problem is more complex than the traditional risk budgeting problem. The formulation of the…
This paper explores option portfolio optimization when the underlying returns are skew-elliptical t-distributed. We use the variance and value at risk (VaR) to measure portfolio risk. The novelty of our work is the departure from the…
Machine learning (ML) methods have been successfully employed in identifying variables that can predict the equity premium of individual stocks. In this paper, we investigate if ML can also be helpful in selecting variables relevant for…
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice…
This paper aims to develop new mathematical and computational tools for modeling the distribution of portfolio returns across portfolios. We establish relevant mathematical formulas and propose efficient algorithms, drawing upon powerful…
We introduce a new numerical approximation method for functionals of factor credit portfolio models based on the theory of mod-$\phi$ convergence and mod-$\phi$ approximation schemes. The method can be understood as providing correction…
Considering the shortcomings of the traditional sample covariance matrix estimation, this paper proposes an improved global minimum variance portfolio model and named spectral corrected and regularized global minimum variance portfolio…
In academic literature portfolio risk management and hedging are often versed in the language of stochastic control and Hamilton--Jacobi--Bellman~(HJB) equations in continuous time. In practice the continuous-time framework of stochastic…
Nested stochastic modeling has been on the rise in many fields of the financial industry. Such modeling arises whenever certain components of a stochastic model are stochastically determined by other models. There are at least two main…
This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…
In this paper, we propose a sparse equity portfolio optimization (SEPO) based on the mean-variance portfolio selection model. Aimed at minimizing transaction cost by avoiding small investments, this new model includes $\ell_0$-norm…
In this paper we present a new approach to control variates for improving computational efficiency of Ensemble Monte Carlo. We present the approach using simulation of paths of a time-dependent nonlinear stochastic equation. The core idea…
When approximating the expectations of a functional of a solution to a stochastic differential equation, the numerical performance of deterministic quadrature methods, such as sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may…