We present efficient partial differential equation (PDE) methods for continuous time mean-variance portfolio allocation problems when the underlying risky asset follows a jump-diffusion. The standard formulation of mean-variance optimal portfolio allocation problems, where the total wealth is...

In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the...

Many problem classes in Finance lead to high-dimensional partial differential equations (PDEs), which need to be solved efficiently. Currently, several methods exist to either circumnavigate the curse of dimensionality or use parallel High Performance Computing to calculate solutions despite it....

The rapid development of artificial intelligence methods contributes to their wide applications for forecasting various financial risks in recent years. This study introduces a novel explainable case-based reasoning (CBR) approach without a requirement of rich expertise in financial risk....

One of the most important factors to control for the achievements of investment portfolio returns is risk. If we only think that a 100% positive return is needed to recover a portfolio loss of 50%, we can understand why. With the advent of the exponential growth of technology usage in markets,...

Bernardo and Ledoit (2000) develop a very appealing framework to compute pricing bounds based on the so-called gain-loss ratio. Their method has many advantages and very interesting properties and so far one important drawback: the complexity of the numerical computation of the pricing bounds....

Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic differentiation (AD), also known as algorithmic...

In this paper, motivated by the approximation of Martingale Optimal Transport problems, we are interested in sampling methods preserving the convex order for two probability measures µ and ν on ℝ^d, with ν dominating µ. When (X_i)1≤i≤I (resp. (Y_j)1≤j≤J ) are independent and...

This chapter discusses computational methods for approximating portfolio and asset pricing problems. Formulation of these problems is usually specified along with components, preferences, payoffs, etc., that are analytic functions. This implies that the solutions to these problems acquire this...

Several swap rate derivatives e.g. constant maturity swaps can only be valued after a convexity correction. One approach is to use a Taylor series expansion to gain an analytical approximation but the result is neither a tradeable asset nor can the information of the volatility cube be included....