Data-driven discovery of “hidden physics''---ie, machine learning of differential equation
models underlying observed data---has recently been approached by embedding the …

Many financial assets, such as currencies, commodities, and equity stocks, exhibit both
jumps and stochastic volatility, which are especially prominent in the market after the …

In general, no analytical formulas exist for pricing discretely monitored exotic options, even
when a geometric Brownian motion governs the risk-neutral underlying. While specialized …

This paper proposes a new approach to solve finite-horizon optimal stopping problems for a
class of Markov processes that includes one-dimensional diffusions, birth–death processes …

Abstract Continuous time Markov Chain (CTMC) approximation techniques have received
increasing attention in the option pricing literature, due to their ability to solve complex …

This paper extends and refines the method of option pricing by frame projection of
riskneutral densities to incorporate general basis splines (B-splines), including the cubic …

The prices of Asian options, which are among the most important options in financial
engineering, can often be written in terms of Laplace transforms. However, computable error …

We construct efficient and accurate numerical algorithms for pricing discretely monitored
barrier and Bermudan style options under time-changed Lévy processes by applying the fast …

This paper studies additive subordination, which we show is a useful technique for
constructing time-inhomogeneous Markov processes with analytical tractability. This …

Using the weighted and shifted Lubich difference (WSLD) operator, we propose an efficient
and stable difference scheme for solving space tempered fractional diffusion equations. The …