This paper develops an analytical approach to compute the explicit asymptotic formulas for the probability that a time-inhomogeneous diffusion process does not cross a non-flat, lower/upper boundary. We derive the explicit formulas for the first four terms and provide the error bound. The...

This paper shows that a small-time Hermite expansion is feasible for multivariate diffusions. By introducing an innovative quasi-Lamperti transform, which unitizes the diffusion matrix at the initial time, we derive explicit recursive formulas for the expansion coefficients of transition...

We study optimal effort and compensation in a continuous-time model with three-sided moral hazard and cost synergies. One agent exerts initial effort to start the project; the other two agents exert ongoing effort to manage it. The project generates cash flow at a fixed rate over its lifespan;...

The stochastic-alpha-beta-rho (SABR) model is widely used by practitioners in interest rate and foreign exchange markets. The probability of hitting zero sheds light on the arbitrage-free small strike implied volatility of the SABR model, and the survival probability is also closely related to...

The stochastic-alpha-beta-rho (SABR) model is widely used in fixed income and foreign exchange markets as a benchmark. The underlying process may hit zero with a positive probability and therefore an absorbing boundary at zero should be specified to avoid arbitrage opportunities. However, a...

The after-hour fixed-price trading, such as Taiwan Stock Exchange (TWSE)'s and Nasdaq's Extended Trading Close, provides investors with the opportunity to trade at the closing price shortly after regular trading hours with full transparency. This paper examines the impact of disclosed unfilled...

Exchanges, including Nasdaq’s Extended Trading Close introduced in 2022, have implemented the after-hour fixed-price trading (hereinafter referred to as the fixed-price session) to enhance liquidity. Although the fixed trading price eliminates temporary price impact, execution risk remains....