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...

One of the important issues in behavioral analysis is that the time consistency property is lost due to the distortion in performance probability. The standard approach in performance optimization, the dynamic programming, fails to work in this area. In this paper, we propose to use an...

This supplementary material for "Asymptotics for the Survival Probability of Time-Inhomogeneous Diffusion Processes" contains (i) some facts related to the normal density and distribution functions (Section 1), which are used in the calculation of explicit formulas in Equation (19) (Section 2);...

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...