• Kyungpook Mathematical Journal
• /
• v.45 no.4
• /
• pp.471-480
• /
• 2005

This paper deals with some useful methods of solving the one-dimensional integral equation of Fredholm type. Application of the reduction techniques with a view to inverting a class of integral equation with Lauricella function in the kernel, Riemann-Liouville fractional integral operators as well as Weyl operators have been made to reduce to this class to generalized Stieltjes transform and inversion of which yields solution of the integral equation. Use of Mellin transform technique has also been made to solve the Fredholm integral equation pertaining to certain polynomials and H-functions.

• East Asian mathematical journal
• /
• v.32 no.3
• /
• pp.301-310
• /
• 2016

Lookback options, in the terminology of nance, are a type of exotic option with path dependency whose the payoff depends on the optimal (maximum or minimum) underlying asset's price occurring over the life of the option. In this paper, we exploit Mellin transform techniques to find a closed-form solution for European lookback options in Black-Scholes model.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.345-360
• /
• 2018

In finance, barrier options are options contracts with a payoff that depends on whether the price of the underlying asset hits a predetermined barrier level during the option's lifetime. Based on exotic options and random fluctuations of interest rates in the marketplace, we consider discount barrier options with a stochastic interest rate driven by the Hull-White process. This paper derives the closed-form solutions of the discount barrier option and the discount double barrier option using Mellin transform methods and the PDE (partial differential equation) method of images.