We develop approximate formulae expressed in terms of elementary functions for the
density, the price and the Greeks of path dependent options of Asian style, in a general local …

Asian options incorporate the average stock price in the terminal payoff. Examination of the
Asian option partial differential equation (PDE) has resulted in many equations of reduced …

We demonstrate the power of symmetry in the resolution of some evolution partial differential
equations which arise in various aspects of finance. The essential theme is that which Lie …

The 2008 financial crisis forced investors to be more concerned with the risk management of
financial instruments, especially derivatives. The main objective of this paper is to study the …

The optimal investment-consumption problem under the constant elasticity of variance
(CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry …

Previous analysis and research on the power option–one of the exotic options–have
focused on the interest rate of the stock and its volatility as constant parameters throughout …

In recent years, many advanced techniques have been applied to financial problems;
however, very few scholars have used the Lie theory. The purpose of this study was to …

A significant portion of the mathematical finance literature is devoted to constructing exact
pricing formulas for a variety of contingent claims whose underlying assets are assumed to …

Анотація Використовуючи класичний метод Лі-Овсяннікова, знайдено максимальну
алгебру інваріантності рівняння, яке випливає з рівняння ціноутворення азійських …

In this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie
algebras. To do it, we use the nilpotent Lie algebra, g_n, formed of n× n strictly upper …