Obstacle problem for Arithmetic Asian options
Laura Monti, Andrea Pascucci
TL;DR
This paper establishes the existence, regularity, and a Feynman-Kac representation for the strong solution of the free boundary problem in pricing American Asian options with arithmetic averaging.
Contribution
It provides the first rigorous mathematical analysis of the obstacle problem for American Asian options with arithmetic average, including existence, regularity, and representation formulas.
Findings
Proved existence and regularity of the solution.
Derived a Feynman-Kac representation formula.
Analyzed the free boundary problem in detail.
Abstract
We prove existence, regularity and a Feynman-Ka\v{c} representation formula of the strong solution to the free boundary problem arising in the financial problem of the pricing of the American Asian option with arithmetic average.
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Taxonomy
TopicsStochastic processes and financial applications · Insurance, Mortality, Demography, Risk Management · advanced mathematical theories