Mathematical Models and Methods in Applied Sciences · 2001 · 139 citations · 16 references
BusinessEconomicsFinanceAsset PricingDifferential EquationsFinancial EconomicsArbitrage PricingNumerical Methods In FinanceOption PricingOption Pricing ModelsPartial Differential Equation ModelsPartial Differential EquationsElliptic Partial Differential EquationsNo-arbitrage ConditionsNonlinear Partial Differential EquationsNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsParabolic Partial Differential EquationsPartial Differential Equation SystemsWeak Form Of Partial Differential Equations
We analyze partial differential equations arising in the evaluation of Asian options. The equations are strongly degenerate partial differential equations in three dimensions. We show that the solution of the no-arbitrage partial differential equation is sufficiently regular and standard numerical methods can be employed to approximate it.
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Hypoelliptic second order differential equations
Lars Hörmander · Acta Mathematica · 1967 · 2.4K citations · Full text
A pricing method for options based on average asset values
A. G. Z. Kemna, A.C.F. Vorst · Journal of Banking & Finance · 1990 · 644 citations
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Business, Finance, Mathematics +14