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Convergence analysis of a monotonic penalty method for American option pricing. (English) Zbl 1154.91029
Under the non-arbitrage assumption the American option pricing problem can be stated as linear differential complementarity problem with a Black-Scholes differential operator. Using variational theory and corresponding weighted Sobolev spaces a coerciveness result can be shown, which gives the existence of a unique solution. Then a monotonic penalty approach is studied. The penalized problems are uniquely solvable and the solutions are sufficiently smooth. Convergence analysis follows (with full proofs). For a combination of two power penalty methods convergence rates can be given, containing several such rates for special penalty approaches.
MSC:
91B28Finance etc. (MSC2000)
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
90C48Programming in abstract spaces
49M30Other numerical methods in calculus of variations
49J40Variational methods including variational inequalities