Lévy-Sheffer Systems and the Longstaff-Schwartz Algorithm for ...

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The Longstaff-Schwartz Algorithm ◮ Approximation one: replace conditional expectations in the dynamic programming principle by projections on a finite set of functions taken from a suitable basis ◮ Approximation two: use Monte- Carlo simulations and least squares regression to compute the value function of the first approximation.
Convergence Results ◮ K basis functions, N Monte Carlo paths ◮ Partial results by Longstaff, Schwartz (2001) (2 exercise times) ◮ Clément, Lamberton, Protter (2002): ◮ Almost sure convergence of first approximation, as K to infinity ◮ K fixed: N to infinity, almost sure convergence of the MC procedure to the value function of approximation 1.
Page 1 and 2: Lévy-Sheffer Systems and the Longs
Page 3 and 4: Motivation ◮ Many financial instr
Page 5 and 6: Algorithms ◮ An optimal stopping
Page 7 and 8: Dynamic Programming ◮ Vn(x) = val
Page 9 and 10: The Longstaff-Schwartz Algorithm
Page 11: The Longstaff-Schwartz Algorithm
Page 15 and 16: Results of Glasserman and Yu (2004)
Page 17 and 18: Results of Glasserman and Yu (2004)
Page 19 and 20: The Models ◮ Geometric Poisson pr
Page 21 and 22: Properties of the Meixner Process
Page 23 and 24: Lévy-Sheffer Systems ◮ Sheffer S
Page 25 and 26: Examples of Lévy-Sheffer Systems
Page 27 and 28: Convergence Results (SG 2008) ◮ N
Page 29 and 30: Proof Ingredients of the Convergenc
Page 31: References ◮ J.F. Carriere: Valua

Lévy-Sheffer Systems and the Longstaff-Schwartz Algorithm for ...

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