Recent Advances in Financial Engineering 2009: Proceedings by Masaaki Kijima, Chiaki Hara, Kei-Ichi Tanaka, Yukio

By Masaaki Kijima, Chiaki Hara, Kei-Ichi Tanaka, Yukio Muromachi

This booklet comprises eleven papers in keeping with learn offered on the KIER-TMU overseas Workshop on monetary Engineering, held in Tokyo in 2009. The Workshop, organised by means of Kyoto University's Institute of financial study (KIER) and Tokyo Metropolitan collage (TMU), is the successor to the Daiwa overseas Workshop on monetary Engineering held from 2004 to 2008 by way of Professor Kijima (the Chair of this Workshop) and his colleagues. educational researchers and practitioners alike have provided the newest examine on monetary engineering at this overseas venue. those papers handle cutting-edge options in monetary engineering, and feature passed through a rigorous choice technique to make this ebook an effective one. This quantity should be of curiosity to lecturers, practitioners, and graduate scholars within the box of quantitative finance and monetary engineering.

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Extra info for Recent Advances in Financial Engineering 2009: Proceedings of the KIER-TMU International Workshop on Financial Engineering 2009

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Proof. 1. Continuity can be proved as follows. 1, Φ∗ and Φ∗ respectively are semicontinuous supersolution and subsolution of the RS HJB PIDE (23) subject to terminal condition (25). 1 is that Φ∗ ≥ Φ∗ and hence Φ∗ = Φ∗ is a continuous viscosity solution of the RS HJB PIDE (23) subject to terminal condition (25). Hence, Φ = Φ∗ = Φ∗ and it is the unique continuous viscosity solution of the RS HJB PIDE (23) subject to terminal condition (25). Now that we have proved uniqueness and continuity of the viscosity solution Φ to the RS HJB PIDE (23) subject to terminal condition (25), we can deduce that the RS HJB PIDE (27) subject to terminal condition (28) also has a unique ˜ continuous viscosity solution.

Function Φ Step 2: Viscosity Subsolution Let (t0 , x0 ) ∈ Q := [0, t] × Rn and u ∈ C 1,2 (Q) satisfy ˜ ∗ − u)(t0 , x0 ) = max (Φ ˜ ∗ (t, x) − u(t, x)) 0 = (Φ (44) ˜ ≤Φ ˜∗ ≤ u Φ (45) (t,x)∈Q and hence on Q. Let (tk , xk ) be a sequence in Q such that lim (tk , xk ) = (t0 , x0 ) k→∞ ˜ k , xk ) = Φ ˜ ∗ (t0 , x0 ) lim Φ(t k→∞ ˜ k , xk ) − u(tk , xk ). Since u is of class C 1,2 , and define the sequence {ξ}k as ξk := Φ(t limk→∞ ξk = 0. May 3, 2010 13:34 Proceedings Trim Size: 9in x 6in 001 25 Fix h ∈ J and consider a constant control hˆ = h.

21. D. Duffie, D. Filipovic, and W. Schachermayer. Affine processes and applications in finance. Annals of Applied Probability, 13:984–1053, 2003. 22. D. -L. Lions. PDE solutions of stochastic differential utility. Journal of Mathematical Economics, 21(6):577–606, 1992. 23. D. Duffie, J. Pan, and K. Singleton. Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68(6):1343–1376, 2000. 24. D. Duffie and K. J. Singleton. Credit Risk: Pricing, Measurement and Management. Princeton University Press, 2003.

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