Abstract
In this chapter we provide the proofs of the most demanding results of Chaps. 12–14. Have you noticed the (∗∗) in the title? It means “very difficult”. Given the dual nature of the proposed audience for the book (scholars and quants), I have provided in the first chapters a lot of background material. Yet I didn’t want to avoid the sometimes difficult mathematical technique that is needed for deep understanding. So, for the convenience of readers, we signal sections that contain advanced material with an asterisk (*) or even a double asterisk (**) for the still more difficult portions.
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Notes
- 1.
Cf. (12.63) for the definition of \(|\widehat{v} - \widehat{v} ^{\prime}| \).
- 2.
Nonnegative function from [0,∞] to itself, continuous and null at 0.
- 3.
Given the continuity of u.
- 4.
Given the continuity of v.
- 5.
See for instance the proof of the comparison principle of Proposition 12.1.10 in [87].
- 6.
Note that the following argument only works at T and cannot be adapted to the case of problem \((\mathcal{V}1)\) on the whole of \(\partial\mathcal{D}\); see the comment at the beginning of the proof.
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Crépey, S. (2013). Technical Proofs (∗∗). In: Financial Modeling. Springer Finance(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37113-4_15
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