Quantitative Analysis.
Trading Platform.
Python for Excel.
Author.

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I.Basic math.
II.Pricing and Hedging.
III.Explicit techniques.
IV.Data Analysis.
V.Implementation tools.
VI.Basic Math II.
VII.Implementation tools II.
1.Calculational Linear Algebra.
2.Wavelet Analysis.
3.Finite element method.
4.Construction of approximation spaces.
5.Time discretization.
6.Variational inequalities.
7.Lattice approach to derivative pricing.
A.Basic definitions of the lattice approach.
B.Markov Generator for smooth process. Dyson decomposition. Kolmogorov equations.
C.Path-Integral representation of Markov generator.
D.Markov generator for piecewise smooth process.
a.Change of measure on lattice between jumps.
b.Change of measure at jump points.
c.Connection to generic change of numeraire.
d.Monotonic processes and martingales.
e.Self financing strategies. Arbitrage. Fundamental theorem of finance.
E.Fast exponentiation.
Bibliography.
Forum Notation Index Contents

Connection to generic change of numeraire.

e previously introduced the change of measure in the section ( Change of measure definition ) with the defining property

MATH(change of measure requirement)
where the $X_{T}$ is any process, $a_{t}$ is some martingale process starting at $a_{0}=1$, MATH is the original expectation and MATH is the new expectation defined by the process $a_{t}$. In context of the present chapterMATH where we restricted our attention to Markov processes MATH. We are seeking a transformation rule for a new propagator $\tilde{P}$ that corresponds to MATH:MATH for any Markov processes MATH. Let $a_{t}$ be a markov process MATH. According to the formula ( change of measure requirement) MATH If we set MATH for a variety of $y^{\ast}$ thenMATH Consequently,MATH

Summary

The change of measure given by the Markov process MATH according to the formulaMATH transforms the pair $P_{m},L_{m}$ into the pair MATH according to the formulasMATH





Forum Notation Index Contents


















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