1. Mathematical
Finance
Mario Dell’Era
Probability
Theory
Probability Space
Joint and Conditional
Probability
Random Variable
Moments
Conditional expected
value
Law of Large
Numbers
Theorem of Central
Limit
Stochastic
Processes
Characteristics of
Stochastic
Processes
L´evy’s Processes
Wiener’s Processes
Poisson’s Processes
Itˆo’s Processes
Martingale
Radon Nikodym’s
Theorem
Girsanov’s Theorem
Feynman-Kaˇc’s
Theorem
Mario Dell’Era
Quantitative Risk Analyst
E-QuanT bootcamp 2014 at IMT in Lucca(IT) 13-17 October 2014
Mario Dell’Era (Quantitative Risk Analyst) Mathematical Finance E-QuanT Bootcamp 2014 0 / 43

2. Mathematical
Finance
Mario Dell’Era
Probability
Theory
Probability Space
Joint and Conditional
Probability
Random Variable
Moments
Conditional expected
value
Law of Large
Numbers
Theorem of Central
Limit
Stochastic
Processes
Characteristics of
Stochastic
Processes
L´evy’s Processes
Wiener’s Processes
Poisson’s Processes
Itˆo’s Processes
Martingale
Radon Nikodym’s
Theorem
Girsanov’s Theorem
Feynman-Kaˇc’s
Theorem
Mathematical Finance
with MatLab
Mario Dell’Era
Analyst at IntesaSanpaolo and External Professor at Pisa University
m.dellera@be-tse.it
Quantitative Risk Analyst
E-QuanT bootcamp 2014
Mario Dell’Era (Quantitative Risk Analyst) Mathematical Finance E-QuanT Bootcamp 2014 1 / 43

3. Mathematical
Finance
Mario Dell’Era
Probability
Theory
Probability Space
Joint and Conditional
Probability
Random Variable
Moments
Conditional expected
value
Law of Large
Numbers
Theorem of Central
Limit
Stochastic
Processes
Characteristics of
Stochastic
Processes
L´evy’s Processes
Wiener’s Processes
Poisson’s Processes
Itˆo’s Processes
Martingale
Radon Nikodym’s
Theorem
Girsanov’s Theorem
Feynman-Kaˇc’s
Theorem
1 Probability Theory
Probability Space
Joint and Conditional Probability
Random Variable
Moments
Conditional expected value
Law of Large Numbers
Theorem of Central Limit
2 Stochastic Processes
Characteristics of Stochastic Processes
L´evy’s Processes
Wiener’s Processes
Poisson’s Processes
Itˆo’s Processes
Martingale
Radon Nikodym’s Theorem
Girsanov’s Theorem
Feynman-Kaˇc’s Theorem
Mario Dell’Era (Quantitative Risk Analyst) Mathematical Finance E-QuanT Bootcamp 2014 1 / 43