Sem 3 UNS Finance

Sem 3 UNS Finance

Applications  @  UNS  30 ECTS credits

Mathematical modelling applications to finance

The semester in Nice (UNS) will focus on "Mathematical Modelling Applications to Finance". Given the economic and social landscape, it aims to train engineers provided with a double strong ability, in both rigorous mathematics and tools from the specific application field, together with a deep experience in informatics. Precisely, students will be supplied with a strong theoretical and numerical mathematical and computational background as used in banks and insurance companies and will be given a solid knowledge in financial analysis including a specific course about the related stakes and rules that have emerged since the financial crisis. In particular, major objectives of the master are to train highly qualified engineers able both to apply sophisticated mathematical tools to describe, analyze and simulate complex systems such as trading markets and to keep thinking their activity as connected with real economy. Most of the lectures will be given within the framework of the Master's programme "Mathematics and Interaction" that will start in next September in Nice. Indeed, a branch of this new programme will consist of a continuation of the older Master's programme "Engineering Mathematics in Economy and Actuarial Sciences", referred to as IMEA in the French denomination. In addition to the academic courses, workshops will be organized in collaboration with professionals lecturers from local or national companies or researchers from the Economy Department or from other institutions such as INRIA. Public research institutions and private industrial groups are the principal employers for engineers issued from this track, including banks, universities, companies specialized in simulation and consulting from any industrial field, etc...

 

Below you can find information about the subjects for this semester.

Stochastic calculus [6 credits]

  • ECTS credits 6
  • Semester 3
  • University University of Nice - Sophia Antipolis
  • Topics

     

     - Brownian motion, Markov Property
    - Continuous time Martingals, Doob's theorem
    - Stochastic Integral
    - Ito formula
    - Introduction to Black Scholes model

Probabilistic numerical methods [6 credits]

  • ECTS credits 6
  • Semester 3
  • University University of Nice - Sophia Antipolis
  • Topics

     

     - Introduction Monte Carlo methods
    - Simulation of SDE (Stochastic differential Equation)
    - Euler's scheme, speed of convergence
    - Monte Carlo for PDE, Feynman Ka formula
    - Application to Black Scholes
    - Hitting time

Numerical methods for PDE, application to mathematical finance [6 credits]

  • ECTS credits 6
  • Semester 3
  • University University of Nice - Sophia Antipolis
  • Topics

     

     - Finite Volumn discretization for scalar hyperbolic equation
    - FV discretization for linear hyperbolic equation
    - FV discretization for non linear hyperbolic equation
    - FV discretization for elliptic equation
    - Detail: maximum principle, Poincare inequality, consistency, stability, CFL condition

Statistical inference in the regression setting [6 credits]

  • ECTS credits 6
  • Semester 3
  • University University of Nice - Sophia Antipolis
  • Topics

     

     - Introduction to statistical model
    - Confident interval, confident set
    - Hypothesis testing
    - Build confident set (Slutsky's lemma, stabilizing variance methods)
    - Build test (power of the test), estimator (maximum likelihood)
    - Distribution function, quartile function

Stochastic control for mathematical finance [6 credits]

  • ECTS credits 6
  • Semester 3
  • University University of Nice - Sophia Antipolis
  • Topics

     

    - One period controlled models in finance
    - Dynamic programming principle for discrete models
    - Dynamic programming principle for time discrete models
    - Time continuous models
    - Detail: allocation problem, controlled SDE (stochastic differential equation)

Home Program structure Third Semester UNS Math. Mod. App. to Finance

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University of L'Aquila, Italy (UAQ)

Department of Information Engineering, Computer Science and Mathematics, via Vetoio (Coppito), 1 – 67100 L’Aquila (Italy)

Autonomous University of Barcelona, Catalonia - Spain (UAB)

Departament de Matemàtiques, Edifici Cc - Campus UAB 08193 Bellaterra – Catalonia

Gdansk University of Technology, Poland (GUT)

Department of Solid State Physics, G. Narutowicza 11/12, 80-952 Gdansk, Poland

University of Hamburg, Germany (UHH)

Department of Mathematics
Bundesstr. 55 20146 Hamburg - Germany

University of Nice - Sophia Antipolis, France (UNS)

Laboratoire J.A.Dieudonné
Parc Valrose, France-06108 NICE Cedex 2

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