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Section: New Results

Financial Mathematics

Participants : Mireille Bossy, Paul Charton, El Hadj Aly Dia, Dalia Ibrahim, Denis Talay, Etienne Tanré.

Published works and preprints

  • In collaboration with N. Maïzi (CMA – Mines Paristech) and O. Pourtallier (Coprin team, INRIA Sophia Antipolis – Méditerranée), M. Bossy, and E.H.A. Dia studied the indifference pricing for carbon emission allowances, as a short term model value of carbon (see Section  7.1.2 ). The indifference pricing methodology describes the way an industrial agent on the emission allowances market chooses his production strategy. An utility function represents the preferences of the producer and its risk aversion. The outputs of its production have stochastic prices on the market, so that the optimal production strategy arises as the solution of a stochastic control problem.

    We extended the model hypotheses under which we get the well-posedness of the stochastic control problem and the associated HJB equation. We exhibited a simple case (marginal costs constant in time) where we proved the regularity of the value function via the explicit solution of the stochastic control problem [24] , http://hal.inria.fr/hal-00645033/en . This particular case now can serve as a benchmark for the numerical solver currently developed in the framework of the ADEME Convention. It will also serve as a demonstrator case, with the objective of a public diffusion of the simulator CarbonQuant.

  • M. Cissé (ENSAE-Sénégal), P. Patie (Univ. libre de Bruxelles) and E. Tanré have solved explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion [17] , http://hal.inria.fr/inria-00458901/en/ .

Other works in progress

  • P. Charton continued his PhD. under the supervision of M. Deaconu and A. Lejay. He studied some hedging strategies for day ahead markets of wind energy.

  • Mathematical modelling for technical analysis techniques Since November 2009, D. Ibrahim has been working on her PhD. thesis on Mathematical modeling of technical analysis in finance, under supervision of D. Talay and E. Tanré. The aim of her work is to study the performances of a technical analysis tool designed to detect changes in the volatility term: the Bollinger Bands. First, she studied the performances of this indicator in a modified Black-Scholes model such that the rate of volatility changes at an unknown random time τ, independent of the Brownian motion governing the prices. She is interested to study whether this indicator can detect the changes in the volatility. So, she aims to study the tail probability of this indicator by using Karamata's Tauberian Theorem for Laplace-Stieltjes transforms.

    Secondly, she exhibited a mathematical optimal strategy by modifying usual techniques in both the dual and the classical PDE approaches in stochastic control theory, in order to circumvent the discontinuity of the filtration generated by the price process.

    This work is part of the contract with FINRISK (see Section  8.3 ).

  • P. Protter (Columbia University) and D. Talay started to develop a new bubble time evolution model.