On a parabolic free boundary equation modeling price formation

Mathematical Models and Methods in Applied Sciences

Volumn 19, Issue 10, 2009, Pages 1929-1957

  Markowich, P A ^a,b   Matevosyan, N ^a   Pietschmann, J F ^a   Wolfram, M T ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

Free boundary problem; Partial differential equations; Price formation

Indexed keywords

DYNAMICAL FORMATION; EVOLUTION EQUATIONS; EXISTENCE AND UNIQUENESS; EXISTENCE AND UNIQUENESS OF SOLUTION; FREE BOUNDARY; FREE BOUNDARY PROBLEM; FREE-BOUNDARY PROBLEMS; LOCAL SOLUTION; NUMERICAL RESULTS; PRICE FORMATION;

COMPUTATIONAL FLUID DYNAMICS; PARTIAL DIFFERENTIAL EQUATIONS;

COSTS;

EID: 72549117081     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202509003978     Document Type: Article

References (14)

1. F. Castella, L. Erdös, F. Frommlet and P. A. Markowich, Fokker-Planck equations as scaling limits of reversible quantum systems, J. Statist. Phys. 100 (2000) 543-601.
2. C. Cercignani, Kinetic Theories and the Boltzmann Equation: Lectures Given at the 1st 1981 Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), held at Mon-tecatini, Italy, June 10-18, 1981 (Springer, 1984).
3. M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math. 93 (1971) 265-298.
4. L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, Vol.19 (Amer. Math. Soc, 1998).
5. M. D. M. Gonzalez and M. P. Gualdani, Asymptotics for a free-boundary problem in price formation, preprint.
6. M. D. M. Gonzalez and M. P. Gualdani, Asymptotics for a symmetric equation in price formation, AMO, 2008.
7. J.-M. Lasry and P.-L. Lions, Jeux à champ Moyen. I. Le cas stationnaire, C. R. Math. Acad. Sci. Paris 343 (2006) 619-625.
8. J.-M. Lasry and P.-L. Lions, Jeux à champ Moyen. II. Horizon finiet contrǒle optimal, C. R. Math. Acad. Sci. Paris 343 (2006) 679-684.
9. J.-M. Lasry and P.-L. Lions, Mean-field games, Jpn. J. Math. 2 (2007) 229-260.
10. P.-L. Lions and J.-M. Lasry, Towards a self-consistent theory of volatility, J. Math. Pures Appl. 86 (2006) 541-551.
11. P.-L. Lions and J.-M. Lasry, Instantaneous self-fulfilling of long-term prophecies on the probabilistic distribution of financial asset values, Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 361-368.
12. P.-L. Lions and J.-M. Lasry, Large investor trading impacts on volatility, in Paris - Princeton Lectures on Mathematical Finance 2004, Lecture Notes in Math., Vol.1919 (Springer, 2007), pp. 173-190.
13. P.-L. Lions and J.-M. Lasry, Large investor trading impacts on volatility, Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 311-323.
14. G. Rein, Collisionless kinetic equations from astrophysics - the Vlasov-Poisson system, in Evolutionary Equations (Elsevier, 2006).