List of Main Publications of Michael Mania

  1. On certain sufficient conditions of existence of a weak solution of stochastic differential equations. (Russian) Soobshch. Akad. Nauk Gruz. SSR  84 (1976), No. 3, 569-572.

  2. On the absolutely continuity and singularity of probability distributions of random fields. Soviet Math. Dokl.  22 (1980), No. 1,. 115-118.

  3. Delta-Martingales and their set of convergence. Soobshch. Akad. Nauk Gruz. SSR 99 (1980), No. 1, 45-48.

  4. On the conditions of an optimal control existence for controlled process with dominated family of measures. Proceedings of Int. Conference in Stochastic Optimization, Kiev, 1984, 148-150.

  5. A weak convergence of exponential martingales in H 1. Proc. of an International Conference of Young Sciencists, Varna, September 1985, 117-121.

  6. Optimal locally absolutely continuous change of measure. Finite set of decisions. I. Stochastics 21 (1987), No. 2, 131-185 (with R. Chitashvili).

  7. Optimal locally absolutely continuous change of measure. Finite set of decisions. II. Optimization problems. Stochastics 21 (1987), No. 3, 187-229 (with R. Chitashvili).

  8. On optimal controls in the problem of locally absolutely continuous change of measure (compact sets of decisions). Probability theory and mathematical statistics, Vol. I (Vilnius, 1985), 331-356, VNU Sci. Press, Utrecht, 1987 (with R. Chitashvili).

  9. Line integrals, stable space of martingales, compactization problems in optimal controls. Stochastic differential systems, Proc. IFIP-WG 7/1 Work. Conf., Eisenach/GDR 1986, Lecture Notes in Control and Inform. Science, 96, 253-271, 1987 (with R. Chitashvili). 

  10. On the sets of convergence of multiparameter martingales. Proc A. Razmadze Math. Inst. 92 (1989), 60-73.

  11. Decomposition of the maximum of semimartingales and generalized Itô's formula. New trends in probability and statistics, Vol. 1 (Bakuriani, 1990), 301-350, VSP, Utrecht, 1991 (with R. Chitashvili).

  12. Generalized Itô formula and derivation of Bellman's equation. Stochastic processes and related topics (Siegmundsberg, 1994), 1-21, Stochastics Monogr., 10, Gordon and Breach, Yverdon, 1996 (with R. Chitashvili).

  13. On functions transforming Brownian motion into a Dirichlet process. Probability theory and mathematical statistics (Tokyo, 1995), 20-27, World Sci. Publishing, River Edge, NJ, 1996  (with R. Chitashvili).

  14. Characterization of a regular family of semimartingales by line integrals. Georgian Math. J. 3 (1996), No. 6, 525-542 (with R. Chitashvili).

  15. On functions transforming a Wiener process into a semimartingale. Probab. Theory Related Fields 109 (1997), No. 1, 57-76 (with R. Chitashvili).

  16. Semimartingale characterization of generalized derivatives. Stochastics Stochastics Rep. 61 (1997), No. 1-2, 35-66.

  17. Derivation of a generalized Black-Scholes equation. Proc. A. Razmadze Math. Inst. 115 (1997), 121-148.

  18. Solution of Bellman's equation by means of a system of nonlinear singular integral equations. Mem. Differential Equations Math. Phys. 13 (1998), 121-129 (with R. Tevzadze).

  19. Semimartingale functions of a class of diffusion processes. Abstracts of the VII-th
    international Vilnius conference on Probability Theory, Vilnius,
    12-18 August 1998, pp. 317-318.

  20. Stochastic line integrals with respect to local martingales and semimartingales. Proc. A. Razmadze Math. Inst. 120 (1999), 1-26 (with R. Chitashvili).

  21. Quantitative methods of financial analysis. (Georgian) Tbilisi, 1999, 696 pp. (with N. Lazrieva,  G. Mirzashvili, T. Toronjadze, O Glonti and L. Jamburia).

  22. The main insurance principles in mathematical point of view. (Georgian) Tbilisi, 1999, 45 pp. (with G. Mirzashvili).

  23. Probability theory and mathematical statistics for economists. (Georgian) Tbilisi, 2000, 661 pp. (with N. Lazrieva, G. Mari, A. Mosidze, A. Toronjadze, T. Toronjadze and T. Shervashidze).

  24. Semimartingale functions for a class of diffusion processes. (Russian) Teor. Veroyatnost. i Primenen. 45 (2000), No. 2, 374-380; English transl.: Theory Probab. Appl.  45 (2000), No. 2, 337-343 (with R. Tevzadze).

  25. A semimartingale Bellman equation and the variance-optimal martingale measure. Georgian Math. J. 7 (2000), No. 4, 765-792 (with R. Tevzadze).

  26. A general problem of an optimal equivalent change of measure and contingent claim pricing in an incomplete market. Stochastic Process. Appl. 90 (2000), No. 1, 19-42.

  27. A semimartingale backward equation related to the p-optimal martingale measure and the lower price of a contingent claim. Stochastic processes and related topics (Siegmundsburg, 2000), 189-212, Stochastics Monogr., 12, Taylor & Francis, London, 2002 (with R. Tevzadze and M. Santacroce).

  28. Backward stochastic PDE and hedging in incomplete markets. Proc. A. Razmadze Math. Inst. 130 (2002), 39-72 (with R. Tevzadze).

  29. A semimartingale Backward Equation for the mean-variance hedging problem. Reports on Enlarged Sessions of the Seminar of I. Vekua Inst. Appl. Math. 17 (2002), No. 1, 21-25 (with R. Tevzadze).

  30. A semimartingale BSDE related to the minimal entropy martingale measure. Finance Stoch. 7 (2003), No. 3, 385-402 (with R. Tevzadze and M. Santacroce).

  31. A Unified Characterization of the q-optimal and minimal entropy martingale measures. Georgian Math. J. 10 (2003), No. 2, 289-310 (with R. Tevzadze).

  32. Backward Stochastic PDE and Imperfect Hedging. J. Theoret. Appl. Finance 6 (2003), No. 7, 663-692 (with R. Tevzadze).

  33. Semimartingale Backward PDE and Imperfect Hedging, Kolmogorov and contemporary mathematics. Abstracts, Moscow, June 16-21, (2003), 91-92 (with R. Tevzadze).

  34. A semimartingale Bellman equation and the variance-optimal martingale measure under general information flow. SIAM J. Control Optim. 42 (2003), 24 p. (with R. Tevzadze).

  35. The Bellman equation related to the minimal entropy martingale measure. Georgian Math. J. 11 (2004), No. 1, 125-135 (with M. Santacroce and R. Tevzadze).

  36. The change-point problem for continuous martingales. Proc. A. Razmadze Math. Inst. 137 (2005), 39-63 (with T. Kavtaradze and   N. Lazrieva).

  37. Dynamic exponential utility indifference valuation. Ann. Appl. Probab. 15 (2005), no. 3, 2113-2143 (with M Schweizer).

  38. A martingale equation of exponential type. From stochastic calculus to mathematical finance, 507-516, Springer, Berlin, 2006 (with R. Tevzadze).

  39. An exponential martingale equation. Electron. Comm. Probab. 11 (2006), 206-216 (electronic) (with R. Tevzadze). 

  40. A bayesian -  martingale approach to the general disorder problem. Stochastic Proc. Appl. 117 (2007),. 1093–1120 (with T. Kavtaradze, N. Lazrieva and P. Mulliere)

  41. Backward stochastic partial differential equations related to utility maximization and hedging. J. Math. Sci. 153 (2008), No. 3, 292-376 (with R. Tevzadze)

  42. Mean-variance Hedging Under Partial Information.  SIAM J. Control  Optim. 47 (2008), No. 5,  2381-2409  (with R. Tevzadze  and T. Toronjadze)

  43. $L^2$-approximating pricing under restricted information,  math.PR arXiv:0708.4095, to appear in “Applied Mathematics and Optimization “ (with R. Tevzadze and T.Toronjadze)

  44. Exponential hedging under partial information. Finance and Stochastics (accepted) (with M. Santacroce)