 |
|
|
| | | | | |
|
|
|
|
|
An Exponential Martingale Equation
|
Revaz NIkoloz Tevzadze,
Mikhael Gvanji Mania,
|
Abstract
We prove an existence of a unique solution of an exponential
martingale equation in the class of BMO martingales. The
solution is used to characterize optimal martingale measures.
|
Full text: PDF
Pages: 206-216
Published on: September 27, 2006
|
Bibliography
- Biagini, Francesca; Guasoni, Paolo; Pratelli, Maurizio. Mean-variance hedging for stochastic volatility models.
Math. Finance 10 (2000), no. 2, 109--123. MR1802593 (2001m:91078)
- Delbaen, Freddy; Schachermayer, Walter. The variance-optimal martingale measure for continuous processes.
Bernoulli 2 (1996), no. 1, 81--105. MR1394053 (97c:60115)
- Dellacherie, Claude; Meyer, Paul-André. Probabilités et potentiel. Chapitres V à VIII.
Industrial Topics], 1385. Hermann, Paris, 1980. xviii+476 pp. ISBN: 2-7056-1385-4 MR0566768 (82b:60001)
- De Donno, M.; Guasoni, P.; Pratelli, M. Super-replication and utility maximization in large financial
Stochastic Process. Appl. 115 (2005), no. 12, 2006--2022. MR2178505 (2006i:60089)
- El Karoui, N.; Peng, S.; Quenez, M. C. Backward stochastic differential equations in finance.
Math. Finance 7 (1997), no. 1, 1--71. MR1434407 (98d:90030)
- Grandits, Peter; Rheinländer, Thorsten. On the minimal entropy martingale measure.
Ann. Probab. 30 (2002), no. 3, 1003--1038. MR1920099 (2003e:28040)
- Hobson, David. Stochastic volatility models, correlation, and the $q$-optimal
Math. Finance 14 (2004), no. 4, 537--556. MR2092922 (2006a:60123)
- Jacod, Jean. Calcul stochastique et problèmes de martingales.
(French) [Stochastic calculus and martingale problems] Lecture Notes in Mathematics, 714. Springer, Berlin, 1979. x+539 pp. ISBN: 3-540-09253-6 MR0542115 (81e:60053)
- Kazamaki, Norihiko. Continuous exponential martingales and BMO.
Lecture Notes in Mathematics, 1579. Springer-Verlag, Berlin, 1994. viii+91 pp. ISBN: 3-540-58042-5 MR1299529 (95k:60110)
- Kobylanski, Magdalena. Backward stochastic differential equations and partial differential
Ann. Probab. 28 (2000), no. 2, 558--602. MR1782267 (2001h:60110)
- Laurent, Jean Paul; Pham, Huyên. Dynamic programming and mean-variance hedging.
Finance Stoch. 3 (1999), no. 1, 83--110. MR1805322 (2001m:91092)
- Lepeltier, J.-P.; San Martín, J.. Existence for BSDE with superlinear-quadratic coefficient.
Stochastics Stochastics Rep. 63 (1998), no. 3-4, 227--240. MR1658083 (99j:60087)
- Mania, M.; Tevzadze, R. A semimartingale Bellman equation and the variance-optimal martingale
Georgian Math. J. 7 (2000), no. 4, 765--792. MR1811929 (2001m:91097)
- Mania, Michael; Tevzadze, Revaz. A martingale equation of exponential type.
507--516, Springer, Berlin, 2006. MR2234287
- M. Mania, M. Santacroce and R. Tevzadze, A
Semimartingale backward equation related to the $p$-optimal
martingale measure and the minimal price of contingent claims,
Stoch. Processes and Related Topics, Stochastics Monogr.,
12 Taylor Francis. (2002), 169-202.
- Mania, Michael; Tevzadze, Revaz. A semimartingale backward equation and the variance-optimal martingale
SIAM J. Control Optim. 42 (2003), no. 5, 1703--1726 (electronic). MR2046382 (2005b:60168)
- Rheinländer, Thorsten. An entropy approach to the Stein and Stein model with correlation.
Finance Stoch. 9 (2005), no. 3, 399--413. MR2211715
- Schweizer, Martin. Approximation pricing and the variance-optimal martingale measure.
Ann. Probab. 24 (1996), no. 1, 206--236. MR1387633 (97c:60120)
|
|
|
|
|
|
|
|
| | | | |
Electronic Communications in Probability. ISSN: 1083-589X |
|
Context