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  • Anna Gerardi (a1) and Paola Tardelli (a1)


This article considers the asset price movements in a financial market when risky asset prices are modeled by marked point processes. Their dynamics depend on an underlying event arrivals process, modeled again by a marked point process. Taking into account the presence of catastrophic events, the possibility of common jump times between the risky asset price process and the arrivals process is allowed. By setting and solving a suitable control problem, the characterization of the minimal entropy martingale measure is obtained. In a particular case, a pricing problem is also discussed.



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1.Ansel, J.P. & Stricker, C. (1993). Unicité et existence de la loi minimale. Séminaire de Probabilités XXVII. Lecture Notes in Mathematics Vol. 1557, Berlin: Springer, 2229.
2.Bellini, F. & Frittelli, M. (2002). On the existence of minimax martingale measures. Mathematical Finance 12(1): 121.
3.Biagini, S. & Frittelli, M. (2005). Utility maximization in incomplete markets for unbounded processes. Finance and Stochastics 9(4): 493517.
4.Brémaud, P. (1981). Point processes and queues. Springer Series in Statistics. New York: Springer-Verlag.
5.Ceci, C. (2006). Risk minimizing hedging for a partially observed high frequency data model. Stochastics 78(1): 1331.
6.Ceci, C. & Gerardi, A. (2009). Pricing for geometric marked point processes under partial information: Entropy approach. International Journal of Theoretical and Applied Finance 12: 179207.
7.Centanni, S. & Minozzo, M. (2006). Estimation and filtering by reversible jump MCMC for a doubly stochastic Poisson model for ultra-high-frequency financial data. Statistical Modelling 6(2): 97118.
8.Centanni, S. & Minozzo, M. (2006). A Monte Carlo approach to filtering for a class of marked doubly stochastic Poisson processes. Journal of the American Statistical Association 101(476): 15821597.
9.Delbaen, F., Grandits, P., Rheinlander, T., Samperi, D., Schweizer, M. & Stricker, C. (2002). Exponential hedging and entropic penalties. Mathematical Finance 12(2): 99123.
10.Doléans-Dade, C. (1970). Quelques applications de la formule de changement de variables pour le semimartingales. Zeitschriftfür Wahrscheinlichkeitstheorie und Verwunde Gebiete 16: 181194.
11.Ethier, S.N. & Kurtz, T.G. (1986). Markov processes: Characterization and convergence. Wiley Series in Probability and Mathematical Statistics. New York: Wiley.
12.Follmer, H. & Schweizer, M. (1991). Hedging of contingent claims under incomplete information. Stochastic Monographs, 5. New York: Gordon and Breach, 389414.
13.Frey, R. (2000). Risk minimization with incomplete information in a model for high frequency data. INFORMS Applied Probability Conference (Ulm, 1999). Mathematical Finance 10(2): 215225.
14.Frey, R. & Runggaldier, W.J. (2001). A nonlinear filtering approach to volatility estimation with a view towards high frequency data. Information modeling in finance (Evry, 2000). International Journal of Theoretical and Applied Finance 4(2): 199210.
15.Frey, R. & Runggaldier, W.J. (2009). Credit risk and incomplete information: A nonlinear filtering approach. To appear in Finance and Stochastics. Preprint. Available from
16.Frittelli, M. (2000). The minimal entropy martingale measure and the valuation problem in incomplete market. Mathematical Finance 10(1): 3952.
17.Fujiwara, T. & Miyahara, Y. (2003). The minimal entropy martingale measures for geometric Lévy processes. Finance and Stochastics 7(4): 509531.
18.Gerardi, A. & Tardelli, P. (2006). Filtering on a partially observed ultra-high-frequency data model. Acta Applicandae Mathematical 91(2) 193205.
19.Gombani, A. & Jaschke, S., & Runggaldier, W.J. (2007). Consistent price systems for subfiltrations. ESAIM Probability and Statistics 11: 3539.
20.Grandits, P. & Rheinlander, T. (2002). On the minimal entropy martingale measures. Annals of Probability 30(3): 10031038.
21.Jacod, J. (1975). Multivariate point processes: Predictable projection, Radon–Nikodym derivatives, representation of martingales. Zeitschrift für Wahrscheinlichkeitstheorie und Verwunde Gebiete 31: 235253.
22.Kliemann, W., Koch, G. & Marchetti, F. (1990). On the unnormalized solution of the filtering problem with counting process observations. IEEE Transactions on Information Theory 36(6): 14151425.
23.Mania, M. & Schweizer, M. (2005). Dynamic exponential utility indifference valuation. Annals of Applied Probability 15(3): 21132143.
24.Prigent, J.L. (2001). Option pricing with a general marked point process. Mathematics of Operations Research 26(1): 5066.
25.Ridberg, T.H. & Shephard, N. (2000). A modelling framework for the prices and times of trades made on the New York Stock Exchange. In, Fitzgerald, W.J., Smith, R.L., Walden, A.T. & Young, P.C., (eds) Nonlinear and nonstationary signal processing, Cambridge: Cambridge University Press. 217246.
26.Rogers, L.C.G. & Zane, O. (1998). Designing models for high frequency data, Preprint, University of Bath.
27.Schweizer, M. (1995). On the minimal martingale measure and the Follmer–Schweizer decomposition. Stochastic Analysis and Applications 13(5): 573599.
28.Schweizer, M. (2001). A guided tour through quadratic hedging approaches. In Option pricing, interest rates and risk management. Cambridge: Cambridge University Press. 538574,
29.Zariphopoulou, T. (2001). A solution approach to valuation with unhedgeable risks. Finance and Stochastics 5(1): 6182.


  • Anna Gerardi (a1) and Paola Tardelli (a1)


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