SPIVAK, G. and J. CVITANI ' C (1998) : "Maximizing the probability of a perfect hedge," Preprint, Department of Statistics, Columbia University. Home/Search Document Details and Download
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A Stochastic Control Approach to Risk Management Under.. - Runggaldier, Zaccaria (2000) (Correct)
....the right hand side in (1) corresponds to the smallest shortfall probability. Problems of the type (1) have attracted recently considerable attention (see e.g. Cvitani c and Karatzas (1998) Cvitani c (1998a) Cvitani c (1998b) Follmer and Leukert (1998) Follmer and Leukert (1999) Pham (1998) Spivak and Cvitani c (1998)) Letting, for given S 0 , V 0 (S 0 ) inffV 0 j J 0 (S 0 ; V 0 ) 0g (2) it follows that V 0 V 0 (S 0 ) implies V T ( H T , P Gammaa.s. superhedging) with the optimal strategy in (1) For superhedging, the choice of the underlying probabilistic model for the evolution ....
....model as it becomes successively available. An adaptive approach, corresponding to a Bayesian type criterion, appears thus more appropriate. Such adaptive approaches have already been dealt with in the literature (see e.g. Cvitani c and Karatzas (1998) Cvitani c (1998a) Cvitani c (1998b) Spivak and Cvitani c (1998) and, in the context of portfolio optimization, in Browne and Whitt (1996) Lakner (1995) Lakner (1998) Karatzas and Zhao (1999) In all these papers the uncertainty is only in the stock appreciation rate. The tools are mainly probabilistic in nature (involving also measure transformation) and ....
SPIVAK, G. and J. CVITANI ' C (1998) : "Maximizing the probability of a perfect hedge," Preprint, Department of Statistics, Columbia University.
A Bayesian adaptive control approach to risk.. - Runggaldier.. (2000) (Correct)
....words and phrases. Risk management, shortfall risk minimization, restricted information, dynamic programming, Bayesian inference. The authors wish to thank an anonymous referee for useful comments and suggestions. 2 W. Runggaldier, B. Trivellato and T. Vargiolu considerable attention (see e.g. [2, 3, 4, 5, 7, 8, 9, 10, 16]) Let, for a given S 0 , V 0 (S 0 ) inffV 0 j J 0 (S 0 ; V 0 ) 0g: 2) Since J 0 (S 0 ; V 0 ) 0 means that H T V T ( P almost surely (where is the optimal strategy in (1) V 0 (S 0 ) is the minimal initial capital needed to superhedge the claim. It follows that ....
....does not allow one to incorporate additional information on the underlying model as it becomes successively available. Thus, an adaptive approach, corresponding to a Bayesian type criterion, appears more appropriate. Such adaptive approaches have already been dealt with in the literature (see e.g. [2, 3, 4, 5] and, in the context of portfolio optimization, in [1, 11, 12, 13] In all these papers the uncertainty is only in the stock appreciation rate. The tools are mainly probabilistic in nature (involving also measure transformation) and are based on convex duality. An explicit solution is essentially ....
J. Cvitanic and G. Spivak, Maximizing the probability of a perfect hedge, The Annals of Applied Probability, 9 (4) (1999), 1303-1328.
Generalized Neyman-Pearson Lemma Via Convex Duality - Cvitanic, KARATZAS (1999) (Correct)
.... came from Heath (1993) who used the Neyman Pearson lemma as a tool for solving a stochastic control problem that can also be treated by methods of convex duality; for related work along this line, see Karatzas (1997) Cvitani c Karatzas (1998) Cvitani c (1998) Follmer Leukert (1998.a,b) Spivak (1998). 4 3 Results: Analysis Let us begin the statement of results by introducing the set of random variables H : fH 2 L 1 ( H 0; Gamma a:e: and E (HX) ff; 8 X 2 X ff g: 3.1) As is relatively straightforward to check (cf. Section 6) this set is convex, bounded in L 1 ( closed ....
SPIVAK, G. (1998) Maximizing the Probability of Perfect Hedge. Doctoral Dissertation, Department of Statistics, Columbia University.
Conservative Delta Hedging - Mykland (1999) (Correct)
....of this problem is to say that there is some form of incompleteness or other barrier to perfect hedging. This usually is the same as saying that P is unknown (though see, in particular, Delbaen and Schachermayer (1994, 1995) Strategies in such circumstances include super hedging (including Cvitani c (1998), Cvitani c and Karatzas (1992, 1993) Cvitani c, Pham and Touzi (1997, 1999) El Karoui and Quenez (1995) Eberlein and Jacod (1997) Karatzas (1996) Karatzas and Kou (1996, 1998) and Kramkov (1996) mean variance hedging (F ollmer and Schweizer (1991) F ollmer and Sondermann (1986) ....
.... (1986) Schweizer (1990, 1991, 1992, 1993, 1994) and later also Delbaen and Schachermayer (1996) Delbaen, Monat, Schachermayer, Schweizer and Stricker (1997) Laurent and Pham (1999) and Pham, Rheinl ander, and Schweizer (1998) quantile style hedging (see, in particular, K ulldor (1993) Cvitani c (1998), Cvitani c and Spivak (1998) and F ollmer and Leukert (1998, 1999) There is also work on hedging in additional market traded securities, which can be done, for example, in the presence of a stochastic volatility model (see, e.g. Ball and Roma (1994) Ho man, Platen and Schweizer (1992) Hull ....
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Cvitanic, J., and Spivak, G. (1998). Maximizing the probability of a perfect hedge, preprint.
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