1997
DOI: 10.1007/s004400050122
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Abstract: Motivated by a hedging problem in mathematical nance, El Karoui and Quenez 7] and Kramkov 1 4 ] h a ve d e v eloped optional versions of the Doob-Meyer decomposition which hold simultaneously for all equivalent martingale measures. We i n vestigate the general structure of such optional decompositions, both in additive and in multiplicative form, and under constraints corresponding to di erent classes of equivalent measures. As an application, we extend results of Karatzas and Cvitani c 3] on hedging problem… Show more

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Cited by 183 publications
(182 citation statements)
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“…Karatzas and Shreve [18] and Cvitanić and Ma [10]. Previously, convex duality was used to reduce it to a standard stochastic control problem; see Föllmer and Kramkov [14] for the general semimartingale case, and the references therein. Once the reduction is proved, then the Hamilton-Jacobi-Bellman equation associated to the problem is derived by means of a classical dynamic programming on the dual problem; see Broadie, Cvitanić and Soner [7] and Cvitanić, Pham and Touzi [11].…”
Section: Proposition 61 Let µ(T Z U) σ(T Z U) and γ(T Z U Ementioning
confidence: 99%
“…Karatzas and Shreve [18] and Cvitanić and Ma [10]. Previously, convex duality was used to reduce it to a standard stochastic control problem; see Föllmer and Kramkov [14] for the general semimartingale case, and the references therein. Once the reduction is proved, then the Hamilton-Jacobi-Bellman equation associated to the problem is derived by means of a classical dynamic programming on the dual problem; see Broadie, Cvitanić and Soner [7] and Cvitanić, Pham and Touzi [11].…”
Section: Proposition 61 Let µ(T Z U) σ(T Z U) and γ(T Z U Ementioning
confidence: 99%
“…Аналогичные понятия для последовательностей случайных величин вводились в работах [29], [9], а для случайных процессов в непрерывном времени -в работе [13].…”
Section: теорема 1 (о существовании Esd) пусть множество случайных пunclassified
“…Такой подход позволяет с единой точки зрения анализировать ряд моделей рынка, включая мо дели с портфельными ограничениями и модели с бесконечным числом активов. В случае непрерывного времени подобный подход использо вался в работах [8], [13], [15], [17], [33].…”
unclassified
“…In reality, the credit rate is always higher than the deposit rate. Such a market constraint brings new difficulties in the problems of hedging, investing and shortfall risk minimization (see Bergman [4], Kane and Melnikov [13], Korn [15], Bart [3], and also Cvitanić and Karatzas [8], Cvitanić [6,7], Föllmer and Kramkov [11], Karatzas and Shreve [14], Cvitanić, Pham and Touzi [9], Soner and Touzi [21] regarding other market constraints).…”
Section: Introductionmentioning
confidence: 99%