The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets

By Marco Frittelli. 2000

542 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/fd59d6289f991032823a9f3020bdf7c557030182

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Citations in the corpus

Exponential utility maximization under model uncertainty for unbounded endowments (2016, background): “In case of exponential utility function (though in a continuous-time and non-robust setting) [19] and [13] were the first to prove duality and existence, which lead to further analysis, for example a BSDE characterization of the optimal value and solution in an incomplete market and under trading co”
Pricing Via Utility Maximization and Entropy (2000, methodology): “We show under some hypotheses on the set of admissible strategies A that, in the vocabulary of Frittelli (1998), the price p(x, C) is a value coherent with the no-arbitrage principle.”
Investment and Valuation Under Backward and Forward Dynamic Exponential Utilities in a Stochastic Factor Model (2007, background): “…portfolio choice in the traditional framework of exponential utility; see, respectively, Foellmer and Schweizer (1991), Schweizer (1995) and (1999), Bellini and Frittelli (2002) and Frittelli (2000), Rouge and El Karoui (2000), Arai (2001), Delbaen et al. (2002), Kabanov and Stricker (2002)).”
On the Existence of Minimax Martingale Measures (2002, methodology): “…key issue is to show that most existing criteria for selecting a martingale measure in incomplete markets (as the optimal variance measure, Schweizer 1995; the minimal entropy measure, Frittelli 2000b; or the Kakutani Hellinger measure, Grandits 1999) are dual to a utility maximization problem.”
Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs (2011, methodology): “This interpretation is particularly interesting when using the variational formulation of the the entropic risk measure ρ0(ξT ) (see for instance, Frittelli [23], Föllmer & Schied [22]) ρ0(ξT ) = sup Q {EQ(ξT )−Hent(Q/P)|H(Q/P) +∞}.”
Minimal Entropy Martingale Measure (2010, background): “Theorems 1, 2 and Remark 1 of Frittelli (2000) as well as the fact that V ⊂ L∞(P ) yield the following.”
Dynamic exponential utility indifference valuation (2005, background): “4) is well known from [16] and [19]; see Theorem 2.”
Exponential Hedging and Entropic Penalties (2002, background): “1 of Frittelli (2000a) and Proposition 3.2 and the proof of Theorem 4.13 in Grandits/ Rheinländer (1999). Taking logarithms and expectations under Q , we could write explicitly”
Option Pricing: Valuation Models and Applications (2004, unknown): “Other pricing measures, such as the minimal variance measure (Schweizer 1995b, Delbaen and Schachermayer 1996) and the minimal entropy measure (Fritelli 2000) have also been studied.”
Utility-Based Derivative Pricing in Incomplete Markets (2002, background): “However, Bellini and Frittelli (2000) observed that for some standard “distances”, the minimizing measures are in fact minimax measures for HARA-type utility functions (cf. also Goll and Rüschendorf (2001) in this context).”
ANALYTICAL COMPARISONS OF OPTION PRICES IN STOCHASTIC VOLATILITY MODELS (2005, methodology): “A justification for using the minimal entropy measure is its link to some asymptotic exponential utility indifference price, see Frittelli [7].”
Risk measure pricing and hedging in incomplete markets (2006, methodology): “For instance, we have seen the minimal martingale measure by Föllmer and Schweizer [22]; the minimal entropy martingale measure by Miyahara [41] and Frittelli [23]; the minimax measure by Bellini and Frittelli [6]; the minimal distance martingale measure by Goll and Rüschendorf [26]; and the Esscher”
Portfolios and risk premia for the long run. (2012, background): “Exponential utility leads to the minimal-entropy measure Grandits and Rheinländer (2002), Frittelli (2000), Rheinländer (2005).”
Esscher transforms and the minimal entropy martingale measure for exponential Lévy models (2006, methodology): “…both, on maximization of utility, and on the minimum distance martingale measures, a frequent assumption is local boundedness of the asset price processes—see Delbaen et al. (2002) and Frittelli (2000), Bellini and Frittelli (2002) and Grandits and Rheinläder (2002), Goll and Rüschendorf (2001).”