A PDE representation of the density of the minimal entropy martingale measure in stochastic volatility markets

Benth, Fred Espen; Karlsen, Kenneth H.

doi:10.1080/10451120500031736

Cited by 33 publications

(43 citation statements)

References 31 publications

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“…To the best of our knowledge, the only article where ρ is not constant is by Benth and Karlsen [2], who studied a Markovian setting with ρ = ρ(Z s ) depending on the present level of the nontraded asset Z. They showed that the minimal entropy martingale measure can be expressed in terms of the solution of a semilinear PDE for which they proved existence and uniqueness of a classical solution.…”

Section: Comparison With the Literaturementioning

confidence: 99%

Exponential utility indifference valuation in two Brownian settings with stochastic correlation

Frei

Schweizer

2008

Adv. Appl. Probab.

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We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and lower bounds, in terms of bounds on the correlation, for the value V B of the exponential utility maximization problem with the claim B as random endowment. This yields an explicit formula for the indifference value b of B at any time, even with a fairly general stochastic correlation. Earlier results with constant correlation are recovered and extended. The reason why all this works is that, after a transformation to the minimal martingale measure, the value V B enjoys a monotonicity property in the correlation between tradable and nontradable assets.

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Section: Comparison With the Literaturementioning

confidence: 99%

Exponential utility indifference valuation in two Brownian settings with stochastic correlation

Frei

Schweizer

2008

Adv. Appl. Probab.

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“…We outline how smoothness can be established in the case when v (24) has been considered by Pham [26] and Benth and Karlsen [6], and similar techniques could in principle be used to establish that H C is indeed a classical solution to (24). We do not pursue this here, but instead follow Davis [10] and make the transformations…”

Section: Regularity Of the Value Functionmentioning

confidence: 99%

Utility-Based Valuation and Hedging of Basis Risk With Partial Information

Monoyios

2010

Applied Mathematical Finance

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We analyse the valuation and hedging of a claim on a non-traded asset using a correlated traded asset under a partial information scenario, when the asset drifts are unknown constants. Using a Kalman filter and a Gaussian prior distribution for the unknown parameters, a full information model with random drifts is obtained. This is subjected to exponential indifference valuation. An expression for the optimal hedging strategy is derived. An asymptotic expansion for small values of risk aversion is obtained via PDE methods, following on from payoff decompositions and a price representation equation. Analytic and semi-analytic formulae for the terms in the expansion are obtained when the minimal entropy measure coincides with the minimal martingale measure. Simulation experiments are carried out which indicate that the filtering procedure can be beneficial in hedging, but sometimes needs to be augmented with the increased option premium, that takes into account parameter uncertainty, in order to be effective. Empirical examples are presented which conform to these conclusions.

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“…The rigorous result together with necessary assumptions on the market coefficients is given later. Calculations of the type presented below are commonly used in the existing literature (see Musiela and Zariphopoulou [10] or Benth and Karlsen [1]) and are not given here with all details. Notice that if V xx < 0 then the maximum over π in (4.1) is well defined.…”

Section: E(u (X))mentioning

confidence: 99%

Robust portfolio selection under exponential preferences

Zawisza

2010

Appl. Math. (Warsaw)

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A PDE representation of the density of the minimal entropy martingale measure in stochastic volatility markets

Cited by 33 publications

References 31 publications

Exponential utility indifference valuation in two Brownian settings with stochastic correlation

Exponential utility indifference valuation in two Brownian settings with stochastic correlation

Utility-Based Valuation and Hedging of Basis Risk With Partial Information

Robust portfolio selection under exponential preferences

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