Additional logarithmic utility of an insider

Amendinger, Jürgen; Imkeller, Peter; Schweizer, Martin

doi:10.1016/s0304-4149(98)00014-3

Cited by 144 publications

(141 citation statements)

References 12 publications

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“…Furthermore, we follow the line of reasoning outlined in [20], where a similar type of problem is dealt with. The results we use are also nicely summarised in Section 2 of [1]. Define the enlarged filtration by…”

Section: Guided Proposals For Filtered Bridgesmentioning

confidence: 98%

Bayesian estimation of incompletely observed diffusions

Meulen

Schauer

2017

Stochastics

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We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on an unknown parameter. A data-augmentation algorithm for drawing from the posterior distribution is presented which is based on simulating diffusion bridges conditional on a noisy incomplete observation at an intermediate time.The dynamics of such filtered bridges are derived and it is shown how these can be simulated using a generalised version of the guided proposals introduced in Schauer, Van der Meulen and Van Zanten (2017, Bernoulli 23(4A)). ARTICLE HISTORY

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Section: Guided Proposals For Filtered Bridgesmentioning

confidence: 98%

Bayesian estimation of incompletely observed diffusions

Meulen

Schauer

2017

Stochastics

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“…We refer here to Karatzas and Pikovsky (1996), Amendinger et al (1998), Grorud and Pontier (1998) and Imkeller et al (2001). All these works consider the differential of utility between the two agents (as previously described) and one important conclusion is that the differential is the relative entropy of the additional r.v.…”

Section: Introductionmentioning

confidence: 99%

“…We quote also a result by Jacod (1985) who states that, under the above assumptions, S is also a semimartingale with respect to the enlarged filtration G and provides its canonical decomposition. Finally, we recall the representation of p G and its inverse as a stochastic exponential (Amendinger et al (1998)). …”

Section: Introductionmentioning

confidence: 99%

Some results on quadratic hedging with insider trading

Campi

2005

Stochastics

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We consider the hedging problem in an arbitrage-free financial market, where there are two kinds of investors with different levels of information about the future price evolution, described by two filtrations F and G = F ∨ σ(G) where G is a given r.v. representing the additional information. We focus on two types of quadratic approaches to hedge a given square-integrable contingent claim: local risk minimization (LRM) and mean-variance hedging (MVH). By using initial enlargement of filtrations techniques, we solve the hedging problem for both investors and compare their optimal strategies under both approaches.In particular, for LRM, we show that for a large class of additional non trivial r.v.s G both investors will pursue the same locally risk minimizing portfolio strategy and the cost process of the ordinary agent is just the projection on F of that of the insider. In the MVH setting, we study also some general stochastic volatility model, including Hull and White, Heston and Stein and Stein models. In this more specific setting and for r.v.s G which are measurable with respect to the filtration generated by the volatility process, we obtain an expression for the insider optimal strategy in terms of the ordinary agent optimal strategy plus a process admitting a simple backward-type representation.

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“…To answer this question, recent works have proposed some models based on the theory of initial enlargement of filtrations, developed in [19], [20], [21]; the utility maximization problem has been solved in [1], [2] for continuous processes (see also [12], [16], [17]) and the same approach has been taken in [11] in the context of processes with jumps. One drawback of the enlargement approach is that it leads to arbitrage possibilities, whereas the initial market is arbitrage-free.…”

Section: Introductionmentioning

confidence: 99%

The financial value of a weak information on a financial market

Nguyen-Ngoc

Baudoin

2004

Finance and Stochastics

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Abstract. The results of [4] are extended under weaker assumptions to d-dimensional and possibly discontinuous processes and applied to the modelling of weak anticipations both on complete and incomplete financial markets. In the case of a complete market, we show that there exists a minimal probability measure associated with an anticipation. Remarkably, this minimal probability does not depend on the selected utility function. The approach is also shown to be flexible enough to allow corrections on the initial anticipation. Moreover, at the end of the paper, we study another kind of conditioning: The pathwise conditioning. Throughout the paper, Markovian models are studied in details as canonical examples.

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Additional logarithmic utility of an insider

Cited by 144 publications

References 12 publications

Bayesian estimation of incompletely observed diffusions

Bayesian estimation of incompletely observed diffusions

Some results on quadratic hedging with insider trading

The financial value of a weak information on a financial market

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