Chances for the honest in honest versus insider trading

2003

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.

SSRN Electronic Journal, 2007

The continuous-time version of Kyle's (1985) model of asset pricing with asymmetric information is studied, and generalized in various directions, i.e., by allowing time-varying noise trading, and by allowing the orders of the noise traders to be correlated with the insider's signal. From rather simple assumptions we are able to derive the optimal trade for an insider; the trading intensity satisfies a deterministic integral equation, given perfect inside information. We use a new technique called forward integration in order to find the optimal trading strategy. This is an extension of the stochastic integral which takes account of the informational asymmetry inherent in this problem. The market makers' price response is found by the use of filtering theory. The novelty is our approach, which could be extended in scope.

Asia-Pacific Journal of Financial Studies, 2009

In this paper we perform theoretical and empirical analyses on the insiders' optimal "stealth" strategy and expected profits from mimicking trading when the insiders' trading information is publicly available. When insiders select a mixed strategy of AR (1) process as the information exposure strategy in a multi-period model, we find the optimal AR (1) coefficient that maximizes the insiders' profit is negative. Also, (1) the greater the transaction volume of mimicking traders in the market and the longer the information exposure period, the closer the optimum AR (1) coefficient becomes to -1; (2) The larger the mimicking transaction volume, the smaller the insider's profit gets; and (3) When the volume of mimicking transaction is large and the private information is not much valuable, the likelihood of loss is high. We also validate certain theoretical results of our model using publicized ownership change data of major shareholders. As a result, we find the strategic evidences in the sample of insider transactions closing within 15 trading days. Also, although mimicking traders' losses have not been reported, they can suffer losses when the private information is not much valuable and the insiders take a significant strategic action.

Quantitative Finance, 2006

We consider a financial market driven by a Le´vy process with filtration fF t g t2½0, T . An insider in this market is an agent who has access to more information than an honest trader. Mathematically, this is modelled by allowing a strategy of an insider to be adapted to a bigger filtration G t F t . The corresponding anticipating stochastic differential equation of the wealth is interpreted in the sense of forward integrals. In this framework, we study the optimal portfolio problem of an insider with logarithmic utility function. Explicit results are given in the case where the jumps are generated by a Poisson process.

2005

An insider is an agent who has access to larger information than the one given by the development of the market events and who takes advantage of this in optimizing his position in the market. In this paper we consider the optimization problem of an insider who is so influential in the market to affect the price dynamics: in this sense he is called a "large" insider. The optimal portfolio problem for a general utility function is studied for a financial market driven by a Lévy process in the framework of forward anticipating calculus.

Advanced Mathematical Methods for Finance, 2011

In this paper we suggest a general stochastic maximum principle for optimal control of anticipating stochastic differential equations driven by a Lévy type of noise. We use techniques of Malliavin calculus and forward integration. We apply our results to study a general optimal portfolio problem of an insider. In particular, we find conditions on the insider information filtration which are sufficient to give the insider an infinite wealth. We also apply the results to find the optimal consumption rate for an insider.

In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit can ever be realised strictly before an honest time, while classical arbitrage opportunities can be realised exactly at an honest time as well as after an honest time. Moreover, stronger arbitrages of the first kind can only be obtained by trading as soon as an honest time occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than NFLVR.

Handbook of Numerical Analysis, 2009

An insider is an agent who has access to larger information than the one given by the development of the market events and who takes advantage of this in optimizing his position in the market . In this paper we consider the optimization problem of an insider who is so influential in the market to affect the price dynamics: in this sense he is called a "large" insider. The optimal portfolio problem for a general utility function is studied for a financial market driven by a Lévy process in the framework of forward anticipating calculus.

SSRN Electronic Journal, 2011

The single auction equilibrium of Kyle's (1985) is studied, in which noise traders may be partially informed, or alternatively they can be manipulated. Unlike Kyle's assumption that the quantity traded by the noise traders is independent of the asset value, we assume that the noise traders are able to correlate their trade with the true price. This has several implications for the equilibrium, one being that the insider's expected profits decrease as the noise traders' ability to correlate positively improve. In the limit, the noise traders do not lose on average, and the insider makes zero expected profits. When the correlation is negative, we interpret this as manipulation. In this case the insider makes the highest expected profits, and the informativeness of prices is at its minimum.

Finance and Stochastics, 2004

In this paper we consider a market driven by a Wiener process where there is an insider and a regular trader. The insider has privileged information which has been deformed by an independent noise vanishing as the revelation time approaches. At this time, the information of every trader is the same. We obtain the semimartingale decomposition of the original Wiener process under dynamical enlargement of the filtration, and we prove that if the rate at which the additional noise in the insider’s information vanishes is slow enough then there is no arbitrage and the additional utility of the insider is finite.

Finance and Stochastics, 2014

In the context of a general continuous financial market model, we study whether the additional information associated with an honest time τ gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit can ever be realised strictly before τ , while classical arbitrage opportunities can be realised exactly at τ as well as after τ . Moreover, stronger arbitrages of the first kind can only be obtained by trading as soon as τ occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than NFLVR.

This paper addresses the question of non-arbitrage (precisely No-Unbounded-Profit-with-Bounded-Risk, NUPBR hereafter) after a specific random time. This study completes the one of Aksamit et al. \cite{aksamit/choulli/deng/jeanblanc}, devoted to the study before the random time, by elaborating results for the part after the random time under consideration. We restrict our attention to honest times, and we characterize the pairs of market and honest time for which the resulting model preserves the NUPBR property. Furthermore, we characterize the honest times that preserve the NUPBR property. These findings are essentially based on new stochastic results that are interesting in themselves. Furthermore, we construct explicitly local martingale deflators for a large class of processes.

SSRN Electronic Journal, 2000

We study the optimal trading strategy of an insider who is subject to the possibility of law penalties due to his or her illegal trading activity. This possibility was absent in previous works. Also, we discuss how to obtain the optimal penalty rule that maximize a welfare function.

Journal of Optimization Theory and Applications, 2013

In this paper we use techniques of Malliavin calculus and forward integration to present a general stochastic maximum principle for anticipating stochastic differential equations driven by a Lévy type of noise. We apply our result to study a general stochastic differential game problem of an insider.

SSRN Electronic Journal, 2019

The continuous-time version of Kyle's (1985) model is studied, in which market makers are not fiduciaries. They have some market power which they utilize to set the price to their advantage, resulting in positive expected profits. This has several implications for the equilibrium, the most important being that by setting a modest fee conditional of the order flow, the market maker is able to obtain a profit of the order of magnitude, and even better than, a perfectly informed insider. Our model also indicates why speculative prices are more volatile than predicted by fundamentals.