Additional utility of insiders with imperfect dynamical information (original) (raw)

Free lunch and arbitrage possibilities in a financial market model with an insider

Stochastic Processes and their Applications, 2001

We consider financial market models based on Wiener space with two agents on different information levels: a regular agent whose information is contained in the natural filtration of the Wiener process W , and an insider who possesses some extra information from the beginning of the trading interval, given by a random variable L which contains information from the whole time interval. Our main concern are variables L describing the maximum of a pricing rule. Since for such L the conditional laws given the smaller knowledge of the regular trader up to fixed times are not absolutely continuous with respect to the law of L, this class of examples cannot be treated by means of the enlargement of filtration techniques as applied so far. We therefore use elements of a Malliavin and Itô calculus for measure valued random variables to give criteria for the preservation of the semimartingale property, the absolute continuity of the conditional laws of L with respect to its law, and the absence of arbitrage. The master example, given by sup t∈[0,1] W t , preserves the semimartingale property, but allows for free lunch with vanishing risk quite generally. We deduce conditions on drift and volatility of price processes, under which we can construct explicit arbitrage strategies. 1991 AMS subject classifications: primary 60 G 48, 90 A 09; secondary 60 H 07, 94 A 17.

Multiperiod securities markets with differential information: martingales and resolution times

2011

We model multiperiod securities markets with differential information. A price system that admits no free lunches is related to martingales when agents have rational expectations. We introduce the concept of resolution time, and show that a better informed agent and a less informed agent must agree on the resolution times of commonly marketed events if they have rational expectations and if there are no free lunches. It then follows that if all elementary events are marketed for a less informed agent then any price system that admits no free lunches to a better informed agent must eliminate any private information asymmetry between the two. We provide an example of a dynamically fully revealing price system that is arbitrage free and yields elementarily complete markets.

Insider Trading With Stochastic Valuation

SSRN Electronic Journal, 2007

This paper studies a model of strategic trading with asymmetric information of an asset whose value follows a Brownian motion. An insider continuously observes a signal that tracks the evolution of the asset fundamental value. At a random time a public announcement reveals the current value of the asset to all the traders. The equilibrium has two regimes separated by an endogenously determined time T. In [0, T), the insider gradually transfers her information to the market and the market's uncertainty about the value of the asset decreases monotonically. By time T all her information is transferred to the market and the price agrees with the market value of the asset. In the interval [T, ∞), the insider trades large volumes and reveals her information immediately, so market prices track the market value perfectly. Despite this market efficiency, the insider is able to collect strictly positive rents after T. † We gratefully acknowledge the feedback of David Pearce. We also thanks Markus Brunnermeier, Lasse Pedersen, and Debraj Ray and seminar participants at NYU.

Some results on quadratic hedging with 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.

Dynamic noisy rational expectations equilibrium with insider information: Welfare and regulation

Journal of Economic Dynamics and Control, 2022

We study equilibria in multi-asset and multi-agent continuous-time economies with asymmetric information and bounded rational noise traders. We establish the existence of two equilibria. First, a full communication equilibrium where the informed agents' signal is disclosed to the market and static policies are optimal. Second, a partial communication equilibrium where the signal disclosed is affine in the informed and noise traders' signals, and dynamic policies are optimal. Here, information asymmetry creates demand for two public funds, as well as a dark pool where private information trades can be implemented. Markets are endogenously complete and equilibrium returns have a three factor structure with stochastic factors and loadings. Results are valid for constant absolute risk averse investors, general vector diffusions for fundamentals, nonlinear terminal payoffs, and non-Gaussian noise trading. Asset price dynamics and public information flows are endogenous, and rational expectations equilibria are special cases of the general results.

Insider Trading with Partially Informed Traders

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.

Dynamic Markov bridges motivated by models of insider trading

Stochastic Processes and Their Applications, 2011

Given a Markovian Brownian martingale Z, we build a process X which is a martingale in its own filtration and satisfies X 1 = Z 1 . We call X a dynamic bridge, because its terminal value Z 1 is not known in advance. We compute explicitly its semimartingale decomposition under both its own filtration F X and the filtration F X,Z jointly generated by X and Z. Our construction is heavily based on parabolic PDE's and filtering techniques. As an application, we explicitly solve an equilibrium model with insider trading, that can be viewed as a non-Gaussian generalization of Back and Pedersen's [3], where insider's additional information evolves over time.

Strategic Insider Trading in Continuous Time: A New Approach

SSRN Electronic Journal, 2019

The continuous-time version of Kyle's (1985) model of asset pricing with asymmetric information is studied, and generalized by allowing time-varying noise trading. 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, which we give a closed form solution to. 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.

A General Maximum Principle for Anticipative Stochastic Control and Applications to Insider Trading

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.