The insider problem in the trinomial model: a discrete-time jump process approach

Abstract

In an incomplete market underpinned by the trinomial model, we consider two investors : an ordinary agent whose decisions are driven by public information and an insider who possesses from the beginning a surplus of information encoded through a random variable for which he or she knows the outcome. Through the definition of an auxiliary model based on a marked binomial process, we handle the trinomial model as a volatility one, and use the stochastic analysis and Malliavin calculus toolboxes available in that context. In particular, we connect the information drift, the drift to eliminate in order to preserve the martingale property within an initial enlargement of filtration in terms of the Malliavin derivative. We solve explicitly the agent and the insider expected logarithmic utility maximisation problems and provide a hedging formula for replicable claims. We identify the insider expected additional utility with the Shannon entropy of the extra information, and examine then the existence of arbitrage opportunities for the insider.

arXiv comment38 pages. Comments are welecome!

References in corpus (6)

• Utility maximization in incomplete markets
• Arbitrage and duality in nondominated discrete-time models
• The Shannon information of filtrations and the additional logarithmic utility of insiders
• Local solution method for the problem of enlargement of filtration
• Non-arbitrage for Informational Discrete Time Market Models
• Malliavin calculus for marked binomial processes: portfolio optimisation in the trinomial model and compound Poisson approximation