A monetary value for initial information in portfolio optimization

Abstract

Abstract. We consider an investor maximizing his expected utility from terminal wealth with portfolio decisions based on the available information flow. This investor faces the opportunity to acquire some additional initial information G. His subjective fair value of this information is defined as the amount of money that he can pay for G such that this cost is balanced out by the informational advantage in terms of maximal expected utility. We study this value for common utility functions in the setting of a complete market modeled by general semimartingales. The main tools are a martingale preserving change of measure and martingale representation results for initially enlarged filtrations.

Optimal investment with inside information and parameter uncertainty

“…Amendinger, Imkeller and Schweizer [3] gave an entropic characterisation of the additional utility achievable by an insider, extended to a semimartingale setting by Ankirchner, Dereich and Imkeller [4]. Amendinger, Becherer and Schweizer [2] used indifference arguments to give a monetary value to inside information in portfolio optimisation. Imkeller [16,17] used the notion of progressive enlargement of filtration to model inside information on a random time that is not a stopping time for regular traders, and used Malliavin calculus to characterise the information drift.…”

The financial value of a weak information on a financial market

“…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.…”

Information uncertainty related to marked random times and optimal investment

“…In general, the observation of a random time, in particular a default time, is modelled by the progressive enlargement of filtration, as proposed by Elliott et al (2000) and Bielecki and Rutkowski (2002). The knowledge of insider information is usually studied by using the initial enlargement of filtration as in Amendinger et al (1998Amendinger et al ( , 2003 and Grorud and Pontier (1998). In this paper, we suppose that the filtration F represents the market information known by all investors, including the default information.…”

“…Both investors aim at maximizing the expected utility from the terminal wealth and each of them will determine their investment strategy based on the corresponding information set. Following Amendinger et al (1998Amendinger et al ( , 2003, we will compare the optimization results and deduce the additional gain of the insider.…”