The value of knowing the market price of risk

TL;DR

This paper investigates how knowing the market price of risk influences optimal investment strategies in continuous-time financial models, comparing scenarios of full, partial, initial, and dynamic information, and quantifying the value of information.

Contribution

It provides a detailed analysis of the impact of market price of risk information on optimal strategies and quantifies the value of different information scenarios in a continuous-time setting.

Findings

Access to more accurate market risk information improves investment strategies.

The value of information depends on whether it is available initially or throughout the period.

Market incompleteness affects the optimal strategies and the valuation of information.

Abstract

This paper presents an optimal allocation problem in a financial market with one risk-free and one risky asset, when the market is driven by a stochastic market price of risk. We solve the problem in continuous time, for an investor with a Constant Relative Risk Aversion (CRRA) utility, under two scenarios: when the market price of risk is observable (the {\em full information case}), and when it is not (the {\em partial information case}). The corresponding market models are complete in the partial information case and incomplete in the other case, hence the two scenarios exhibit rather different features. We study how the access to more accurate information on the market price of risk affects the optimal strategies and we determine the maximal price that the investor would be willing to pay to get such information. In particular, we examine two cases of additional information, when an exact observation of the market price of risk is available either at time $0$ only (the {\em initial information case}), or during the whole investment period (the {\em dynamic information case}).