Optimal investment in markets with over and under-reaction to information

Abstract

In this paper we introduce a jump-diffusion model of shot-noise type for stock prices, taking into account over and under-reaction of the market to incoming news. We work in a partial information setting, by supposing that standard investors do not have access to the market direction, the drift, (modeled via a random variable) after a jump. We focus on the expected (logarithmic) utility maximization problem by providing the optimal investment strategy in explicit form, both under full (i.e., from the insider point of view, aware of the right kind of market reaction at any time) and under partial information (i.e., from the standard investor viewpoint, who needs to infer the kind of market reaction from data). We test our results on market data relative to Enron and Ahold. The three main contributions of this paper are: the introduction of a new market model dealing with over and under-reaction to news, the explicit computation of the optimal filter dynamics using an original approach combining enlargement of filtrations with Innovation Theory and the application of the optimal portfolio allocation rule to market data

A Gamma Ornstein-Uhlenbeck Model Driven by a Hawkes Process

“…Since the sample starts in a period of mild volatility we can reasonably assume that the Hawkes intensity, at this time, is close to its minimal level, which we denote by λ. The jumps are detected as the larger positive fluctuations using the algorithm detailed in Callegaro et al [14].…”

“…We can reproduce this effect with only positive jumps in VIX and an exponential mean-reversion speed. Moreover, the method adopted to identify jumps is unable to detect relatively small jumps (see [14]). In particular, jumps smaller than three standard deviations of the other increments are classified as usual Brownian noise.…”

Commodity Asian option pricing and simulation in a 4-factor model with jump clusters

“…2 along with jump occurrences (black bars). In order to detect jumps we employ the iterated re-weighted least squares technique developed in Callegaro et al ( 2017 ) (see also Bernis et al, 2021 for more implementation details). Jump occurrences are displayed in Fig.…”

A non-zero-sum reinsurance-investment game with delay and asymmetric information

“…[34] and [22] studied optimal consumption and investment problem with partial information. [9] researched optimal investment problem with over and under-reaction to information. [18] analyzed the Merton portfolio optimization problem when the growth rate is an unobserved Gaussian process whose level is estimated by filtering from observations of the stock price.…”