Animal Spirits and Value at Risk Estimation

Risk-sensitive investment in a finite-factor model

“…The details are straightforward and are left to the reader. Similar calculations can be found in , Davis & Lleo (2014).…”

“…Application of risk-sensitive control to asset management problems was pioneered by Bielecki & Pliska (2003) and a considerable literature has developed since then. References can be found in Davis & Lleo (2014), and one of the models studied there and in the paper includes jumps in both the assets and the factors; however, for technical reason we were obliged to exclude simultaneous asset and factor jumps, so the model presented here is not a special case.…”

Estimating animal spirits: conservative risk calculation

“…In the case of the exponential O-U, the increments of the log of the process are Gaussian, conditionally on the previous observation. See Andruszkiewicz et al (2014) for details and exact formulae.…”

“…Our implementation is based on Rabiner and Juang (1993), with a slight extension to handle the fact that (modified) observations are only conditionally Gaussian in the exponential O-U case. After estimation we use the Viterbi algorithm to calculate the most likely path of the hidden factor process (see Andruszkiewicz et al 2014 for details).…”

“…Proposition 5.1 Assume that at each point in time T 0 ≤ t ≤ T we are given a distribution forecast for the value of process X : Proof For proof see Diebold et al (1998) or Andruszkiewicz et al (2014). index releases are scheduled around the middle of the relevant month, and the final release is around the end of the month.…”