1. ### Linear-Quadratic Stochastic Differential Games on Random Directed Networks

Yichen Feng, Jean-Pierre Fouque, Tomoyuki Ichiba

Department of Statistics and Applied Probability, South Hall, University of California, Santa Barbara, CA 93106, USA.

Abstract: The study of linear-quadratic stochastic differential games on directed networks was initiated in Feng, Fouque & Ichiba [7]. In that work, the game on a directed chain with finite or infinite players was defined as well as the game on a deterministic directed tree, and their Nash equilibria were computed. The current work continues the analysis by first developing a random directed chain structure by assuming the interaction between every two neighbors is random. We solve explicitly for an open-loop Nash equilibrium for the system and we find that the dynamics under equilibrium is an infinite-dimensional Gaussian process described by a Catalan Markov chain introduced in [7]. The discussion about stochastic differential games is extended to a random two-sided directed chain and a random directed tree structure.

Keywords: Linear-quadratic stochastic games, random directed chain network, Nash equilibrium.

2. ### Covid-19: Correlation Between Confirmed Cases and Deaths – Greece & Cyprus

Nicholas G. Berketis

International Shipping, Finance and Management of the Athens University of Economics and Business, Athens, Greece.

Abstract:

What is the daily correlation of Confirmed versus Death Cases in Covid-19? In other words, people who have passed away, on average, how many days ago they were reported (i.e. “Confirmed”) as Covid-19 new cases?

To answer this question, we can take the correlation between the Daily Confirmed vs Daily Deaths and trying different lag values of the confirmed cases, since the assumption is that it will take some days for someone to pass away since he / she has been diagnosed with Covid-19.

The problem with the data is that are affected by the number of tests and also during some days like weekends they do not report all the cases. This implies that our analysis is not valid, but we shall try to check the results.

The analysis is based on R (Version 4.0.3 – 10th October, 2020), an integrated language and environment for statistical computing and graphics. R provides a wide variety of statistical and graphical techniques.