Publications
This chapter presents a survey of some recent methods used in economics and finance to account for cyclical dependence and account for their multifaced dynamics: nonlinearities, extreme events, asymmetries, non-stationarity, time-varying moments. To circumvent the caveats of the standard spectral analysis, new tools are now used based on copula spectrum, quantile spectrum and Laplace periodogram in both non-parametric and parametric contexts. The chapter presents a comprehensive overview of both theoretical and empirical issues as well as a computational approach to explain how the methods can be implemented using the R Package.
The Pareto model is very popular in risk management, since simple analytical formulas can be derived for financial downside risk measures (value-at-risk, expected shortfall) or reinsurance premiums and related quantities (large claim index, return period). Nevertheless, in practice, distributions are (strictly) Pareto only in the tails, above (possible very) large threshold. Therefore, it could be interesting to take into account second-order behavior to provide a better fit. In this article, we present how to go from a strict Pareto model to Pareto-type distributions. We discuss inference, derive formulas for various measures and indices, and finally provide applications on insurance losses and financial risks.
In this paper, we tackle a generic optimal regime switching problem where the decision-making process is not the same from one regime to another. Precisely, we consider a simple model of optimal switching from competition to cooperation. To this end, we solve a two-stage optimal control problem. In the first stage, two players engage in a dynamic game with a common state variable and one control for each player. We solve for open-loop strategies with a linear state equation and linear-quadratic payoffs. More importantly, the players may also consider the possibility to switch at finite time to a cooperative regime with the associated joint optimization of the sum of the individual payoffs. Using theoretical analysis and numerical exercises, we study the optimal switching strategy from competition to cooperation. We also discuss reverse switching.
