Showing papers by "David Landriault published in 2021"

Optimal dynamic risk sharing under the time-consistent mean-variance criterion

Abstract: In this paper, we consider a dynamic Pareto optimal risk‐sharing problem under the time‐consistent mean‐variance criterion. A group of n insurers is assumed to share an exogenous risk whose dynamics is modeled by a Levy process. By solving the extended Hamilton–Jacobi–Bellman equation using the Lagrange multiplier method, an explicit form of the time‐consistent equilibrium risk‐bearing strategy for each insurer is obtained. We show that equilibrium risk‐bearing strategies are mixtures of two common risk‐sharing arrangements, namely, the proportional and stop‐loss strategies. Their explicit forms allow us to thoroughly examine the analytic properties of the equilibrium risk‐bearing strategies. We later consider two extensions to the original model by introducing a set of financial investment opportunities and allowing for insurers' ambiguity towards the exogenous risk distribution. We again explicitly solve for the equilibrium risk‐bearing strategies and further examine the impact of the extension component (investment or ambiguity) on these strategies. Finally, we consider an application of our results in the classical risk‐sharing problem of a pure exchange economy.

An insurance risk process with a generalized income process: A solvency analysis

Abstract: In ruin theory, an insurer’s income process is usually assumed to grow at a deterministic rate of c > 0 over time. For instance, both the well-known Cramer–Lundberg risk process and the Sparre Andersen risk model have this assumption built in the construction of their respective surplus processes. This assumption is mainly considered for purposes of mathematical tractability, but generally fails to accurately model an insurer’s income dynamics. To better characterize the variability and uncertainty of an insurer’s income process, several papers have studied insurance risk models with random incomes where the main emphasis is placed on carrying the related Gerber–Shiu analysis. However, a systematic and quantitative understanding of how the more volatile income processes impact an insurer’s solvency risk is still lacking. This paper aims to fill this gap in the literature by quantitatively assessing the impact of the choice of income process on some finite-time and infinite-time ruin quantities. To carry this analysis, we consider a generalized Sparre Andersen risk model with a random income process which renews at claim instants. For exponentially distributed claim sizes, we derive explicit expressions for some joint distributions involving the time to ruin and the number of claims until ruin. As special cases of the proposed insurance risk process, we consider income processes modelled by a subordinator or a particular varying premium rate model. Numerical examples are then carried to draw important risk management implications of a solvency nature for the insurer.

On the analysis of deep drawdowns for the Lévy insurance risk model

Abstract: In this paper, we study the magnitude and the duration of deep drawdowns for the Levy insurance risk model through the characterization of the Laplace transform of a related stopping time. Relying on a temporal approximation approach (e.g., Li et al. (2018) ), the proposed methodology allows for a unified treatment of processes with bounded and unbounded variation paths whereas these two cases used to be treated separately. In particular, we extend the results of Landriault et al. (2017) and Surya (2019) . We later analyze certain limiting cases of our main results where consistency with some known drawdown results in the literature will be shown.